what is analysis in quantitative research

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• J Korean Med Sci
• v.37(16); 2022 Apr 25

A Practical Guide to Writing Quantitative and Qualitative Research Questions and Hypotheses in Scholarly Articles

Edward barroga.

1 Department of General Education, Graduate School of Nursing Science, St. Luke’s International University, Tokyo, Japan.

Glafera Janet Matanguihan

2 Department of Biological Sciences, Messiah University, Mechanicsburg, PA, USA.

The development of research questions and the subsequent hypotheses are prerequisites to defining the main research purpose and specific objectives of a study. Consequently, these objectives determine the study design and research outcome. The development of research questions is a process based on knowledge of current trends, cutting-edge studies, and technological advances in the research field. Excellent research questions are focused and require a comprehensive literature search and in-depth understanding of the problem being investigated. Initially, research questions may be written as descriptive questions which could be developed into inferential questions. These questions must be specific and concise to provide a clear foundation for developing hypotheses. Hypotheses are more formal predictions about the research outcomes. These specify the possible results that may or may not be expected regarding the relationship between groups. Thus, research questions and hypotheses clarify the main purpose and specific objectives of the study, which in turn dictate the design of the study, its direction, and outcome. Studies developed from good research questions and hypotheses will have trustworthy outcomes with wide-ranging social and health implications.

INTRODUCTION

Scientific research is usually initiated by posing evidenced-based research questions which are then explicitly restated as hypotheses. 1 , 2 The hypotheses provide directions to guide the study, solutions, explanations, and expected results. 3 , 4 Both research questions and hypotheses are essentially formulated based on conventional theories and real-world processes, which allow the inception of novel studies and the ethical testing of ideas. 5 , 6

It is crucial to have knowledge of both quantitative and qualitative research 2 as both types of research involve writing research questions and hypotheses. 7 However, these crucial elements of research are sometimes overlooked; if not overlooked, then framed without the forethought and meticulous attention it needs. Planning and careful consideration are needed when developing quantitative or qualitative research, particularly when conceptualizing research questions and hypotheses. 4

There is a continuing need to support researchers in the creation of innovative research questions and hypotheses, as well as for journal articles that carefully review these elements. 1 When research questions and hypotheses are not carefully thought of, unethical studies and poor outcomes usually ensue. Carefully formulated research questions and hypotheses define well-founded objectives, which in turn determine the appropriate design, course, and outcome of the study. This article then aims to discuss in detail the various aspects of crafting research questions and hypotheses, with the goal of guiding researchers as they develop their own. Examples from the authors and peer-reviewed scientific articles in the healthcare field are provided to illustrate key points.

DEFINITIONS AND RELATIONSHIP OF RESEARCH QUESTIONS AND HYPOTHESES

A research question is what a study aims to answer after data analysis and interpretation. The answer is written in length in the discussion section of the paper. Thus, the research question gives a preview of the different parts and variables of the study meant to address the problem posed in the research question. 1 An excellent research question clarifies the research writing while facilitating understanding of the research topic, objective, scope, and limitations of the study. 5

On the other hand, a research hypothesis is an educated statement of an expected outcome. This statement is based on background research and current knowledge. 8 , 9 The research hypothesis makes a specific prediction about a new phenomenon 10 or a formal statement on the expected relationship between an independent variable and a dependent variable. 3 , 11 It provides a tentative answer to the research question to be tested or explored. 4

Hypotheses employ reasoning to predict a theory-based outcome. 10 These can also be developed from theories by focusing on components of theories that have not yet been observed. 10 The validity of hypotheses is often based on the testability of the prediction made in a reproducible experiment. 8

Conversely, hypotheses can also be rephrased as research questions. Several hypotheses based on existing theories and knowledge may be needed to answer a research question. Developing ethical research questions and hypotheses creates a research design that has logical relationships among variables. These relationships serve as a solid foundation for the conduct of the study. 4 , 11 Haphazardly constructed research questions can result in poorly formulated hypotheses and improper study designs, leading to unreliable results. Thus, the formulations of relevant research questions and verifiable hypotheses are crucial when beginning research. 12

CHARACTERISTICS OF GOOD RESEARCH QUESTIONS AND HYPOTHESES

Excellent research questions are specific and focused. These integrate collective data and observations to confirm or refute the subsequent hypotheses. Well-constructed hypotheses are based on previous reports and verify the research context. These are realistic, in-depth, sufficiently complex, and reproducible. More importantly, these hypotheses can be addressed and tested. 13

There are several characteristics of well-developed hypotheses. Good hypotheses are 1) empirically testable 7 , 10 , 11 , 13 ; 2) backed by preliminary evidence 9 ; 3) testable by ethical research 7 , 9 ; 4) based on original ideas 9 ; 5) have evidenced-based logical reasoning 10 ; and 6) can be predicted. 11 Good hypotheses can infer ethical and positive implications, indicating the presence of a relationship or effect relevant to the research theme. 7 , 11 These are initially developed from a general theory and branch into specific hypotheses by deductive reasoning. In the absence of a theory to base the hypotheses, inductive reasoning based on specific observations or findings form more general hypotheses. 10

TYPES OF RESEARCH QUESTIONS AND HYPOTHESES

Research questions and hypotheses are developed according to the type of research, which can be broadly classified into quantitative and qualitative research. We provide a summary of the types of research questions and hypotheses under quantitative and qualitative research categories in Table 1 .

Research questions in quantitative research

In quantitative research, research questions inquire about the relationships among variables being investigated and are usually framed at the start of the study. These are precise and typically linked to the subject population, dependent and independent variables, and research design. 1 Research questions may also attempt to describe the behavior of a population in relation to one or more variables, or describe the characteristics of variables to be measured ( descriptive research questions ). 1 , 5 , 14 These questions may also aim to discover differences between groups within the context of an outcome variable ( comparative research questions ), 1 , 5 , 14 or elucidate trends and interactions among variables ( relationship research questions ). 1 , 5 We provide examples of descriptive, comparative, and relationship research questions in quantitative research in Table 2 .

Hypotheses in quantitative research

In quantitative research, hypotheses predict the expected relationships among variables. 15 Relationships among variables that can be predicted include 1) between a single dependent variable and a single independent variable ( simple hypothesis ) or 2) between two or more independent and dependent variables ( complex hypothesis ). 4 , 11 Hypotheses may also specify the expected direction to be followed and imply an intellectual commitment to a particular outcome ( directional hypothesis ) 4 . On the other hand, hypotheses may not predict the exact direction and are used in the absence of a theory, or when findings contradict previous studies ( non-directional hypothesis ). 4 In addition, hypotheses can 1) define interdependency between variables ( associative hypothesis ), 4 2) propose an effect on the dependent variable from manipulation of the independent variable ( causal hypothesis ), 4 3) state a negative relationship between two variables ( null hypothesis ), 4 , 11 , 15 4) replace the working hypothesis if rejected ( alternative hypothesis ), 15 explain the relationship of phenomena to possibly generate a theory ( working hypothesis ), 11 5) involve quantifiable variables that can be tested statistically ( statistical hypothesis ), 11 6) or express a relationship whose interlinks can be verified logically ( logical hypothesis ). 11 We provide examples of simple, complex, directional, non-directional, associative, causal, null, alternative, working, statistical, and logical hypotheses in quantitative research, as well as the definition of quantitative hypothesis-testing research in Table 3 .

Research questions in qualitative research

Unlike research questions in quantitative research, research questions in qualitative research are usually continuously reviewed and reformulated. The central question and associated subquestions are stated more than the hypotheses. 15 The central question broadly explores a complex set of factors surrounding the central phenomenon, aiming to present the varied perspectives of participants. 15

There are varied goals for which qualitative research questions are developed. These questions can function in several ways, such as to 1) identify and describe existing conditions ( contextual research question s); 2) describe a phenomenon ( descriptive research questions ); 3) assess the effectiveness of existing methods, protocols, theories, or procedures ( evaluation research questions ); 4) examine a phenomenon or analyze the reasons or relationships between subjects or phenomena ( explanatory research questions ); or 5) focus on unknown aspects of a particular topic ( exploratory research questions ). 5 In addition, some qualitative research questions provide new ideas for the development of theories and actions ( generative research questions ) or advance specific ideologies of a position ( ideological research questions ). 1 Other qualitative research questions may build on a body of existing literature and become working guidelines ( ethnographic research questions ). Research questions may also be broadly stated without specific reference to the existing literature or a typology of questions ( phenomenological research questions ), may be directed towards generating a theory of some process ( grounded theory questions ), or may address a description of the case and the emerging themes ( qualitative case study questions ). 15 We provide examples of contextual, descriptive, evaluation, explanatory, exploratory, generative, ideological, ethnographic, phenomenological, grounded theory, and qualitative case study research questions in qualitative research in Table 4 , and the definition of qualitative hypothesis-generating research in Table 5 .

Qualitative studies usually pose at least one central research question and several subquestions starting with How or What . These research questions use exploratory verbs such as explore or describe . These also focus on one central phenomenon of interest, and may mention the participants and research site. 15

Hypotheses in qualitative research

Hypotheses in qualitative research are stated in the form of a clear statement concerning the problem to be investigated. Unlike in quantitative research where hypotheses are usually developed to be tested, qualitative research can lead to both hypothesis-testing and hypothesis-generating outcomes. 2 When studies require both quantitative and qualitative research questions, this suggests an integrative process between both research methods wherein a single mixed-methods research question can be developed. 1

FRAMEWORKS FOR DEVELOPING RESEARCH QUESTIONS AND HYPOTHESES

Research questions followed by hypotheses should be developed before the start of the study. 1 , 12 , 14 It is crucial to develop feasible research questions on a topic that is interesting to both the researcher and the scientific community. This can be achieved by a meticulous review of previous and current studies to establish a novel topic. Specific areas are subsequently focused on to generate ethical research questions. The relevance of the research questions is evaluated in terms of clarity of the resulting data, specificity of the methodology, objectivity of the outcome, depth of the research, and impact of the study. 1 , 5 These aspects constitute the FINER criteria (i.e., Feasible, Interesting, Novel, Ethical, and Relevant). 1 Clarity and effectiveness are achieved if research questions meet the FINER criteria. In addition to the FINER criteria, Ratan et al. described focus, complexity, novelty, feasibility, and measurability for evaluating the effectiveness of research questions. 14

The PICOT and PEO frameworks are also used when developing research questions. 1 The following elements are addressed in these frameworks, PICOT: P-population/patients/problem, I-intervention or indicator being studied, C-comparison group, O-outcome of interest, and T-timeframe of the study; PEO: P-population being studied, E-exposure to preexisting conditions, and O-outcome of interest. 1 Research questions are also considered good if these meet the “FINERMAPS” framework: Feasible, Interesting, Novel, Ethical, Relevant, Manageable, Appropriate, Potential value/publishable, and Systematic. 14

As we indicated earlier, research questions and hypotheses that are not carefully formulated result in unethical studies or poor outcomes. To illustrate this, we provide some examples of ambiguous research question and hypotheses that result in unclear and weak research objectives in quantitative research ( Table 6 ) 16 and qualitative research ( Table 7 ) 17 , and how to transform these ambiguous research question(s) and hypothesis(es) into clear and good statements.

a These statements were composed for comparison and illustrative purposes only.

b These statements are direct quotes from Higashihara and Horiuchi. 16

a This statement is a direct quote from Shimoda et al. 17

The other statements were composed for comparison and illustrative purposes only.

CONSTRUCTING RESEARCH QUESTIONS AND HYPOTHESES

To construct effective research questions and hypotheses, it is very important to 1) clarify the background and 2) identify the research problem at the outset of the research, within a specific timeframe. 9 Then, 3) review or conduct preliminary research to collect all available knowledge about the possible research questions by studying theories and previous studies. 18 Afterwards, 4) construct research questions to investigate the research problem. Identify variables to be accessed from the research questions 4 and make operational definitions of constructs from the research problem and questions. Thereafter, 5) construct specific deductive or inductive predictions in the form of hypotheses. 4 Finally, 6) state the study aims . This general flow for constructing effective research questions and hypotheses prior to conducting research is shown in Fig. 1 .

Research questions are used more frequently in qualitative research than objectives or hypotheses. 3 These questions seek to discover, understand, explore or describe experiences by asking “What” or “How.” The questions are open-ended to elicit a description rather than to relate variables or compare groups. The questions are continually reviewed, reformulated, and changed during the qualitative study. 3 Research questions are also used more frequently in survey projects than hypotheses in experiments in quantitative research to compare variables and their relationships.

Hypotheses are constructed based on the variables identified and as an if-then statement, following the template, ‘If a specific action is taken, then a certain outcome is expected.’ At this stage, some ideas regarding expectations from the research to be conducted must be drawn. 18 Then, the variables to be manipulated (independent) and influenced (dependent) are defined. 4 Thereafter, the hypothesis is stated and refined, and reproducible data tailored to the hypothesis are identified, collected, and analyzed. 4 The hypotheses must be testable and specific, 18 and should describe the variables and their relationships, the specific group being studied, and the predicted research outcome. 18 Hypotheses construction involves a testable proposition to be deduced from theory, and independent and dependent variables to be separated and measured separately. 3 Therefore, good hypotheses must be based on good research questions constructed at the start of a study or trial. 12

In summary, research questions are constructed after establishing the background of the study. Hypotheses are then developed based on the research questions. Thus, it is crucial to have excellent research questions to generate superior hypotheses. In turn, these would determine the research objectives and the design of the study, and ultimately, the outcome of the research. 12 Algorithms for building research questions and hypotheses are shown in Fig. 2 for quantitative research and in Fig. 3 for qualitative research.

EXAMPLES OF RESEARCH QUESTIONS FROM PUBLISHED ARTICLES

• EXAMPLE 1. Descriptive research question (quantitative research)
• - Presents research variables to be assessed (distinct phenotypes and subphenotypes)
• “BACKGROUND: Since COVID-19 was identified, its clinical and biological heterogeneity has been recognized. Identifying COVID-19 phenotypes might help guide basic, clinical, and translational research efforts.
• RESEARCH QUESTION: Does the clinical spectrum of patients with COVID-19 contain distinct phenotypes and subphenotypes? ” 19
• EXAMPLE 2. Relationship research question (quantitative research)
• - Shows interactions between dependent variable (static postural control) and independent variable (peripheral visual field loss)
• “Background: Integration of visual, vestibular, and proprioceptive sensations contributes to postural control. People with peripheral visual field loss have serious postural instability. However, the directional specificity of postural stability and sensory reweighting caused by gradual peripheral visual field loss remain unclear.
• Research question: What are the effects of peripheral visual field loss on static postural control ?” 20
• EXAMPLE 3. Comparative research question (quantitative research)
• - Clarifies the difference among groups with an outcome variable (patients enrolled in COMPERA with moderate PH or severe PH in COPD) and another group without the outcome variable (patients with idiopathic pulmonary arterial hypertension (IPAH))
• “BACKGROUND: Pulmonary hypertension (PH) in COPD is a poorly investigated clinical condition.
• RESEARCH QUESTION: Which factors determine the outcome of PH in COPD?
• STUDY DESIGN AND METHODS: We analyzed the characteristics and outcome of patients enrolled in the Comparative, Prospective Registry of Newly Initiated Therapies for Pulmonary Hypertension (COMPERA) with moderate or severe PH in COPD as defined during the 6th PH World Symposium who received medical therapy for PH and compared them with patients with idiopathic pulmonary arterial hypertension (IPAH) .” 21
• EXAMPLE 4. Exploratory research question (qualitative research)
• - Explores areas that have not been fully investigated (perspectives of families and children who receive care in clinic-based child obesity treatment) to have a deeper understanding of the research problem
• “Problem: Interventions for children with obesity lead to only modest improvements in BMI and long-term outcomes, and data are limited on the perspectives of families of children with obesity in clinic-based treatment. This scoping review seeks to answer the question: What is known about the perspectives of families and children who receive care in clinic-based child obesity treatment? This review aims to explore the scope of perspectives reported by families of children with obesity who have received individualized outpatient clinic-based obesity treatment.” 22
• EXAMPLE 5. Relationship research question (quantitative research)
• - Defines interactions between dependent variable (use of ankle strategies) and independent variable (changes in muscle tone)
• “Background: To maintain an upright standing posture against external disturbances, the human body mainly employs two types of postural control strategies: “ankle strategy” and “hip strategy.” While it has been reported that the magnitude of the disturbance alters the use of postural control strategies, it has not been elucidated how the level of muscle tone, one of the crucial parameters of bodily function, determines the use of each strategy. We have previously confirmed using forward dynamics simulations of human musculoskeletal models that an increased muscle tone promotes the use of ankle strategies. The objective of the present study was to experimentally evaluate a hypothesis: an increased muscle tone promotes the use of ankle strategies. Research question: Do changes in the muscle tone affect the use of ankle strategies ?” 23

EXAMPLES OF HYPOTHESES IN PUBLISHED ARTICLES

• EXAMPLE 1. Working hypothesis (quantitative research)
• - A hypothesis that is initially accepted for further research to produce a feasible theory
• “As fever may have benefit in shortening the duration of viral illness, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response when taken during the early stages of COVID-19 illness .” 24
• “In conclusion, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response . The difference in perceived safety of these agents in COVID-19 illness could be related to the more potent efficacy to reduce fever with ibuprofen compared to acetaminophen. Compelling data on the benefit of fever warrant further research and review to determine when to treat or withhold ibuprofen for early stage fever for COVID-19 and other related viral illnesses .” 24
• EXAMPLE 2. Exploratory hypothesis (qualitative research)
• - Explores particular areas deeper to clarify subjective experience and develop a formal hypothesis potentially testable in a future quantitative approach
• “We hypothesized that when thinking about a past experience of help-seeking, a self distancing prompt would cause increased help-seeking intentions and more favorable help-seeking outcome expectations .” 25
• “Conclusion
• Although a priori hypotheses were not supported, further research is warranted as results indicate the potential for using self-distancing approaches to increasing help-seeking among some people with depressive symptomatology.” 25
• EXAMPLE 3. Hypothesis-generating research to establish a framework for hypothesis testing (qualitative research)
• “We hypothesize that compassionate care is beneficial for patients (better outcomes), healthcare systems and payers (lower costs), and healthcare providers (lower burnout). ” 26
• Compassionomics is the branch of knowledge and scientific study of the effects of compassionate healthcare. Our main hypotheses are that compassionate healthcare is beneficial for (1) patients, by improving clinical outcomes, (2) healthcare systems and payers, by supporting financial sustainability, and (3) HCPs, by lowering burnout and promoting resilience and well-being. The purpose of this paper is to establish a scientific framework for testing the hypotheses above . If these hypotheses are confirmed through rigorous research, compassionomics will belong in the science of evidence-based medicine, with major implications for all healthcare domains.” 26
• EXAMPLE 4. Statistical hypothesis (quantitative research)
• - An assumption is made about the relationship among several population characteristics ( gender differences in sociodemographic and clinical characteristics of adults with ADHD ). Validity is tested by statistical experiment or analysis ( chi-square test, Students t-test, and logistic regression analysis)
• “Our research investigated gender differences in sociodemographic and clinical characteristics of adults with ADHD in a Japanese clinical sample. Due to unique Japanese cultural ideals and expectations of women's behavior that are in opposition to ADHD symptoms, we hypothesized that women with ADHD experience more difficulties and present more dysfunctions than men . We tested the following hypotheses: first, women with ADHD have more comorbidities than men with ADHD; second, women with ADHD experience more social hardships than men, such as having less full-time employment and being more likely to be divorced.” 27
• “Statistical Analysis
• ( text omitted ) Between-gender comparisons were made using the chi-squared test for categorical variables and Students t-test for continuous variables…( text omitted ). A logistic regression analysis was performed for employment status, marital status, and comorbidity to evaluate the independent effects of gender on these dependent variables.” 27

EXAMPLES OF HYPOTHESIS AS WRITTEN IN PUBLISHED ARTICLES IN RELATION TO OTHER PARTS

• EXAMPLE 1. Background, hypotheses, and aims are provided
• “Pregnant women need skilled care during pregnancy and childbirth, but that skilled care is often delayed in some countries …( text omitted ). The focused antenatal care (FANC) model of WHO recommends that nurses provide information or counseling to all pregnant women …( text omitted ). Job aids are visual support materials that provide the right kind of information using graphics and words in a simple and yet effective manner. When nurses are not highly trained or have many work details to attend to, these job aids can serve as a content reminder for the nurses and can be used for educating their patients (Jennings, Yebadokpo, Affo, & Agbogbe, 2010) ( text omitted ). Importantly, additional evidence is needed to confirm how job aids can further improve the quality of ANC counseling by health workers in maternal care …( text omitted )” 28
• “ This has led us to hypothesize that the quality of ANC counseling would be better if supported by job aids. Consequently, a better quality of ANC counseling is expected to produce higher levels of awareness concerning the danger signs of pregnancy and a more favorable impression of the caring behavior of nurses .” 28
• “This study aimed to examine the differences in the responses of pregnant women to a job aid-supported intervention during ANC visit in terms of 1) their understanding of the danger signs of pregnancy and 2) their impression of the caring behaviors of nurses to pregnant women in rural Tanzania.” 28
• EXAMPLE 2. Background, hypotheses, and aims are provided
• “We conducted a two-arm randomized controlled trial (RCT) to evaluate and compare changes in salivary cortisol and oxytocin levels of first-time pregnant women between experimental and control groups. The women in the experimental group touched and held an infant for 30 min (experimental intervention protocol), whereas those in the control group watched a DVD movie of an infant (control intervention protocol). The primary outcome was salivary cortisol level and the secondary outcome was salivary oxytocin level.” 29
• “ We hypothesize that at 30 min after touching and holding an infant, the salivary cortisol level will significantly decrease and the salivary oxytocin level will increase in the experimental group compared with the control group .” 29
• EXAMPLE 3. Background, aim, and hypothesis are provided
• “In countries where the maternal mortality ratio remains high, antenatal education to increase Birth Preparedness and Complication Readiness (BPCR) is considered one of the top priorities [1]. BPCR includes birth plans during the antenatal period, such as the birthplace, birth attendant, transportation, health facility for complications, expenses, and birth materials, as well as family coordination to achieve such birth plans. In Tanzania, although increasing, only about half of all pregnant women attend an antenatal clinic more than four times [4]. Moreover, the information provided during antenatal care (ANC) is insufficient. In the resource-poor settings, antenatal group education is a potential approach because of the limited time for individual counseling at antenatal clinics.” 30
• “This study aimed to evaluate an antenatal group education program among pregnant women and their families with respect to birth-preparedness and maternal and infant outcomes in rural villages of Tanzania.” 30
• “ The study hypothesis was if Tanzanian pregnant women and their families received a family-oriented antenatal group education, they would (1) have a higher level of BPCR, (2) attend antenatal clinic four or more times, (3) give birth in a health facility, (4) have less complications of women at birth, and (5) have less complications and deaths of infants than those who did not receive the education .” 30

Research questions and hypotheses are crucial components to any type of research, whether quantitative or qualitative. These questions should be developed at the very beginning of the study. Excellent research questions lead to superior hypotheses, which, like a compass, set the direction of research, and can often determine the successful conduct of the study. Many research studies have floundered because the development of research questions and subsequent hypotheses was not given the thought and meticulous attention needed. The development of research questions and hypotheses is an iterative process based on extensive knowledge of the literature and insightful grasp of the knowledge gap. Focused, concise, and specific research questions provide a strong foundation for constructing hypotheses which serve as formal predictions about the research outcomes. Research questions and hypotheses are crucial elements of research that should not be overlooked. They should be carefully thought of and constructed when planning research. This avoids unethical studies and poor outcomes by defining well-founded objectives that determine the design, course, and outcome of the study.

Disclosure: The authors have no potential conflicts of interest to disclose.

Author Contributions:

• Conceptualization: Barroga E, Matanguihan GJ.
• Methodology: Barroga E, Matanguihan GJ.
• Writing - original draft: Barroga E, Matanguihan GJ.
• Writing - review & editing: Barroga E, Matanguihan GJ.

• Privacy Policy

Home » Quantitative Research – Methods, Types and Analysis

Quantitative Research – Methods, Types and Analysis

Table of Contents

Quantitative Research

Quantitative research is a type of research that collects and analyzes numerical data to test hypotheses and answer research questions . This research typically involves a large sample size and uses statistical analysis to make inferences about a population based on the data collected. It often involves the use of surveys, experiments, or other structured data collection methods to gather quantitative data.

Quantitative Research Methods

Quantitative Research Methods are as follows:

Descriptive Research Design

Descriptive research design is used to describe the characteristics of a population or phenomenon being studied. This research method is used to answer the questions of what, where, when, and how. Descriptive research designs use a variety of methods such as observation, case studies, and surveys to collect data. The data is then analyzed using statistical tools to identify patterns and relationships.

Correlational Research Design

Correlational research design is used to investigate the relationship between two or more variables. Researchers use correlational research to determine whether a relationship exists between variables and to what extent they are related. This research method involves collecting data from a sample and analyzing it using statistical tools such as correlation coefficients.

Quasi-experimental Research Design

Quasi-experimental research design is used to investigate cause-and-effect relationships between variables. This research method is similar to experimental research design, but it lacks full control over the independent variable. Researchers use quasi-experimental research designs when it is not feasible or ethical to manipulate the independent variable.

Experimental Research Design

Experimental research design is used to investigate cause-and-effect relationships between variables. This research method involves manipulating the independent variable and observing the effects on the dependent variable. Researchers use experimental research designs to test hypotheses and establish cause-and-effect relationships.

Survey Research

Survey research involves collecting data from a sample of individuals using a standardized questionnaire. This research method is used to gather information on attitudes, beliefs, and behaviors of individuals. Researchers use survey research to collect data quickly and efficiently from a large sample size. Survey research can be conducted through various methods such as online, phone, mail, or in-person interviews.

Quantitative Research Analysis Methods

Here are some commonly used quantitative research analysis methods:

Statistical Analysis

Statistical analysis is the most common quantitative research analysis method. It involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis can be used to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.

Regression Analysis

Regression analysis is a statistical technique used to analyze the relationship between one dependent variable and one or more independent variables. Researchers use regression analysis to identify and quantify the impact of independent variables on the dependent variable.

Factor Analysis

Factor analysis is a statistical technique used to identify underlying factors that explain the correlations among a set of variables. Researchers use factor analysis to reduce a large number of variables to a smaller set of factors that capture the most important information.

Structural Equation Modeling

Structural equation modeling is a statistical technique used to test complex relationships between variables. It involves specifying a model that includes both observed and unobserved variables, and then using statistical methods to test the fit of the model to the data.

Time Series Analysis

Time series analysis is a statistical technique used to analyze data that is collected over time. It involves identifying patterns and trends in the data, as well as any seasonal or cyclical variations.

Multilevel Modeling

Multilevel modeling is a statistical technique used to analyze data that is nested within multiple levels. For example, researchers might use multilevel modeling to analyze data that is collected from individuals who are nested within groups, such as students nested within schools.

Applications of Quantitative Research

Quantitative research has many applications across a wide range of fields. Here are some common examples:

• Market Research : Quantitative research is used extensively in market research to understand consumer behavior, preferences, and trends. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform marketing strategies, product development, and pricing decisions.
• Health Research: Quantitative research is used in health research to study the effectiveness of medical treatments, identify risk factors for diseases, and track health outcomes over time. Researchers use statistical methods to analyze data from clinical trials, surveys, and other sources to inform medical practice and policy.
• Social Science Research: Quantitative research is used in social science research to study human behavior, attitudes, and social structures. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform social policies, educational programs, and community interventions.
• Education Research: Quantitative research is used in education research to study the effectiveness of teaching methods, assess student learning outcomes, and identify factors that influence student success. Researchers use experimental and quasi-experimental designs, as well as surveys and other quantitative methods, to collect and analyze data.
• Environmental Research: Quantitative research is used in environmental research to study the impact of human activities on the environment, assess the effectiveness of conservation strategies, and identify ways to reduce environmental risks. Researchers use statistical methods to analyze data from field studies, experiments, and other sources.

Characteristics of Quantitative Research

Here are some key characteristics of quantitative research:

• Numerical data : Quantitative research involves collecting numerical data through standardized methods such as surveys, experiments, and observational studies. This data is analyzed using statistical methods to identify patterns and relationships.
• Large sample size: Quantitative research often involves collecting data from a large sample of individuals or groups in order to increase the reliability and generalizability of the findings.
• Objective approach: Quantitative research aims to be objective and impartial in its approach, focusing on the collection and analysis of data rather than personal beliefs, opinions, or experiences.
• Control over variables: Quantitative research often involves manipulating variables to test hypotheses and establish cause-and-effect relationships. Researchers aim to control for extraneous variables that may impact the results.
• Replicable : Quantitative research aims to be replicable, meaning that other researchers should be able to conduct similar studies and obtain similar results using the same methods.
• Statistical analysis: Quantitative research involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis allows researchers to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.
• Generalizability: Quantitative research aims to produce findings that can be generalized to larger populations beyond the specific sample studied. This is achieved through the use of random sampling methods and statistical inference.

Examples of Quantitative Research

Here are some examples of quantitative research in different fields:

• Market Research: A company conducts a survey of 1000 consumers to determine their brand awareness and preferences. The data is analyzed using statistical methods to identify trends and patterns that can inform marketing strategies.
• Health Research : A researcher conducts a randomized controlled trial to test the effectiveness of a new drug for treating a particular medical condition. The study involves collecting data from a large sample of patients and analyzing the results using statistical methods.
• Social Science Research : A sociologist conducts a survey of 500 people to study attitudes toward immigration in a particular country. The data is analyzed using statistical methods to identify factors that influence these attitudes.
• Education Research: A researcher conducts an experiment to compare the effectiveness of two different teaching methods for improving student learning outcomes. The study involves randomly assigning students to different groups and collecting data on their performance on standardized tests.
• Environmental Research : A team of researchers conduct a study to investigate the impact of climate change on the distribution and abundance of a particular species of plant or animal. The study involves collecting data on environmental factors and population sizes over time and analyzing the results using statistical methods.
• Psychology : A researcher conducts a survey of 500 college students to investigate the relationship between social media use and mental health. The data is analyzed using statistical methods to identify correlations and potential causal relationships.
• Political Science: A team of researchers conducts a study to investigate voter behavior during an election. They use survey methods to collect data on voting patterns, demographics, and political attitudes, and analyze the results using statistical methods.

How to Conduct Quantitative Research

Here is a general overview of how to conduct quantitative research:

• Develop a research question: The first step in conducting quantitative research is to develop a clear and specific research question. This question should be based on a gap in existing knowledge, and should be answerable using quantitative methods.
• Develop a research design: Once you have a research question, you will need to develop a research design. This involves deciding on the appropriate methods to collect data, such as surveys, experiments, or observational studies. You will also need to determine the appropriate sample size, data collection instruments, and data analysis techniques.
• Collect data: The next step is to collect data. This may involve administering surveys or questionnaires, conducting experiments, or gathering data from existing sources. It is important to use standardized methods to ensure that the data is reliable and valid.
• Analyze data : Once the data has been collected, it is time to analyze it. This involves using statistical methods to identify patterns, trends, and relationships between variables. Common statistical techniques include correlation analysis, regression analysis, and hypothesis testing.
• Interpret results: After analyzing the data, you will need to interpret the results. This involves identifying the key findings, determining their significance, and drawing conclusions based on the data.
• Communicate findings: Finally, you will need to communicate your findings. This may involve writing a research report, presenting at a conference, or publishing in a peer-reviewed journal. It is important to clearly communicate the research question, methods, results, and conclusions to ensure that others can understand and replicate your research.

When to use Quantitative Research

Here are some situations when quantitative research can be appropriate:

• To test a hypothesis: Quantitative research is often used to test a hypothesis or a theory. It involves collecting numerical data and using statistical analysis to determine if the data supports or refutes the hypothesis.
• To generalize findings: If you want to generalize the findings of your study to a larger population, quantitative research can be useful. This is because it allows you to collect numerical data from a representative sample of the population and use statistical analysis to make inferences about the population as a whole.
• To measure relationships between variables: If you want to measure the relationship between two or more variables, such as the relationship between age and income, or between education level and job satisfaction, quantitative research can be useful. It allows you to collect numerical data on both variables and use statistical analysis to determine the strength and direction of the relationship.
• To identify patterns or trends: Quantitative research can be useful for identifying patterns or trends in data. For example, you can use quantitative research to identify trends in consumer behavior or to identify patterns in stock market data.
• To quantify attitudes or opinions : If you want to measure attitudes or opinions on a particular topic, quantitative research can be useful. It allows you to collect numerical data using surveys or questionnaires and analyze the data using statistical methods to determine the prevalence of certain attitudes or opinions.

Purpose of Quantitative Research

The purpose of quantitative research is to systematically investigate and measure the relationships between variables or phenomena using numerical data and statistical analysis. The main objectives of quantitative research include:

• Description : To provide a detailed and accurate description of a particular phenomenon or population.
• Explanation : To explain the reasons for the occurrence of a particular phenomenon, such as identifying the factors that influence a behavior or attitude.
• Prediction : To predict future trends or behaviors based on past patterns and relationships between variables.
• Control : To identify the best strategies for controlling or influencing a particular outcome or behavior.

Quantitative research is used in many different fields, including social sciences, business, engineering, and health sciences. It can be used to investigate a wide range of phenomena, from human behavior and attitudes to physical and biological processes. The purpose of quantitative research is to provide reliable and valid data that can be used to inform decision-making and improve understanding of the world around us.

Advantages of Quantitative Research

There are several advantages of quantitative research, including:

• Objectivity : Quantitative research is based on objective data and statistical analysis, which reduces the potential for bias or subjectivity in the research process.
• Reproducibility : Because quantitative research involves standardized methods and measurements, it is more likely to be reproducible and reliable.
• Generalizability : Quantitative research allows for generalizations to be made about a population based on a representative sample, which can inform decision-making and policy development.
• Precision : Quantitative research allows for precise measurement and analysis of data, which can provide a more accurate understanding of phenomena and relationships between variables.
• Efficiency : Quantitative research can be conducted relatively quickly and efficiently, especially when compared to qualitative research, which may involve lengthy data collection and analysis.
• Large sample sizes : Quantitative research can accommodate large sample sizes, which can increase the representativeness and generalizability of the results.

Limitations of Quantitative Research

There are several limitations of quantitative research, including:

• Limited understanding of context: Quantitative research typically focuses on numerical data and statistical analysis, which may not provide a comprehensive understanding of the context or underlying factors that influence a phenomenon.
• Simplification of complex phenomena: Quantitative research often involves simplifying complex phenomena into measurable variables, which may not capture the full complexity of the phenomenon being studied.
• Potential for researcher bias: Although quantitative research aims to be objective, there is still the potential for researcher bias in areas such as sampling, data collection, and data analysis.
• Limited ability to explore new ideas: Quantitative research is often based on pre-determined research questions and hypotheses, which may limit the ability to explore new ideas or unexpected findings.
• Limited ability to capture subjective experiences : Quantitative research is typically focused on objective data and may not capture the subjective experiences of individuals or groups being studied.
• Ethical concerns : Quantitative research may raise ethical concerns, such as invasion of privacy or the potential for harm to participants.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

You may also like

Questionnaire – Definition, Types, and Examples

Case Study – Methods, Examples and Guide

Observational Research – Methods and Guide

Qualitative Research Methods

Explanatory Research – Types, Methods, Guide

Survey Research – Types, Methods, Examples

Quantitative Data Analysis: A Comprehensive Guide

By: Ofem Eteng Published: May 18, 2022

Related Articles

A healthcare giant successfully introduces the most effective drug dosage through rigorous statistical modeling, saving countless lives. A marketing team predicts consumer trends with uncanny accuracy, tailoring campaigns for maximum impact.

Table of Contents

These trends and dosages are not just any numbers but are a result of meticulous quantitative data analysis. Quantitative data analysis offers a robust framework for understanding complex phenomena, evaluating hypotheses, and predicting future outcomes.

In this blog, we’ll walk through the concept of quantitative data analysis, the steps required, its advantages, and the methods and techniques that are used in this analysis. Read on!

What is Quantitative Data Analysis?

Quantitative data analysis is a systematic process of examining, interpreting, and drawing meaningful conclusions from numerical data. It involves the application of statistical methods, mathematical models, and computational techniques to understand patterns, relationships, and trends within datasets.

Quantitative data analysis methods typically work with algorithms, mathematical analysis tools, and software to gain insights from the data, answering questions such as how many, how often, and how much. Data for quantitative data analysis is usually collected from close-ended surveys, questionnaires, polls, etc. The data can also be obtained from sales figures, email click-through rates, number of website visitors, and percentage revenue increase. 

Quantitative Data Analysis vs Qualitative Data Analysis

When we talk about data, we directly think about the pattern, the relationship, and the connection between the datasets – analyzing the data in short. Therefore when it comes to data analysis, there are broadly two types – Quantitative Data Analysis and Qualitative Data Analysis.

Quantitative data analysis revolves around numerical data and statistics, which are suitable for functions that can be counted or measured. In contrast, qualitative data analysis includes description and subjective information – for things that can be observed but not measured.

Let us differentiate between Quantitative Data Analysis and Quantitative Data Analysis for a better understanding.

Data Preparation Steps for Quantitative Data Analysis

Quantitative data has to be gathered and cleaned before proceeding to the stage of analyzing it. Below are the steps to prepare a data before quantitative research analysis:

• Step 1: Data Collection

Before beginning the analysis process, you need data. Data can be collected through rigorous quantitative research, which includes methods such as interviews, focus groups, surveys, and questionnaires.

• Step 2: Data Cleaning

Once the data is collected, begin the data cleaning process by scanning through the entire data for duplicates, errors, and omissions. Keep a close eye for outliers (data points that are significantly different from the majority of the dataset) because they can skew your analysis results if they are not removed.

This data-cleaning process ensures data accuracy, consistency and relevancy before analysis.

• Step 3: Data Analysis and Interpretation

Now that you have collected and cleaned your data, it is now time to carry out the quantitative analysis. There are two methods of quantitative data analysis, which we will discuss in the next section.

However, if you have data from multiple sources, collecting and cleaning it can be a cumbersome task. This is where Hevo Data steps in. With Hevo, extracting, transforming, and loading data from source to destination becomes a seamless task, eliminating the need for manual coding. This not only saves valuable time but also enhances the overall efficiency of data analysis and visualization, empowering users to derive insights quickly and with precision

Hevo is the only real-time ELT No-code Data Pipeline platform that cost-effectively automates data pipelines that are flexible to your needs. With integration with 150+ Data Sources (40+ free sources), we help you not only export data from sources & load data to the destinations but also transform & enrich your data, & make it analysis-ready.

Start for free now!

Now that you are familiar with what quantitative data analysis is and how to prepare your data for analysis, the focus will shift to the purpose of this article, which is to describe the methods and techniques of quantitative data analysis.

Methods and Techniques of Quantitative Data Analysis

Quantitative data analysis employs two techniques to extract meaningful insights from datasets, broadly. The first method is descriptive statistics, which summarizes and portrays essential features of a dataset, such as mean, median, and standard deviation.

Inferential statistics, the second method, extrapolates insights and predictions from a sample dataset to make broader inferences about an entire population, such as hypothesis testing and regression analysis.

An in-depth explanation of both the methods is provided below:

• Descriptive Statistics
• Inferential Statistics

1) Descriptive Statistics

Descriptive statistics as the name implies is used to describe a dataset. It helps understand the details of your data by summarizing it and finding patterns from the specific data sample. They provide absolute numbers obtained from a sample but do not necessarily explain the rationale behind the numbers and are mostly used for analyzing single variables. The methods used in descriptive statistics include: 

• Mean:   This calculates the numerical average of a set of values.
• Median: This is used to get the midpoint of a set of values when the numbers are arranged in numerical order.
• Mode: This is used to find the most commonly occurring value in a dataset.
• Percentage: This is used to express how a value or group of respondents within the data relates to a larger group of respondents.
• Frequency: This indicates the number of times a value is found.
• Range: This shows the highest and lowest values in a dataset.
• Standard Deviation: This is used to indicate how dispersed a range of numbers is, meaning, it shows how close all the numbers are to the mean.
• Skewness: It indicates how symmetrical a range of numbers is, showing if they cluster into a smooth bell curve shape in the middle of the graph or if they skew towards the left or right.

2) Inferential Statistics

In quantitative analysis, the expectation is to turn raw numbers into meaningful insight using numerical values, and descriptive statistics is all about explaining details of a specific dataset using numbers, but it does not explain the motives behind the numbers; hence, a need for further analysis using inferential statistics.

Inferential statistics aim to make predictions or highlight possible outcomes from the analyzed data obtained from descriptive statistics. They are used to generalize results and make predictions between groups, show relationships that exist between multiple variables, and are used for hypothesis testing that predicts changes or differences.

There are various statistical analysis methods used within inferential statistics; a few are discussed below.

• Cross Tabulations: Cross tabulation or crosstab is used to show the relationship that exists between two variables and is often used to compare results by demographic groups. It uses a basic tabular form to draw inferences between different data sets and contains data that is mutually exclusive or has some connection with each other. Crosstabs help understand the nuances of a dataset and factors that may influence a data point.
• Regression Analysis: Regression analysis estimates the relationship between a set of variables. It shows the correlation between a dependent variable (the variable or outcome you want to measure or predict) and any number of independent variables (factors that may impact the dependent variable). Therefore, the purpose of the regression analysis is to estimate how one or more variables might affect a dependent variable to identify trends and patterns to make predictions and forecast possible future trends. There are many types of regression analysis, and the model you choose will be determined by the type of data you have for the dependent variable. The types of regression analysis include linear regression, non-linear regression, binary logistic regression, etc.
• Monte Carlo Simulation: Monte Carlo simulation, also known as the Monte Carlo method, is a computerized technique of generating models of possible outcomes and showing their probability distributions. It considers a range of possible outcomes and then tries to calculate how likely each outcome will occur. Data analysts use it to perform advanced risk analyses to help forecast future events and make decisions accordingly.
• Analysis of Variance (ANOVA): This is used to test the extent to which two or more groups differ from each other. It compares the mean of various groups and allows the analysis of multiple groups.
• Factor Analysis:   A large number of variables can be reduced into a smaller number of factors using the factor analysis technique. It works on the principle that multiple separate observable variables correlate with each other because they are all associated with an underlying construct. It helps in reducing large datasets into smaller, more manageable samples.
• Cohort Analysis: Cohort analysis can be defined as a subset of behavioral analytics that operates from data taken from a given dataset. Rather than looking at all users as one unit, cohort analysis breaks down data into related groups for analysis, where these groups or cohorts usually have common characteristics or similarities within a defined period.
• MaxDiff Analysis: This is a quantitative data analysis method that is used to gauge customers’ preferences for purchase and what parameters rank higher than the others in the process. 
• Cluster Analysis: Cluster analysis is a technique used to identify structures within a dataset. Cluster analysis aims to be able to sort different data points into groups that are internally similar and externally different; that is, data points within a cluster will look like each other and different from data points in other clusters.
• Time Series Analysis: This is a statistical analytic technique used to identify trends and cycles over time. It is simply the measurement of the same variables at different times, like weekly and monthly email sign-ups, to uncover trends, seasonality, and cyclic patterns. By doing this, the data analyst can forecast how variables of interest may fluctuate in the future. 
• SWOT analysis: This is a quantitative data analysis method that assigns numerical values to indicate strengths, weaknesses, opportunities, and threats of an organization, product, or service to show a clearer picture of competition to foster better business strategies

How to Choose the Right Method for your Analysis?

Choosing between Descriptive Statistics or Inferential Statistics can be often confusing. You should consider the following factors before choosing the right method for your quantitative data analysis:

1. Type of Data

The first consideration in data analysis is understanding the type of data you have. Different statistical methods have specific requirements based on these data types, and using the wrong method can render results meaningless. The choice of statistical method should align with the nature and distribution of your data to ensure meaningful and accurate analysis.

2. Your Research Questions

When deciding on statistical methods, it’s crucial to align them with your specific research questions and hypotheses. The nature of your questions will influence whether descriptive statistics alone, which reveal sample attributes, are sufficient or if you need both descriptive and inferential statistics to understand group differences or relationships between variables and make population inferences.

Pros and Cons of Quantitative Data Analysis

1. Objectivity and Generalizability:

• Quantitative data analysis offers objective, numerical measurements, minimizing bias and personal interpretation.
• Results can often be generalized to larger populations, making them applicable to broader contexts.

Example: A study using quantitative data analysis to measure student test scores can objectively compare performance across different schools and demographics, leading to generalizable insights about educational strategies.

2. Precision and Efficiency:

• Statistical methods provide precise numerical results, allowing for accurate comparisons and prediction.
• Large datasets can be analyzed efficiently with the help of computer software, saving time and resources.

Example: A marketing team can use quantitative data analysis to precisely track click-through rates and conversion rates on different ad campaigns, quickly identifying the most effective strategies for maximizing customer engagement.

3. Identification of Patterns and Relationships:

• Statistical techniques reveal hidden patterns and relationships between variables that might not be apparent through observation alone.
• This can lead to new insights and understanding of complex phenomena.

Example: A medical researcher can use quantitative analysis to pinpoint correlations between lifestyle factors and disease risk, aiding in the development of prevention strategies.

1. Limited Scope:

• Quantitative analysis focuses on quantifiable aspects of a phenomenon ,  potentially overlooking important qualitative nuances, such as emotions, motivations, or cultural contexts.

Example: A survey measuring customer satisfaction with numerical ratings might miss key insights about the underlying reasons for their satisfaction or dissatisfaction, which could be better captured through open-ended feedback.

2. Oversimplification:

• Reducing complex phenomena to numerical data can lead to oversimplification and a loss of richness in understanding.

Example: Analyzing employee productivity solely through quantitative metrics like hours worked or tasks completed might not account for factors like creativity, collaboration, or problem-solving skills, which are crucial for overall performance.

3. Potential for Misinterpretation:

• Statistical results can be misinterpreted if not analyzed carefully and with appropriate expertise.
• The choice of statistical methods and assumptions can significantly influence results.

This blog discusses the steps, methods, and techniques of quantitative data analysis. It also gives insights into the methods of data collection, the type of data one should work with, and the pros and cons of such analysis.

Gain a better understanding of data analysis with these essential reads:

• Data Analysis and Modeling: 4 Critical Differences
• Exploratory Data Analysis Simplified 101
• 25 Best Data Analysis Tools in 2024

Carrying out successful data analysis requires prepping the data and making it analysis-ready. That is where Hevo steps in.

Want to give Hevo a try? Sign Up for a 14-day free trial and experience the feature-rich Hevo suite first hand. You may also have a look at the amazing Hevo price , which will assist you in selecting the best plan for your requirements.

Share your experience of understanding Quantitative Data Analysis in the comment section below! We would love to hear your thoughts.

Ofem is a freelance writer specializing in data-related topics, who has expertise in translating complex concepts. With a focus on data science, analytics, and emerging technologies.

No-code Data Pipeline for your Data Warehouse

• Data Analysis
• Data Warehouse
• Quantitative Data Analysis

Continue Reading

Saloni Agarwal

Enterprise Data Lake: A Simplified Guide

Riya Bothra

An Expert Guide To Enterprise Data Analysis

Gcp storage buckets list: efficient data organizing strategy, i want to read this e-book.

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, automatically generate references for free.

• Knowledge Base
• Methodology
• What Is Quantitative Research? | Definition & Methods

What Is Quantitative Research? | Definition & Methods

Published on 4 April 2022 by Pritha Bhandari . Revised on 10 October 2022.

Quantitative research is the process of collecting and analysing numerical data. It can be used to find patterns and averages, make predictions, test causal relationships, and generalise results to wider populations.

Quantitative research is the opposite of qualitative research , which involves collecting and analysing non-numerical data (e.g. text, video, or audio).

Quantitative research is widely used in the natural and social sciences: biology, chemistry, psychology, economics, sociology, marketing, etc.

• What is the demographic makeup of Singapore in 2020?
• How has the average temperature changed globally over the last century?
• Does environmental pollution affect the prevalence of honey bees?
• Does working from home increase productivity for people with long commutes?

Table of contents

Quantitative research methods, quantitative data analysis, advantages of quantitative research, disadvantages of quantitative research, frequently asked questions about quantitative research.

You can use quantitative research methods for descriptive, correlational or experimental research.

• In descriptive research , you simply seek an overall summary of your study variables.
• In correlational research , you investigate relationships between your study variables.
• In experimental research , you systematically examine whether there is a cause-and-effect relationship between variables.

Correlational and experimental research can both be used to formally test hypotheses , or predictions, using statistics. The results may be generalised to broader populations based on the sampling method used.

To collect quantitative data, you will often need to use operational definitions that translate abstract concepts (e.g., mood) into observable and quantifiable measures (e.g., self-ratings of feelings and energy levels).

Prevent plagiarism, run a free check.

Once data is collected, you may need to process it before it can be analysed. For example, survey and test data may need to be transformed from words to numbers. Then, you can use statistical analysis to answer your research questions .

Descriptive statistics will give you a summary of your data and include measures of averages and variability. You can also use graphs, scatter plots and frequency tables to visualise your data and check for any trends or outliers.

Using inferential statistics , you can make predictions or generalisations based on your data. You can test your hypothesis or use your sample data to estimate the population parameter .

You can also assess the reliability and validity of your data collection methods to indicate how consistently and accurately your methods actually measured what you wanted them to.

Quantitative research is often used to standardise data collection and generalise findings . Strengths of this approach include:

• Replication

Repeating the study is possible because of standardised data collection protocols and tangible definitions of abstract concepts.

• Direct comparisons of results

The study can be reproduced in other cultural settings, times or with different groups of participants. Results can be compared statistically.

• Large samples

Data from large samples can be processed and analysed using reliable and consistent procedures through quantitative data analysis.

• Hypothesis testing

Using formalised and established hypothesis testing procedures means that you have to carefully consider and report your research variables, predictions, data collection and testing methods before coming to a conclusion.

Despite the benefits of quantitative research, it is sometimes inadequate in explaining complex research topics. Its limitations include:

• Superficiality

Using precise and restrictive operational definitions may inadequately represent complex concepts. For example, the concept of mood may be represented with just a number in quantitative research, but explained with elaboration in qualitative research.

• Narrow focus

Predetermined variables and measurement procedures can mean that you ignore other relevant observations.

• Structural bias

Despite standardised procedures, structural biases can still affect quantitative research. Missing data , imprecise measurements or inappropriate sampling methods are biases that can lead to the wrong conclusions.

• Lack of context

Quantitative research often uses unnatural settings like laboratories or fails to consider historical and cultural contexts that may affect data collection and results.

Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.

Quantitative methods allow you to test a hypothesis by systematically collecting and analysing data, while qualitative methods allow you to explore ideas and experiences in depth.

In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .

Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organisations.

Operationalisation means turning abstract conceptual ideas into measurable observations.

For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioural avoidance of crowded places, or physical anxiety symptoms in social situations.

Before collecting data , it’s important to consider how you will operationalise the variables that you want to measure.

Reliability and validity are both about how well a method measures something:

• Reliability refers to the  consistency of a measure (whether the results can be reproduced under the same conditions).
• Validity   refers to the  accuracy of a measure (whether the results really do represent what they are supposed to measure).

If you are doing experimental research , you also have to consider the internal and external validity of your experiment.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the ‘Cite this Scribbr article’ button to automatically add the citation to our free Reference Generator.

Bhandari, P. (2022, October 10). What Is Quantitative Research? | Definition & Methods. Scribbr. Retrieved 22 April 2024, from https://www.scribbr.co.uk/research-methods/introduction-to-quantitative-research/

Is this article helpful?

Pritha Bhandari

Quantitative Research

• Reference work entry
• First Online: 13 January 2019
• Cite this reference work entry

• Leigh A. Wilson 2 , 3  

4223 Accesses

4 Citations

Quantitative research methods are concerned with the planning, design, and implementation of strategies to collect and analyze data. Descartes, the seventeenth-century philosopher, suggested that how the results are achieved is often more important than the results themselves, as the journey taken along the research path is a journey of discovery. High-quality quantitative research is characterized by the attention given to the methods and the reliability of the tools used to collect the data. The ability to critique research in a systematic way is an essential component of a health professional’s role in order to deliver high quality, evidence-based healthcare. This chapter is intended to provide a simple overview of the way new researchers and health practitioners can understand and employ quantitative methods. The chapter offers practical, realistic guidance in a learner-friendly way and uses a logical sequence to understand the process of hypothesis development, study design, data collection and handling, and finally data analysis and interpretation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

• Available as PDF
• Read on any device
• Instant download
• Own it forever
• Available as EPUB and PDF
• Durable hardcover edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Babbie ER. The practice of social research. 14th ed. Belmont: Wadsworth Cengage; 2016.

Google Scholar  

Descartes. Cited in Halverston, W. (1976). In: A concise introduction to philosophy, 3rd ed. New York: Random House; 1637.

Doll R, Hill AB. The mortality of doctors in relation to their smoking habits. BMJ. 1954;328(7455):1529–33. https://doi.org/10.1136/bmj.328.7455.1529 .

Article   Google Scholar  

Liamputtong P. Research methods in health: foundations for evidence-based practice. 3rd ed. Melbourne: Oxford University Press; 2017.

McNabb DE. Research methods in public administration and nonprofit management: quantitative and qualitative approaches. 2nd ed. New York: Armonk; 2007.

Merriam-Webster. Dictionary. http://www.merriam-webster.com . Accessed 20th December 2017.

Olesen Larsen P, von Ins M. The rate of growth in scientific publication and the decline in coverage provided by Science Citation Index. Scientometrics. 2010;84(3):575–603.

Pannucci CJ, Wilkins EG. Identifying and avoiding bias in research. Plast Reconstr Surg. 2010;126(2):619–25. https://doi.org/10.1097/PRS.0b013e3181de24bc .

Petrie A, Sabin C. Medical statistics at a glance. 2nd ed. London: Blackwell Publishing; 2005.

Portney LG, Watkins MP. Foundations of clinical research: applications to practice. 3rd ed. New Jersey: Pearson Publishing; 2009.

Sheehan J. Aspects of research methodology. Nurse Educ Today. 1986;6:193–203.

Wilson LA, Black DA. Health, science research and research methods. Sydney: McGraw Hill; 2013.

Download references

Author information

Authors and affiliations.

School of Science and Health, Western Sydney University, Penrith, NSW, Australia

Leigh A. Wilson

Faculty of Health Science, Discipline of Behavioural and Social Sciences in Health, University of Sydney, Lidcombe, NSW, Australia

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Leigh A. Wilson .

Editor information

Editors and affiliations.

Pranee Liamputtong

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this entry

Cite this entry.

Wilson, L.A. (2019). Quantitative Research. In: Liamputtong, P. (eds) Handbook of Research Methods in Health Social Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-10-5251-4_54

Download citation

DOI : https://doi.org/10.1007/978-981-10-5251-4_54

Published : 13 January 2019

Publisher Name : Springer, Singapore

Print ISBN : 978-981-10-5250-7

Online ISBN : 978-981-10-5251-4

eBook Packages : Social Sciences Reference Module Humanities and Social Sciences Reference Module Business, Economics and Social Sciences

Share this entry

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Publish with us

Policies and ethics

• Find a journal
• Track your research

Quantitative and Qualitative Research

• I NEED TO . . .

What is Quantitative Research?

• What is Qualitative Research?
• Quantitative vs Qualitative
• Step 1: Accessing CINAHL
• Step 2: Create a Keyword Search
• Step 3: Create a Subject Heading Search
• Step 4: Repeat Steps 1-3 for Second Concept
• Step 5: Repeat Steps 1-3 for Quantitative Terms
• Step 6: Combining All Searches
• Step 7: Adding Limiters
• Step 8: Save Your Search!
• What Kind of Article is This?
• More Research Help This link opens in a new window

Quantitative methodology is the dominant research framework in the social sciences. It refers to a set of strategies, techniques and assumptions used to study psychological, social and economic processes through the exploration of numeric patterns . Quantitative research gathers a range of numeric data. Some of the numeric data is intrinsically quantitative (e.g. personal income), while in other cases the numeric structure is  imposed (e.g. ‘On a scale from 1 to 10, how depressed did you feel last week?’). The collection of quantitative information allows researchers to conduct simple to extremely sophisticated statistical analyses that aggregate the data (e.g. averages, percentages), show relationships among the data (e.g. ‘Students with lower grade point averages tend to score lower on a depression scale’) or compare across aggregated data (e.g. the USA has a higher gross domestic product than Spain). Quantitative research includes methodologies such as questionnaires, structured observations or experiments and stands in contrast to qualitative research. Qualitative research involves the collection and analysis of narratives and/or open-ended observations through methodologies such as interviews, focus groups or ethnographies.

Coghlan, D., Brydon-Miller, M. (2014).  The SAGE encyclopedia of action research  (Vols. 1-2). London, : SAGE Publications Ltd doi: 10.4135/9781446294406

What is the purpose of quantitative research?

The purpose of quantitative research is to generate knowledge and create understanding about the social world. Quantitative research is used by social scientists, including communication researchers, to observe phenomena or occurrences affecting individuals. Social scientists are concerned with the study of people. Quantitative research is a way to learn about a particular group of people, known as a sample population. Using scientific inquiry, quantitative research relies on data that are observed or measured to examine questions about the sample population.

Allen, M. (2017).  The SAGE encyclopedia of communication research methods  (Vols. 1-4). Thousand Oaks, CA: SAGE Publications, Inc doi: 10.4135/9781483381411

How do I know if the study is a quantitative design?  What type of quantitative study is it?

Quantitative Research Designs: Descriptive non-experimental, Quasi-experimental or Experimental?

Studies do not always explicitly state what kind of research design is being used.  You will need to know how to decipher which design type is used.  The following video will help you determine the quantitative design type.

• << Previous: I NEED TO . . .
• Next: What is Qualitative Research? >>
• Last Updated: Dec 8, 2023 10:05 PM
• URL: https://libguides.uta.edu/quantitative_and_qualitative_research

University of Texas Arlington Libraries 702 Planetarium Place · Arlington, TX 76019 · 817-272-3000

• Internet Privacy
• Accessibility
• Problems with a guide? Contact Us.

What is quantitative research?

Last updated

20 February 2023

Reviewed by

Quantitative methods and data are used by some business owners, for example, to evaluate their business, diagnose issues, and identify opportunities.

Quantitative research is used throughout the natural and social sciences, including economics, sociology, chemistry, biology, psychology, and marketing. 

Researchers use quantitative research to get objective, robust, and representative answers from individuals. Researchers gather quantitative data from sample groups of people and generalize it to a larger population. This is to, in some instances, explain a given phenomenon and answer questions about the population, such as product preferences, political persuasion, or demography.

For example, a hotel owner in the US can conduct quantitative research, perhaps via a questionnaire, on a small sample of their customers to understand their opinions about their products and services. The analyzed quantitative data from this questionnaire can be generalized to the larger population of their customers. The hotel can use these opinions to maintain or improve its service provision.

Make research less tedious

Dovetail streamlines research to help you uncover and share actionable insights

• Quantitative research methods

Researchers employ various quantitative research methods to determine certain phenomena.

Observation

This method involves gathering information by simply observing behaviors or counting subjects relevant to a study. For example, a researcher could sit in a classroom and observe students when a teacher is teaching, recording those who are and are not paying attention.

Survey is one of the most popular and well-known quantitative methods. It involves asking individuals questions either physically or, most typically nowadays, online. These questions are usually in the form of a questionnaire that individuals can respond to, using a mix of single, multichoice, ranking, rating, and occasionally open-ended questions .

For example, a researcher could administer a questionnaire to first-year international college students about their college experiences using various question formats.

Experimental

This scientific approach is conducted with two sets of data, i.e., independent and dependent variables . Usually, researchers approach experimental studies with specific hypotheses to test. They may use two groups of participants: one who would receive the “treatment” and one who would not.

For example, a researcher might wish to test a short-term mindfulness treatment for individuals with depression. In this case, the independent or manipulated variable would be the mindfulness treatment group. One group would receive the mindfulness treatment, and another would not. In this case, the “experiment” would be to see if the individuals who received the mindfulness treatment experienced fewer depressive symptoms than those who did not.

• What is quantitative analysis?

Quantitative analysis is a process that involves manipulating and evaluating collected, measurable data. The goal is to understand the behavior of a given phenomenon and answer a research question (and, in a scientific setting, prove or disprove a hypothesis).

A business owner, for example, may analyze quantitative sales data and consumer quantitative data using a questionnaire. By doing this, the owner can figure out if their business is doing well or if they need to make changes to improve.

If you are a business owner, you could consider quantitative analysis to better understand your business's past, present, and potential future.

• What do quantitative analysts do?

A quantitative analyst is an expert in designing, developing, and implementing algorithms to answer research questions. They use quantitative research methods to help companies make appropriate business and financial decisions.

The primary responsibility of a quantitative analyst is to apply quantitative methods to identify opportunities and evaluate risks.

Quantitative analysts are important to staff in any business because:

They manage portfolio risks

They test a new trading strategy

They program and implement a new trading strategy

They improve signals used to evaluate trade ideas

• Understanding quantitative analysis

Analysts use quantitative analysis to analyze a business's past, present, and future. You can also use quantitative analysis to determine the progress of your business.

State governments also use quantitative analysis to make monetary and other economic policy decisions. It is used in the financial services industry to analyze investment opportunities. For example, a business owner can use quantitative analysis to determine when to sell or purchase securities based on macroeconomic conditions.

Quantitative analysis versus qualitative analysis

If you are pursuing a career in research or business analysis, it is essential to understand the two concepts—quantitative and qualitative analysis.

Quantitative analysis, at a very basic level, relies on using numbers and discrete values collected from the research. In contrast, qualitative analysis relies on content (e.g., language or text data) that either can’t be expressed in numbers or doesn’t have sufficient scale to be counted or coded.

A business owner wanting to better understand their business might use a representative quantitative sample of customers to generate insight by completing a questionnaire. A website owner could analyze quantitative metrics associated with their website to understand which aspects of the site are working well and which elements need to be optimized. These include the length of visit, number of links clicked, and areas of the site visited.

Various measures could be correlated by sales (or other outcomes) to determine the UX and marketing strategy linked to the site.

Businesses might use qualitative analysis to get a greater depth of understanding or look at the ‘why’ behind the ‘what.’ For example, they might ask customers, who gave a low quantitative score for a provided product, why they gave that rating and how they might improve the said product.

• Advantages of quantitative research

Quantitative research, done right, can help drive a business's success and generate a general understanding of key business metrics and customer behavior, wants, and needs. Quantitative research should be considered for the following reasons: 

It is efficient and fast

An experienced quantitative researcher can complete the reporting and analysis phase efficiently and quickly with a defined reporting structure and outputs while taking some time to define and structure questions (versus unstructured qualitative data ).

It is objective and requires limited interpretation

Quantitative research relies on standardized statistical processes and rules to answer research questions. If performed correctly, data generated from small sample groups can be extrapolated to represent the views of larger populations.

It is focused

Owing to its structure, the goals of quantitative research are determined at the beginning of the study, forcing researchers to clearly understand and define the objectives of their studies.

• Disadvantages of quantitative research

It’s only appropriate in certain cases

This method is only relevant when data can be captured and reflected in numbers. It cannot be used in situations where data is non-numerical, e.g., long-form verbal or textual responses that are not easily coded down into numerical responses.

It’s challenging to analyze the data collected

When quantitative research is collected, it can be difficult to make sense of the numbers without knowing statistical methods. Knowledge of research methods and data analytic techniques is essential for drawing conclusions about the study questions. These programs and methods take time to learn and can be time-consuming and complicated.

• What are the limitations of quantitative research?

Requires vast resources

This method requires a considerable investment of time, energy, and finance. One needs to prepare and structure questions, test their understanding and relevance, and determine how to distribute them to the respondents. Some respondents may expect payment or incentives to respond to the questions (this may be in the form of entry into a prize draw.)

Requires many respondents

Quantitative research generally requires access to (relative to other methods) large samples to ensure inferences made from the research are robust and reliable. Finding this audience, especially where the incidence is low can be both time-consuming and expensive.

Research is limited in its scope

What quantitative research can explore is limited due to the need to agree on the specific questions to be asked and analyzed versus qualitative research. The latter doesn’t define specific numbers and forms of questions in advance.

Why is it called quantitative research?

It is called quantitative research because it involves the use of ‘quantities’ of things—things that can be expressed in numbers or measured.

What does quantitative research answer?

Quantitative research answers questions measuring value or size, which can be expressed in numbers. It answers questions such as how many, how much, and how often.

For example, you can study the number of individuals who wish to study at American universities and their traits. Questions can include how many come from low, medium, or high socio-economic brackets, how many want to study law versus humanities, and what proportion feel excited versus anxious about the prospect of undertaking higher education.

Get started today

Go from raw data to valuable insights with a flexible research platform

Editor’s picks

Last updated: 21 December 2023

Last updated: 16 December 2023

Last updated: 6 October 2023

Last updated: 25 November 2023

Last updated: 12 May 2023

Last updated: 15 February 2024

Last updated: 11 March 2024

Last updated: 12 December 2023

Last updated: 18 May 2023

Last updated: 6 March 2024

Last updated: 10 April 2023

Last updated: 20 December 2023

Latest articles

Related topics, log in or sign up.

Get started for free

Quantitative Data Analysis 101

The lingo, methods and techniques, explained simply.

By: Derek Jansen (MBA)  and Kerryn Warren (PhD) | December 2020

Quantitative data analysis is one of those things that often strikes fear in students. It’s totally understandable – quantitative analysis is a complex topic, full of daunting lingo , like medians, modes, correlation and regression. Suddenly we’re all wishing we’d paid a little more attention in math class…

The good news is that while quantitative data analysis is a mammoth topic, gaining a working understanding of the basics isn’t that hard , even for those of us who avoid numbers and math . In this post, we’ll break quantitative analysis down into simple , bite-sized chunks so you can approach your research with confidence.

Overview: Quantitative Data Analysis 101

• What (exactly) is quantitative data analysis?
• When to use quantitative analysis
• How quantitative analysis works

The two “branches” of quantitative analysis

• Descriptive statistics 101
• Inferential statistics 101
• How to choose the right quantitative methods
• Recap & summary

What is quantitative data analysis?

Despite being a mouthful, quantitative data analysis simply means analysing data that is numbers-based – or data that can be easily “converted” into numbers without losing any meaning.

For example, category-based variables like gender, ethnicity, or native language could all be “converted” into numbers without losing meaning – for example, English could equal 1, French 2, etc.

This contrasts against qualitative data analysis, where the focus is on words, phrases and expressions that can’t be reduced to numbers. If you’re interested in learning about qualitative analysis, check out our post and video here .

What is quantitative analysis used for?

Quantitative analysis is generally used for three purposes.

• Firstly, it’s used to measure differences between groups . For example, the popularity of different clothing colours or brands.
• Secondly, it’s used to assess relationships between variables . For example, the relationship between weather temperature and voter turnout.
• And third, it’s used to test hypotheses in a scientifically rigorous way. For example, a hypothesis about the impact of a certain vaccine.

Again, this contrasts with qualitative analysis , which can be used to analyse people’s perceptions and feelings about an event or situation. In other words, things that can’t be reduced to numbers.

How does quantitative analysis work?

Well, since quantitative data analysis is all about analysing numbers , it’s no surprise that it involves statistics . Statistical analysis methods form the engine that powers quantitative analysis, and these methods can vary from pretty basic calculations (for example, averages and medians) to more sophisticated analyses (for example, correlations and regressions).

Sounds like gibberish? Don’t worry. We’ll explain all of that in this post. Importantly, you don’t need to be a statistician or math wiz to pull off a good quantitative analysis. We’ll break down all the technical mumbo jumbo in this post.

Need a helping hand?

As I mentioned, quantitative analysis is powered by statistical analysis methods . There are two main “branches” of statistical methods that are used – descriptive statistics and inferential statistics . In your research, you might only use descriptive statistics, or you might use a mix of both , depending on what you’re trying to figure out. In other words, depending on your research questions, aims and objectives . I’ll explain how to choose your methods later.

So, what are descriptive and inferential statistics?

Well, before I can explain that, we need to take a quick detour to explain some lingo. To understand the difference between these two branches of statistics, you need to understand two important words. These words are population and sample .

First up, population . In statistics, the population is the entire group of people (or animals or organisations or whatever) that you’re interested in researching. For example, if you were interested in researching Tesla owners in the US, then the population would be all Tesla owners in the US.

However, it’s extremely unlikely that you’re going to be able to interview or survey every single Tesla owner in the US. Realistically, you’ll likely only get access to a few hundred, or maybe a few thousand owners using an online survey. This smaller group of accessible people whose data you actually collect is called your sample .

So, to recap – the population is the entire group of people you’re interested in, and the sample is the subset of the population that you can actually get access to. In other words, the population is the full chocolate cake , whereas the sample is a slice of that cake.

So, why is this sample-population thing important?

Well, descriptive statistics focus on describing the sample , while inferential statistics aim to make predictions about the population, based on the findings within the sample. In other words, we use one group of statistical methods – descriptive statistics – to investigate the slice of cake, and another group of methods – inferential statistics – to draw conclusions about the entire cake. There I go with the cake analogy again…

With that out the way, let’s take a closer look at each of these branches in more detail.

Branch 1: Descriptive Statistics

Descriptive statistics serve a simple but critically important role in your research – to describe your data set – hence the name. In other words, they help you understand the details of your sample . Unlike inferential statistics (which we’ll get to soon), descriptive statistics don’t aim to make inferences or predictions about the entire population – they’re purely interested in the details of your specific sample .

When you’re writing up your analysis, descriptive statistics are the first set of stats you’ll cover, before moving on to inferential statistics. But, that said, depending on your research objectives and research questions , they may be the only type of statistics you use. We’ll explore that a little later.

So, what kind of statistics are usually covered in this section?

Some common statistical tests used in this branch include the following:

• Mean – this is simply the mathematical average of a range of numbers.
• Median – this is the midpoint in a range of numbers when the numbers are arranged in numerical order. If the data set makes up an odd number, then the median is the number right in the middle of the set. If the data set makes up an even number, then the median is the midpoint between the two middle numbers.
• Mode – this is simply the most commonly occurring number in the data set.
• In cases where most of the numbers are quite close to the average, the standard deviation will be relatively low.
• Conversely, in cases where the numbers are scattered all over the place, the standard deviation will be relatively high.
• Skewness . As the name suggests, skewness indicates how symmetrical a range of numbers is. In other words, do they tend to cluster into a smooth bell curve shape in the middle of the graph, or do they skew to the left or right?

Feeling a bit confused? Let’s look at a practical example using a small data set.

On the left-hand side is the data set. This details the bodyweight of a sample of 10 people. On the right-hand side, we have the descriptive statistics. Let’s take a look at each of them.

First, we can see that the mean weight is 72.4 kilograms. In other words, the average weight across the sample is 72.4 kilograms. Straightforward.

Next, we can see that the median is very similar to the mean (the average). This suggests that this data set has a reasonably symmetrical distribution (in other words, a relatively smooth, centred distribution of weights, clustered towards the centre).

In terms of the mode , there is no mode in this data set. This is because each number is present only once and so there cannot be a “most common number”. If there were two people who were both 65 kilograms, for example, then the mode would be 65.

Next up is the standard deviation . 10.6 indicates that there’s quite a wide spread of numbers. We can see this quite easily by looking at the numbers themselves, which range from 55 to 90, which is quite a stretch from the mean of 72.4.

And lastly, the skewness of -0.2 tells us that the data is very slightly negatively skewed. This makes sense since the mean and the median are slightly different.

As you can see, these descriptive statistics give us some useful insight into the data set. Of course, this is a very small data set (only 10 records), so we can’t read into these statistics too much. Also, keep in mind that this is not a list of all possible descriptive statistics – just the most common ones.

But why do all of these numbers matter?

While these descriptive statistics are all fairly basic, they’re important for a few reasons:

• Firstly, they help you get both a macro and micro-level view of your data. In other words, they help you understand both the big picture and the finer details.
• Secondly, they help you spot potential errors in the data – for example, if an average is way higher than you’d expect, or responses to a question are highly varied, this can act as a warning sign that you need to double-check the data.
• And lastly, these descriptive statistics help inform which inferential statistical techniques you can use, as those techniques depend on the skewness (in other words, the symmetry and normality) of the data.

Simply put, descriptive statistics are really important , even though the statistical techniques used are fairly basic. All too often at Grad Coach, we see students skimming over the descriptives in their eagerness to get to the more exciting inferential methods, and then landing up with some very flawed results.

Don’t be a sucker – give your descriptive statistics the love and attention they deserve!

Branch 2: Inferential Statistics

As I mentioned, while descriptive statistics are all about the details of your specific data set – your sample – inferential statistics aim to make inferences about the population . In other words, you’ll use inferential statistics to make predictions about what you’d expect to find in the full population.

What kind of predictions, you ask? Well, there are two common types of predictions that researchers try to make using inferential stats:

• Firstly, predictions about differences between groups – for example, height differences between children grouped by their favourite meal or gender.
• And secondly, relationships between variables – for example, the relationship between body weight and the number of hours a week a person does yoga.

In other words, inferential statistics (when done correctly), allow you to connect the dots and make predictions about what you expect to see in the real world population, based on what you observe in your sample data. For this reason, inferential statistics are used for hypothesis testing – in other words, to test hypotheses that predict changes or differences.

Of course, when you’re working with inferential statistics, the composition of your sample is really important. In other words, if your sample doesn’t accurately represent the population you’re researching, then your findings won’t necessarily be very useful.

For example, if your population of interest is a mix of 50% male and 50% female , but your sample is 80% male , you can’t make inferences about the population based on your sample, since it’s not representative. This area of statistics is called sampling, but we won’t go down that rabbit hole here (it’s a deep one!) – we’ll save that for another post .

What statistics are usually used in this branch?

There are many, many different statistical analysis methods within the inferential branch and it’d be impossible for us to discuss them all here. So we’ll just take a look at some of the most common inferential statistical methods so that you have a solid starting point.

First up are T-Tests . T-tests compare the means (the averages) of two groups of data to assess whether they’re statistically significantly different. In other words, do they have significantly different means, standard deviations and skewness.

This type of testing is very useful for understanding just how similar or different two groups of data are. For example, you might want to compare the mean blood pressure between two groups of people – one that has taken a new medication and one that hasn’t – to assess whether they are significantly different.

Kicking things up a level, we have ANOVA, which stands for “analysis of variance”. This test is similar to a T-test in that it compares the means of various groups, but ANOVA allows you to analyse multiple groups , not just two groups So it’s basically a t-test on steroids…

Next, we have correlation analysis . This type of analysis assesses the relationship between two variables. In other words, if one variable increases, does the other variable also increase, decrease or stay the same. For example, if the average temperature goes up, do average ice creams sales increase too? We’d expect some sort of relationship between these two variables intuitively , but correlation analysis allows us to measure that relationship scientifically .

Lastly, we have regression analysis – this is quite similar to correlation in that it assesses the relationship between variables, but it goes a step further to understand cause and effect between variables, not just whether they move together. In other words, does the one variable actually cause the other one to move, or do they just happen to move together naturally thanks to another force? Just because two variables correlate doesn’t necessarily mean that one causes the other.

Stats overload…

I hear you. To make this all a little more tangible, let’s take a look at an example of a correlation in action.

Here’s a scatter plot demonstrating the correlation (relationship) between weight and height. Intuitively, we’d expect there to be some relationship between these two variables, which is what we see in this scatter plot. In other words, the results tend to cluster together in a diagonal line from bottom left to top right.

As I mentioned, these are are just a handful of inferential techniques – there are many, many more. Importantly, each statistical method has its own assumptions and limitations.

For example, some methods only work with normally distributed (parametric) data, while other methods are designed specifically for non-parametric data. And that’s exactly why descriptive statistics are so important – they’re the first step to knowing which inferential techniques you can and can’t use.

How to choose the right analysis method

To choose the right statistical methods, you need to think about two important factors :

• The type of quantitative data you have (specifically, level of measurement and the shape of the data). And,
• Your research questions and hypotheses

Let’s take a closer look at each of these.

Factor 1 – Data type

The first thing you need to consider is the type of data you’ve collected (or the type of data you will collect). By data types, I’m referring to the four levels of measurement – namely, nominal, ordinal, interval and ratio. If you’re not familiar with this lingo, check out the video below.

Why does this matter?

Well, because different statistical methods and techniques require different types of data. This is one of the “assumptions” I mentioned earlier – every method has its assumptions regarding the type of data.

For example, some techniques work with categorical data (for example, yes/no type questions, or gender or ethnicity), while others work with continuous numerical data (for example, age, weight or income) – and, of course, some work with multiple data types.

If you try to use a statistical method that doesn’t support the data type you have, your results will be largely meaningless . So, make sure that you have a clear understanding of what types of data you’ve collected (or will collect). Once you have this, you can then check which statistical methods would support your data types here .

If you haven’t collected your data yet, you can work in reverse and look at which statistical method would give you the most useful insights, and then design your data collection strategy to collect the correct data types.

Another important factor to consider is the shape of your data . Specifically, does it have a normal distribution (in other words, is it a bell-shaped curve, centred in the middle) or is it very skewed to the left or the right? Again, different statistical techniques work for different shapes of data – some are designed for symmetrical data while others are designed for skewed data.

This is another reminder of why descriptive statistics are so important – they tell you all about the shape of your data.

Factor 2: Your research questions

The next thing you need to consider is your specific research questions, as well as your hypotheses (if you have some). The nature of your research questions and research hypotheses will heavily influence which statistical methods and techniques you should use.

If you’re just interested in understanding the attributes of your sample (as opposed to the entire population), then descriptive statistics are probably all you need. For example, if you just want to assess the means (averages) and medians (centre points) of variables in a group of people.

On the other hand, if you aim to understand differences between groups or relationships between variables and to infer or predict outcomes in the population, then you’ll likely need both descriptive statistics and inferential statistics.

So, it’s really important to get very clear about your research aims and research questions, as well your hypotheses – before you start looking at which statistical techniques to use.

Never shoehorn a specific statistical technique into your research just because you like it or have some experience with it. Your choice of methods must align with all the factors we’ve covered here.

Time to recap…

You’re still with me? That’s impressive. We’ve covered a lot of ground here, so let’s recap on the key points:

• Quantitative data analysis is all about  analysing number-based data  (which includes categorical and numerical data) using various statistical techniques.
• The two main  branches  of statistics are  descriptive statistics  and  inferential statistics . Descriptives describe your sample, whereas inferentials make predictions about what you’ll find in the population.
• Common  descriptive statistical methods include  mean  (average),  median , standard  deviation  and  skewness .
• Common  inferential statistical methods include  t-tests ,  ANOVA ,  correlation  and  regression  analysis.
• To choose the right statistical methods and techniques, you need to consider the  type of data you’re working with , as well as your  research questions  and hypotheses.

Psst... there’s more!

This post was based on one of our popular Research Bootcamps . If you're working on a research project, you'll definitely want to check this out ...

You Might Also Like:

74 Comments

Hi, I have read your article. Such a brilliant post you have created.

Thank you for the feedback. Good luck with your quantitative analysis.

Thank you so much.

Thank you so much. I learnt much well. I love your summaries of the concepts. I had love you to explain how to input data using SPSS

Amazing and simple way of breaking down quantitative methods.

This is beautiful….especially for non-statisticians. I have skimmed through but I wish to read again. and please include me in other articles of the same nature when you do post. I am interested. I am sure, I could easily learn from you and get off the fear that I have had in the past. Thank you sincerely.

Send me every new information you might have.

i need every new information

Thank you for the blog. It is quite informative. Dr Peter Nemaenzhe PhD

It is wonderful. l’ve understood some of the concepts in a more compréhensive manner

Your article is so good! However, I am still a bit lost. I am doing a secondary research on Gun control in the US and increase in crime rates and I am not sure which analysis method I should use?

Based on the given learning points, this is inferential analysis, thus, use ‘t-tests, ANOVA, correlation and regression analysis’

Well explained notes. Am an MPH student and currently working on my thesis proposal, this has really helped me understand some of the things I didn’t know.

I like your page..helpful

wonderful i got my concept crystal clear. thankyou!!

This is really helpful , thank you

Thank you so much this helped

Wonderfully explained

thank u so much, it was so informative

THANKYOU, this was very informative and very helpful

This is great GRADACOACH I am not a statistician but I require more of this in my thesis

Include me in your posts.

This is so great and fully useful. I would like to thank you again and again.

Glad to read this article. I’ve read lot of articles but this article is clear on all concepts. Thanks for sharing.

Thank you so much. This is a very good foundation and intro into quantitative data analysis. Appreciate!

You have a very impressive, simple but concise explanation of data analysis for Quantitative Research here. This is a God-send link for me to appreciate research more. Thank you so much!

Avery good presentation followed by the write up. yes you simplified statistics to make sense even to a layman like me. Thank so much keep it up. The presenter did ell too. i would like more of this for Qualitative and exhaust more of the test example like the Anova.

This is a very helpful article, couldn’t have been clearer. Thank you.

Awesome and phenomenal information.Well done

The video with the accompanying article is super helpful to demystify this topic. Very well done. Thank you so much.

thank you so much, your presentation helped me a lot

I don’t know how should I express that ur article is saviour for me 🥺😍

It is well defined information and thanks for sharing. It helps me a lot in understanding the statistical data.

I gain a lot and thanks for sharing brilliant ideas, so wish to be linked on your email update.

Very helpful and clear .Thank you Gradcoach.

Thank for sharing this article, well organized and information presented are very clear.

VERY INTERESTING AND SUPPORTIVE TO NEW RESEARCHERS LIKE ME. AT LEAST SOME BASICS ABOUT QUANTITATIVE.

An outstanding, well explained and helpful article. This will help me so much with my data analysis for my research project. Thank you!

wow this has just simplified everything i was scared of how i am gonna analyse my data but thanks to you i will be able to do so

simple and constant direction to research. thanks

This is helpful

Great writing!! Comprehensive and very helpful.

Do you provide any assistance for other steps of research methodology like making research problem testing hypothesis report and thesis writing?

Thank you so much for such useful article!

Amazing article. So nicely explained. Wow

Very insightfull. Thanks

I am doing a quality improvement project to determine if the implementation of a protocol will change prescribing habits. Would this be a t-test?

The is a very helpful blog, however, I’m still not sure how to analyze my data collected. I’m doing a research on “Free Education at the University of Guyana”

tnx. fruitful blog!

So I am writing exams and would like to know how do establish which method of data analysis to use from the below research questions: I am a bit lost as to how I determine the data analysis method from the research questions.

Do female employees report higher job satisfaction than male employees with similar job descriptions across the South African telecommunications sector? – I though that maybe Chi Square could be used here. – Is there a gender difference in talented employees’ actual turnover decisions across the South African telecommunications sector? T-tests or Correlation in this one. – Is there a gender difference in the cost of actual turnover decisions across the South African telecommunications sector? T-tests or Correlation in this one. – What practical recommendations can be made to the management of South African telecommunications companies on leveraging gender to mitigate employee turnover decisions?

Your assistance will be appreciated if I could get a response as early as possible tomorrow

This was quite helpful. Thank you so much.

wow I got a lot from this article, thank you very much, keep it up

Thanks for yhe guidance. Can you send me this guidance on my email? To enable offline reading?

Thank you very much, this service is very helpful.

Every novice researcher needs to read this article as it puts things so clear and easy to follow. Its been very helpful.

Wonderful!!!! you explained everything in a way that anyone can learn. Thank you!!

I really enjoyed reading though this. Very easy to follow. Thank you

Many thanks for your useful lecture, I would be really appreciated if you could possibly share with me the PPT of presentation related to Data type?

Thank you very much for sharing, I got much from this article

This is a very informative write-up. Kindly include me in your latest posts.

Very interesting mostly for social scientists

Thank you so much, very helpfull

You’re welcome 🙂

woow, its great, its very informative and well understood because of your way of writing like teaching in front of me in simple languages.

I have been struggling to understand a lot of these concepts. Thank you for the informative piece which is written with outstanding clarity.

very informative article. Easy to understand

Beautiful read, much needed.

Always greet intro and summary. I learn so much from GradCoach

Quite informative. Simple and clear summary.

I thoroughly enjoyed reading your informative and inspiring piece. Your profound insights into this topic truly provide a better understanding of its complexity. I agree with the points you raised, especially when you delved into the specifics of the article. In my opinion, that aspect is often overlooked and deserves further attention.

Absolutely!!! Thank you

Thank you very much for this post. It made me to understand how to do my data analysis.

Submit a Comment Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

• Print Friendly

Learn / Guides / Quantitative data analysis guide

Back to guides

The ultimate guide to quantitative data analysis

Numbers help us make sense of the world. We collect quantitative data on our speed and distance as we drive, the number of hours we spend on our cell phones, and how much we save at the grocery store.

Our businesses run on numbers, too. We spend hours poring over key performance indicators (KPIs) like lead-to-client conversions, net profit margins, and bounce and churn rates.

But all of this quantitative data can feel overwhelming and confusing. Lists and spreadsheets of numbers don’t tell you much on their own—you have to conduct quantitative data analysis to understand them and make informed decisions.

Last updated

Reading time.

This guide explains what quantitative data analysis is and why it’s important, and gives you a four-step process to conduct a quantitative data analysis, so you know exactly what’s happening in your business and what your users need .

Collect quantitative customer data with Hotjar

Use Hotjar’s tools to gather the customer insights you need to make quantitative data analysis a breeze.

What is quantitative data analysis? 

Quantitative data analysis is the process of analyzing and interpreting numerical data. It helps you make sense of information by identifying patterns, trends, and relationships between variables through mathematical calculations and statistical tests. 

With quantitative data analysis, you turn spreadsheets of individual data points into meaningful insights to drive informed decisions. Columns of numbers from an experiment or survey transform into useful insights—like which marketing campaign asset your average customer prefers or which website factors are most closely connected to your bounce rate. 

Without analytics, data is just noise. Analyzing data helps you make decisions which are informed and free from bias.

What quantitative data analysis is not

But as powerful as quantitative data analysis is, it’s not without its limitations. It only gives you the what, not the why . For example, it can tell you how many website visitors or conversions you have on an average day, but it can’t tell you why users visited your site or made a purchase.

For the why behind user behavior, you need qualitative data analysis , a process for making sense of qualitative research like open-ended survey responses, interview clips, or behavioral observations. By analyzing non-numerical data, you gain useful contextual insights to shape your strategy, product, and messaging. 

Quantitative data analysis vs. qualitative data analysis 

Let’s take an even deeper dive into the differences between quantitative data analysis and qualitative data analysis to explore what they do and when you need them.

The bottom line: quantitative data analysis and qualitative data analysis are complementary processes. They work hand-in-hand to tell you what’s happening in your business and why.  

💡 Pro tip: easily toggle between quantitative and qualitative data analysis with Hotjar Funnels . 

The Funnels tool helps you visualize quantitative metrics like drop-off and conversion rates in your sales or conversion funnel to understand when and where users leave your website. You can break down your data even further to compare conversion performance by user segment.

Spot a potential issue? A single click takes you to relevant session recordings , where you see user behaviors like mouse movements, scrolls, and clicks. With this qualitative data to provide context, you'll better understand what you need to optimize to streamline the user experience (UX) and increase conversions .

Hotjar Funnels lets you quickly explore the story behind the quantitative data

4 benefits of quantitative data analysis

There’s a reason product, web design, and marketing teams take time to analyze metrics: the process pays off big time. 

Four major benefits of quantitative data analysis include:

1. Make confident decisions 

With quantitative data analysis, you know you’ve got data-driven insights to back up your decisions . For example, if you launch a concept testing survey to gauge user reactions to a new logo design, and 92% of users rate it ‘very good’—you'll feel certain when you give the designer the green light. 

Since you’re relying less on intuition and more on facts, you reduce the risks of making the wrong decision. (You’ll also find it way easier to get buy-in from team members and stakeholders for your next proposed project. 🙌)

2. Reduce costs

By crunching the numbers, you can spot opportunities to reduce spend . For example, if an ad campaign has lower-than-average click-through rates , you might decide to cut your losses and invest your budget elsewhere. 

Or, by analyzing ecommerce metrics , like website traffic by source, you may find you’re getting very little return on investment from a certain social media channel—and scale back spending in that area.

3. Personalize the user experience

Quantitative data analysis helps you map the customer journey , so you get a better sense of customers’ demographics, what page elements they interact with on your site, and where they drop off or convert . 

These insights let you better personalize your website, product, or communication, so you can segment ads, emails, and website content for specific user personas or target groups.

4. Improve user satisfaction and delight

Quantitative data analysis lets you see where your website or product is doing well—and where it falls short for your users . For example, you might see stellar results from KPIs like time on page, but conversion rates for that page are low. 

These quantitative insights encourage you to dive deeper into qualitative data to see why that’s happening—looking for moments of confusion or frustration on session recordings, for example—so you can make adjustments and optimize your conversions by improving customer satisfaction and delight.

💡Pro tip: use Net Promoter Score® (NPS) surveys to capture quantifiable customer satisfaction data that’s easy for you to analyze and interpret. 

With an NPS tool like Hotjar, you can create an on-page survey to ask users how likely they are to recommend you to others on a scale from 0 to 10. (And for added context, you can ask follow-up questions about why customers selected the rating they did—rich qualitative data is always a bonus!)

Hotjar graphs your quantitative NPS data to show changes over time

4 steps to effective quantitative data analysis 

Quantitative data analysis sounds way more intimidating than it actually is. Here’s how to make sense of your company’s numbers in just four steps:

1. Collect data

Before you can actually start the analysis process, you need data to analyze. This involves conducting quantitative research and collecting numerical data from various sources, including: 

Interviews or focus groups 

Website analytics

Observations, from tools like heatmaps or session recordings

Questionnaires, like surveys or on-page feedback widgets

Just ensure the questions you ask in your surveys are close-ended questions—providing respondents with select choices to choose from instead of open-ended questions that allow for free responses.

Hotjar’s pricing plans survey template provides close-ended questions

 2. Clean data

Once you’ve collected your data, it’s time to clean it up. Look through your results to find errors, duplicates, and omissions. Keep an eye out for outliers, too. Outliers are data points that differ significantly from the rest of the set—and they can skew your results if you don’t remove them.

By taking the time to clean your data set, you ensure your data is accurate, consistent, and relevant before it’s time to analyze. 

3. Analyze and interpret data

At this point, your data’s all cleaned up and ready for the main event. This step involves crunching the numbers to find patterns and trends via mathematical and statistical methods. 

Two main branches of quantitative data analysis exist: 

Descriptive analysis : methods to summarize or describe attributes of your data set. For example, you may calculate key stats like distribution and frequency, or mean, median, and mode.

Inferential analysis : methods that let you draw conclusions from statistics—like analyzing the relationship between variables or making predictions. These methods include t-tests, cross-tabulation, and factor analysis. (For more detailed explanations and how-tos, head to our guide on quantitative data analysis methods.)

Then, interpret your data to determine the best course of action. What does the data suggest you do ? For example, if your analysis shows a strong correlation between email open rate and time sent, you may explore optimal send times for each user segment.

4. Visualize and share data

Once you’ve analyzed and interpreted your data, create easy-to-read, engaging data visualizations—like charts, graphs, and tables—to present your results to team members and stakeholders. Data visualizations highlight similarities and differences between data sets and show the relationships between variables.

Software can do this part for you. For example, the Hotjar Dashboard shows all of your key metrics in one place—and automatically creates bar graphs to show how your top pages’ performance compares. And with just one click, you can navigate to the Trends tool to analyze product metrics for different segments on a single chart. 

Hotjar Trends lets you compare metrics across segments

Discover rich user insights with quantitative data analysis

Conducting quantitative data analysis takes a little bit of time and know-how, but it’s much more manageable than you might think. 

By choosing the right methods and following clear steps, you gain insights into product performance and customer experience —and you’ll be well on your way to making better decisions and creating more customer satisfaction and loyalty.

FAQs about quantitative data analysis

What is quantitative data analysis.

Quantitative data analysis is the process of making sense of numerical data through mathematical calculations and statistical tests. It helps you identify patterns, relationships, and trends to make better decisions.

How is quantitative data analysis different from qualitative data analysis?

Quantitative and qualitative data analysis are both essential processes for making sense of quantitative and qualitative research .

Quantitative data analysis helps you summarize and interpret numerical results from close-ended questions to understand what is happening. Qualitative data analysis helps you summarize and interpret non-numerical results, like opinions or behavior, to understand why the numbers look like they do.

 If you want to make strong data-driven decisions, you need both.

What are some benefits of quantitative data analysis?

Quantitative data analysis turns numbers into rich insights. Some benefits of this process include: 

Making more confident decisions

Identifying ways to cut costs

Personalizing the user experience

Improving customer satisfaction

What methods can I use to analyze quantitative data?

Quantitative data analysis has two branches: descriptive statistics and inferential statistics. 

Descriptive statistics provide a snapshot of the data’s features by calculating measures like mean, median, and mode. 

Inferential statistics , as the name implies, involves making inferences about what the data means. Dozens of methods exist for this branch of quantitative data analysis, but three commonly used techniques are: 

Cross tabulation

Factor analysis

• Reviews / Why join our community?
• For companies
• Frequently asked questions

Quantitative Research

What is Quantitative Research?

Quantitative research is the methodology which researchers use to test theories about people’s attitudes and behaviors based on numerical and statistical evidence. Researchers sample a large number of users (e.g., through surveys) to indirectly obtain measurable, bias-free data about users in relevant situations.

“Quantification clarifies issues which qualitative analysis leaves fuzzy. It is more readily contestable and likely to be contested. It sharpens scholarly discussion, sparks off rival hypotheses, and contributes to the dynamics of the research process.” — Angus Maddison, Notable scholar of quantitative macro-economic history

• Transcript loading…

See how quantitative research helps reveal cold, hard facts about users which you can interpret and use to improve your designs.

Use Quantitative Research to Find Mathematical Facts about Users

Quantitative research is a subset of user experience (UX) research . Unlike its softer, more individual-oriented “counterpart”, qualitative research , quantitative research means you collect statistical/numerical data to draw generalized conclusions about users’ attitudes and behaviors . Compare and contrast quantitative with qualitative research, below:

Qualitative Research

You Aim to Determine

The “what”, “where” & “when” of the users’ needs & problems – to help keep your project’s focus on track during development

The “why” – to get behind how users approach their problems in their world

Highly structured (e.g., surveys) – to gather data about what users do & find patterns in large user groups

Loosely structured (e.g., contextual inquiries) – to learn why users behave how they do & explore their opinions

Number of Representative Users

Ideally 30+

Often around 5

Level of Contact with Users

Less direct & more remote (e.g., analytics)

More direct & less remote (e.g., usability testing to examine users’ stress levels when they use your design)

Statistically

Reliable – if you have enough test users

Less reliable, with need for great care with handling non-numerical data (e.g., opinions), as your own opinions might influence findings

Quantitative research is often best done from early on in projects since it helps teams to optimally direct product development and avoid costly design mistakes later. As you typically get user data from a distance—i.e., without close physical contact with users—also applying qualitative research will help you investigate why users think and feel the ways they do. Indeed, in an iterative design process quantitative research helps you test the assumptions you and your design team develop from your qualitative research. Regardless of the method you use, with proper care you can gather objective and unbiased data – information which you can complement with qualitative approaches to build a fuller understanding of your target users. From there, you can work towards firmer conclusions and drive your design process towards a more realistic picture of how target users will ultimately receive your product.

Quantitative analysis helps you test your assumptions and establish clearer views of your users in their various contexts.

Quantitative Research Methods You Can Use to Guide Optimal Designs

There are many quantitative research methods, and they help uncover different types of information on users. Some methods, such as A/B testing, are typically done on finished products, while others such as surveys could be done throughout a project’s design process. Here are some of the most helpful methods:

A/B testing – You test two or more versions of your design on users to find the most effective. Each variation differs by just one feature and may or may not affect how users respond. A/B testing is especially valuable for testing assumptions you’ve drawn from qualitative research. The only potential concerns here are scale—in that you’ll typically need to conduct it on thousands of users—and arguably more complexity in terms of considering the statistical significance involved.

Analytics – With tools such as Google Analytics, you measure metrics (e.g., page views, click-through rates) to build a picture (e.g., “How many users take how long to complete a task?”).

Desirability Studies – You measure an aspect of your product (e.g., aesthetic appeal) by typically showing it to participants and asking them to select from a menu of descriptive words. Their responses can reveal powerful insights (e.g., 78% associate the product/brand with “fashionable”).

Surveys and Questionnaires – When you ask for many users’ opinions, you will gain massive amounts of information. Keep in mind that you’ll have data about what users say they do, as opposed to insights into what they do . You can get more reliable results if you incentivize your participants well and use the right format.

Tree Testing – You remove the user interface so users must navigate the site and complete tasks using links alone. This helps you see if an issue is related to the user interface or information architecture.

Another powerful benefit of conducting quantitative research is that you can keep your stakeholders’ support with hard facts and statistics about your design’s performance—which can show what works well and what needs improvement—and prove a good return on investment. You can also produce reports to check statistics against different versions of your product and your competitors’ products.

Most quantitative research methods are relatively cheap. Since no single research method can help you answer all your questions, it’s vital to judge which method suits your project at the time/stage. Remember, it’s best to spend appropriately on a combination of quantitative and qualitative research from early on in development. Design improvements can be costly, and so you can estimate the value of implementing changes when you get the statistics to suggest that these changes will improve usability. Overall, you want to gather measurements objectively, where your personality, presence and theories won’t create bias.

Learn More about Quantitative Research

Take our User Research course to see how to get the most from quantitative research.

See how quantitative research methods fit into your design research landscape .

This insightful piece shows the value of pairing quantitative with qualitative research .

Find helpful tips on combining quantitative research methods in mixed methods research .

Questions related to Quantitative Research

Qualitative and quantitative research differ primarily in the data they produce. Quantitative research yields numerical data to test hypotheses and quantify patterns. It's precise and generalizable. Qualitative research, on the other hand, generates non-numerical data and explores meanings, interpretations, and deeper insights. Watch our video featuring Professor Alan Dix on different types of research methods.

This video elucidates the nuances and applications of both research types in the design field.

In quantitative research, determining a good sample size is crucial for the reliability of the results. William Hudson, CEO of Syntagm, emphasizes the importance of statistical significance with an example in our video. 

He illustrates that even with varying results between design choices, we need to discern whether the differences are statistically significant or products of chance. This ensures the validity of the results, allowing for more accurate interpretations. Statistical tools like chi-square tests can aid in analyzing the results effectively. To delve deeper into these concepts, take William Hudson’s Data-Driven Design: Quantitative UX Research Course . 

Quantitative research is crucial as it provides precise, numerical data that allows for high levels of statistical inference. Our video from William Hudson, CEO of Syntagm, highlights the importance of analytics in examining existing solutions. 

Quantitative methods, like analytics and A/B testing, are pivotal for identifying areas for improvement, understanding user behaviors, and optimizing user experiences based on solid, empirical evidence. This empirical nature ensures that the insights derived are reliable, allowing for practical improvements and innovations. Perhaps most importantly, numerical data is useful to secure stakeholder buy-in and defend design decisions and proposals. Explore this approach in our Data-Driven Design: Quantitative Research for UX Research course and learn from William Hudson’s detailed explanations of when and why to use analytics in the research process.

After establishing initial requirements, statistical data is crucial for informed decisions through quantitative research. William Hudson, CEO of Syntagm, sheds light on the role of quantitative research throughout a typical project lifecycle in this video:

 During the analysis and design phases, quantitative research helps validate user requirements and understand user behaviors. Surveys and analytics are standard tools, offering insights into user preferences and design efficacy. Quantitative research can also be used in early design testing, allowing for optimal design modifications based on user interactions and feedback, and it’s fundamental for A/B and multivariate testing once live solutions are available.

To write a compelling quantitative research question:

Create clear, concise, and unambiguous questions that address one aspect at a time.

Use common, short terms and provide explanations for unusual words.

Avoid leading, compound, and overlapping queries and ensure that questions are not vague or broad.

According to our video by William Hudson, CEO of Syntagm, quality and respondent understanding are vital in forming good questions. 

He emphasizes the importance of addressing specific aspects and avoiding intimidating and confusing elements, such as extensive question grids or ranking questions, to ensure participant engagement and accurate responses. For more insights, see the article Writing Good Questions for Surveys .

Survey research is typically quantitative, collecting numerical data and statistical analysis to make generalizable conclusions. However, it can also have qualitative elements, mainly when it includes open-ended questions, allowing for expressive responses. Our video featuring the CEO of Syntagm, William Hudson, provides in-depth insights into when and how to effectively utilize surveys in the product or service lifecycle, focusing on user satisfaction and potential improvements.

He emphasizes the importance of surveys in triangulating data to back up qualitative research findings, ensuring we have a complete understanding of the user's requirements and preferences.

Descriptive research focuses on describing the subject being studied and getting answers to questions like what, where, when, and who of the research question. However, it doesn’t include the answers to the underlying reasons, or the “why” behind the answers obtained from the research. We can use both f qualitative and quantitative methods to conduct descriptive research. Descriptive research does not describe the methods, but rather the data gathered through the research (regardless of the methods used).

When we use quantitative research and gather numerical data, we can use statistical analysis to understand relationships between different variables. Here’s William Hudson, CEO of Syntagm with more on correlation and how we can apply tests such as Pearson’s r and Spearman Rank Coefficient to our data.

This helps interpret phenomena such as user experience by analyzing session lengths and conversion values, revealing whether variables like time spent on a page affect checkout values, for example.

Random Sampling: Each individual in the population has an equitable opportunity to be chosen, which minimizes biases and simplifies analysis.

Systematic Sampling: Selecting every k-th item from a list after a random start. It's simpler and faster than random sampling when dealing with large populations.

Stratified Sampling: Segregate the population into subgroups or strata according to comparable characteristics. Then, samples are taken randomly from each stratum.

Cluster Sampling: Divide the population into clusters and choose a random sample.

Multistage Sampling: Various sampling techniques are used at different stages to collect detailed information from diverse populations.

Convenience Sampling: The researcher selects the sample based on availability and willingness to participate, which may only represent part of the population.

Quota Sampling: Segment the population into subgroups, and samples are non-randomly selected to fulfill a predetermined quota from each subset.

These are just a few techniques, and choosing the right one depends on your research question, discipline, resource availability, and the level of accuracy required. In quantitative research, there isn't a one-size-fits-all sampling technique; choosing a method that aligns with your research goals and population is critical. However, a well-planned strategy is essential to avoid wasting resources and time, as highlighted in our video featuring William Hudson, CEO of Syntagm.

He emphasizes the importance of recruiting participants meticulously, ensuring their engagement and the quality of their responses. Accurate and thoughtful participant responses are crucial for obtaining reliable results. William also sheds light on dealing with failing participants and scrutinizing response quality to refine the outcomes.

The 4 types of quantitative research are Descriptive, Correlational, Causal-Comparative/Quasi-Experimental, and Experimental Research. Descriptive research aims to depict ‘what exists’ clearly and precisely. Correlational research examines relationships between variables. Causal-comparative research investigates the cause-effect relationship between variables. Experimental research explores causal relationships by manipulating independent variables. To gain deeper insights into quantitative research methods in UX, consider enrolling in our Data-Driven Design: Quantitative Research for UX course.

The strength of quantitative research is its ability to provide precise numerical data for analyzing target variables.This allows for generalized conclusions and predictions about future occurrences, proving invaluable in various fields, including user experience. William Hudson, CEO of Syntagm, discusses the role of surveys, analytics, and testing in providing objective insights in our video on quantitative research methods, highlighting the significance of structured methodologies in eliciting reliable results.

To master quantitative research methods, enroll in our comprehensive course, Data-Driven Design: Quantitative Research for UX . 

This course empowers you to leverage quantitative data to make informed design decisions, providing a deep dive into methods like surveys and analytics. Whether you’re a novice or a seasoned professional, this course at Interaction Design Foundation offers valuable insights and practical knowledge, ensuring you acquire the skills necessary to excel in user experience research. Explore our diverse topics to elevate your understanding of quantitative research methods.

Literature on Quantitative Research

Here’s the entire UX literature on Quantitative Research by the Interaction Design Foundation, collated in one place:

Learn more about Quantitative Research

Take a deep dive into Quantitative Research with our course User Research – Methods and Best Practices .

How do you plan to design a product or service that your users will love , if you don't know what they want in the first place? As a user experience designer, you shouldn't leave it to chance to design something outstanding; you should make the effort to understand your users and build on that knowledge from the outset. User research is the way to do this, and it can therefore be thought of as the largest part of user experience design .

In fact, user research is often the first step of a UX design process—after all, you cannot begin to design a product or service without first understanding what your users want! As you gain the skills required, and learn about the best practices in user research, you’ll get first-hand knowledge of your users and be able to design the optimal product—one that’s truly relevant for your users and, subsequently, outperforms your competitors’ .

This course will give you insights into the most essential qualitative research methods around and will teach you how to put them into practice in your design work. You’ll also have the opportunity to embark on three practical projects where you can apply what you’ve learned to carry out user research in the real world . You’ll learn details about how to plan user research projects and fit them into your own work processes in a way that maximizes the impact your research can have on your designs. On top of that, you’ll gain practice with different methods that will help you analyze the results of your research and communicate your findings to your clients and stakeholders—workshops, user journeys and personas, just to name a few!

By the end of the course, you’ll have not only a Course Certificate but also three case studies to add to your portfolio. And remember, a portfolio with engaging case studies is invaluable if you are looking to break into a career in UX design or user research!

We believe you should learn from the best, so we’ve gathered a team of experts to help teach this course alongside our own course instructors. That means you’ll meet a new instructor in each of the lessons on research methods who is an expert in their field—we hope you enjoy what they have in store for you!

All open-source articles on Quantitative Research

Best practices for qualitative user research.

• 3 years ago

Card Sorting

Understand the User’s Perspective through Research for Mobile UX

• 10 mths ago

7 Simple Ways to Get Better Results From Ethnographic Research

Question Everything

Tree Testing

Adding Quality to Your Design Research with an SSQS Checklist

• 8 years ago

How to Fit Quantitative Research into the Project Lifecycle

Why and When to Use Surveys

Correlation in User Experience

First-Click Testing

What to Test

Rating Scales in UX Research: The Ultimate Guide

Open Access—Link to us!

We believe in Open Access and the  democratization of knowledge . Unfortunately, world-class educational materials such as this page are normally hidden behind paywalls or in expensive textbooks.

If you want this to change , cite this page , link to us, or join us to help us democratize design knowledge !

Privacy Settings

Our digital services use necessary tracking technologies, including third-party cookies, for security, functionality, and to uphold user rights. Optional cookies offer enhanced features, and analytics.

Experience the full potential of our site that remembers your preferences and supports secure sign-in.

Governs the storage of data necessary for maintaining website security, user authentication, and fraud prevention mechanisms.

Enhanced Functionality

Saves your settings and preferences, like your location, for a more personalized experience.

Referral Program

We use cookies to enable our referral program, giving you and your friends discounts.

Error Reporting

We share user ID with Bugsnag and NewRelic to help us track errors and fix issues.

Optimize your experience by allowing us to monitor site usage. You’ll enjoy a smoother, more personalized journey without compromising your privacy.

Analytics Storage

Collects anonymous data on how you navigate and interact, helping us make informed improvements.

Differentiates real visitors from automated bots, ensuring accurate usage data and improving your website experience.

Lets us tailor your digital ads to match your interests, making them more relevant and useful to you.

Advertising Storage

Stores information for better-targeted advertising, enhancing your online ad experience.

Personalization Storage

Permits storing data to personalize content and ads across Google services based on user behavior, enhancing overall user experience.

Advertising Personalization

Allows for content and ad personalization across Google services based on user behavior. This consent enhances user experiences.

Enables personalizing ads based on user data and interactions, allowing for more relevant advertising experiences across Google services.

Receive more relevant advertisements by sharing your interests and behavior with our trusted advertising partners.

Enables better ad targeting and measurement on Meta platforms, making ads you see more relevant.

Allows for improved ad effectiveness and measurement through Meta’s Conversions API, ensuring privacy-compliant data sharing.

LinkedIn Insights

Tracks conversions, retargeting, and web analytics for LinkedIn ad campaigns, enhancing ad relevance and performance.

LinkedIn CAPI

Enhances LinkedIn advertising through server-side event tracking, offering more accurate measurement and personalization.

Google Ads Tag

Tracks ad performance and user engagement, helping deliver ads that are most useful to you.

Share Knowledge, Get Respect!

or copy link

Cite according to academic standards

Simply copy and paste the text below into your bibliographic reference list, onto your blog, or anywhere else. You can also just hyperlink to this page.

New to UX Design? We’re Giving You a Free ebook!

Download our free ebook The Basics of User Experience Design to learn about core concepts of UX design.

In 9 chapters, we’ll cover: conducting user interviews, design thinking, interaction design, mobile UX design, usability, UX research, and many more!

• Search Search Please fill out this field.
• Understanding QA
• Quantitative vs. Qualitative Analysis

Example of Quantitative Analysis in Finance

Drawbacks and limitations of quantitative analaysis, using quantitative finance outside of finance, the bottom line.

• Quantitative Analysis

Quantitative Analysis (QA): What It Is and How It's Used in Finance

Ariel Courage is an experienced editor, researcher, and former fact-checker. She has performed editing and fact-checking work for several leading finance publications, including The Motley Fool and Passport to Wall Street.

Investopedia / Hilary Allison

Quantitative analysis (QA) refers to methods used to understand the behavior of financial markets and make more informed investment or trading decisions. It involves the use of mathematical and statistical techniques to analyze financial data. For instance, by examining past stock prices, earnings reports, and other information, quantitative analysts, often called “ quants ,” aim to forecast where the market is headed.

Unlike fundamental analysis that might focus on a company's management team or industry conditions, quantitative analysis relies chiefly on crunching numbers and complex computations to derive actionable insights.

Quantitative analysis can be a powerful tool, especially in modern markets where data is abundant and computational tools are advanced, enabling a more precise examination of the financial landscape. However, many also believe that the raw numbers produced by quantitative analysis should be combined with the more in-depth understanding and nuance afforded by qualitative analysis .

Key Takeaways

• Quantitative analysis (QA) is a set of techniques that use mathematical and statistical modeling, measurement, and research to understand behavior.
• Quantitative analysis presents financial information in terms of a numerical value.
• It's used for the evaluation of financial instruments and for predicting real-world events such as changes in GDP.
• While powerful, quantitative analysis has some drawbacks that can be supplemented with qualitative analysis.

Understanding Quantitative Analysis

Quantitative analysis (QA) in finance refers to the use of mathematical and statistical techniques to analyze financial & economic data and make trading, investing, and risk management decisions.

QA starts with data collection, where quants gather a vast amount of financial data that might affect the market. This data can include anything from stock prices and company earnings to economic indicators like inflation or unemployment rates. They then use various mathematical models and statistical techniques to analyze this data, looking for trends, patterns, and potential investment opportunities. The outcome of this analysis can help investors decide where to allocate their resources to maximize returns or minimize risks.

Some key aspects of quantitative analysis in finance include:

• Statistical analysis - this aspect of quantitative analysis involves examining data to identify trends and relationships, build predictive models, and make forecasts. Techniques used can include regression analysis , which helps in understanding relationships between variables; time series analysis , which looks at data points collected or recorded at a specific time; and Monte Carlo simulations , a mathematical technique that allows you to account for uncertainty in your analyses and forecasts. Through statistical analysis, quants can uncover insights that may not be immediately apparent, helping investors and financial analysts make more informed decisions.
• Algorithmic trading - this entails using computer algorithms to automate the trading process. Algorithms can be programmed to carry out trades based on a variety of factors such as timing, price movements, liquidity changes, and other market signals. High-frequency trading (HFT), a type of algorithmic trading, involves making a large number of trades within fractions of a second to capitalize on small price movements. This automated approach to trading can lead to more efficient and often profitable trading strategies.
• Risk modeling - risk is an inherent part of financial markets. Risk modeling involves creating mathematical models to measure and quantify various risk exposures within a portfolio. Methods used in risk modeling include Value-at-Risk (VaR) models, scenario analysis , and stress testing . These tools help in understanding the potential downside and uncertainties associated with different investment scenarios, aiding in better risk management and mitigation strategies.
• Derivatives pricing - derivatives are financial contracts whose value is derived from other underlying assets like stocks or bonds. Derivatives pricing involves creating mathematical models to evaluate these contracts and determine their fair prices and risk profiles. A well-known model used in this domain is the Black-Scholes model , which helps in pricing options contracts . Accurate derivatives pricing is crucial for investors and traders to make sound financial decisions regarding buying, selling, or hedging with derivatives.
• Portfolio optimization - This is about constructing a portfolio in such a way that it yields the highest possible expected return for a given level of risk. Techniques like Modern Portfolio Theory (MPT) are employed to find the optimal allocation of assets within a portfolio. By analyzing various asset classes and their expected returns, risks, and correlations, quants can suggest the best mix of investments to achieve specific financial goals while minimizing risk.

The overall goal is to use data, math, statistics, and software to make more informed financial decisions, automate processes, and ultimately generate greater risk-adjusted returns.

Quantitative analysis is widely used in central banking, algorithmic trading, hedge fund management, and investment banking activities. Quantitative analysts, employ advanced skills in programming, statistics, calculus, linear algebra etc. to execute quantitative analysis.

Quantitative Analysis vs. Qualitative Analysis

Quantitative analysis relies heavily on numerical data and mathematical models to make decisions regarding investments and financial strategies. It focuses on the measurable, objective data that can be gathered about a company or a financial instrument.

But analysts also evaluate information that is not easily quantifiable or reduced to numeric values to get a better picture of a company's performance. This important qualitative data can include reputation, regulatory insights, or employee morale. Qualitative analysis thus focuses more on understanding the underlying qualities of a company or a financial instrument, which may not be immediately quantifiable.

Quantitative isn't the opposite of qualitative analysis. They're different and often complementary philosophies. They each provide useful information for informed decisions. When used together. better decisions can be made than using either one in isolation.

Some common uses of qualitative analysis include:

• Management Evaluation: Qualitative analysis is often better at evaluating a company's management team, their experience, and their ability to lead the company toward growth. While quantifiable metrics are useful, they often cannot capture the full picture of management's ability and potential. For example, the leadership skills, vision, and corporate culture instilled by management are intangible factors that can significantly impact a company's success, yet are difficult to measure with numbers alone.
• Industry Analysis: It also includes an analysis of the industry in which the company operates, the competition, and market conditions. For instance, it can explore how changes in technology or societal behaviors could impact the industry. Qualitative approaches can also better identify barriers to entry or exit, which can affect the level of competition and profitability within the industry.
• Brand Value and Company Reputation: The reputation of a company, its brand value, and customer loyalty are also significant factors considered in qualitative analysis. Understanding how consumers perceive the brand, their level of trust, and satisfaction can provide insights into customer loyalty and the potential for sustained revenue. This can be done through focus groups, surveys, or interviews.
• Regulatory Environment: The regulatory environment, potential legal issues, and other external factors that could impact a company are also analyzed qualitatively. Evaluating a company's compliance with relevant laws, regulations, and industry standards to ascertain its legal standing and the potential risk of legal issues. In addition, understanding a company's ethical practices and social responsibility initiatives, that can influence its relationship with stakeholders and the community at large.

Suppose you are interested in investing in a particular company, XYZ Inc. One way to evaluate its potential as an investment is by analyzing its past financial performance using quantitative analysis. Let's say, over the past five years, XYZ Inc. has been growing its revenue at an average rate of 8% per year. You decide to use regression analysis to forecast its future revenue growth. Regression analysis is a statistical method used to examine the relationship between variables.

After collecting the necessary data, you run a simple linear regression with the year as the independent variable and the revenue as the dependent variable. The output gives you a regression equation, let's say, R e v e n u e = 100 + 8 ( Y e a r ) Revenue=100+8(Year) R e v e n u e = 100 + 8 ( Y e a r ) . This equation suggests that for every year, the revenue of XYZ Inc. increases by $8 million, starting from a base of $100 million. This quantitative insight could be instrumental in helping you decide whether XYZ Inc. represents a good investment opportunity based on its historical revenue growth trend.

However, while you can quantify revenue growth for the firm and make predictions, the reasons for why may not be apparent from quantitative number crunching.

Augmenting with Qualitative Analysis

Qualitative analysis can provide a more nuanced understanding of XYZ Inc.'s potential. You decide to delve into the company's management and industry reputation. Through interviews, reviews, and industry reports, you find that the management team at XYZ Inc. is highly regarded with a track record of successful ventures. Moreover, the company has a strong brand value and a loyal customer base.

Additionally, you assess the industry in which XYZ Inc. operates and find it to be stable with a steady demand for the products that XYZ Inc. offers. The regulatory environment is also favorable, and the company has a good relationship with the local communities in which it operates.

By analyzing these qualitative factors, you obtain a more comprehensive understanding of the company's operational environment, the competence of its management team, and its reputation in the market. This qualitative insight complements the quantitative analysis, providing you with a well-rounded view of XYZ Inc.'s investment potential.

Combining both quantitative and qualitative analyses could therefore lead to a more informed investment decision regarding XYZ Inc.

Quantitative analysis, while powerful, comes with certain limitations:

• Data Dependency: Quantitative analysis is heavily dependent on the quality and availability of numerical data. If the data is inaccurate, outdated, or incomplete, the analysis and the subsequent conclusions drawn will be flawed. As they say, 'garbage-in, garbage-out'.
• Complexity: The methods and models used in quantitative analysis can be very complex, requiring a high level of expertise to develop, interpret, and act upon. This complexity can also make it difficult to communicate findings to individuals who lack a quantitative background.
• Lack of Subjectivity: Quantitative analysis often overlooks qualitative factors like management quality, brand reputation, and other subjective factors that can significantly affect a company's performance or a financial instrument's value. In other words, you may have the 'what' without the 'why' or 'how.' Qualitative analysis can augment this blind spot.
• Assumption-based Modeling: Many quantitative models are built on assumptions that may not hold true in real-world situations. For example, assumptions about normal distribution of returns or constant volatility may not reflect actual market conditions.
• Over-reliance on Historical Data: Quantitative analysis often relies heavily on historical data to make predictions about the future. However, past performance is not always indicative of future results, especially in rapidly changing markets or unforeseen situations like economic crises.
• Inability to Capture Human Emotion and Behavior: Markets are often influenced by human emotions and behaviors which can be erratic and hard to predict. Quantitative analysis, being number-driven, struggles to properly account for these human factors.
• Cost and Time Intensive: Developing accurate and reliable quantitative models can be time-consuming and expensive. It requires skilled personnel, sophisticated software tools, and often, extensive computational resources.
• Overfitting: There's a risk of overfitting , where a model might perform exceedingly well on past data but fails to predict future outcomes accurately because it's too tailored to past events.
• Lack of Flexibility: Quantitative models may lack the flexibility to adapt to new information or changing market conditions quickly, which can lead to outdated or incorrect analysis.
• Model Risk: There's inherent model risk involved where the model itself may have flaws or errors that can lead to incorrect analysis and potentially significant financial losses.

Understanding these drawbacks is crucial for analysts and decision-makers to interpret quantitative analysis results accurately and to balance them with qualitative insights for more holistic decision-making.

Quantitative analysis is a versatile tool that extends beyond the realm of finance into a variety of fields. In the domain of social sciences, for instance, it's used to analyze behavioral patterns, social trends, and the impact of policies on different demographics. Researchers employ statistical models to examine large datasets, enabling them to identify correlations, causations, and trends that can provide a deeper understanding of human behaviors and societal dynamics. Similarly, in the field of public policy, quantitative analysis plays a crucial role in evaluating the effectiveness of different policies, analyzing economic indicators, and forecasting the potential impacts of policy changes. By providing a method to measure and analyze data, it aids policymakers in making informed decisions based on empirical evidence.

In the arena of healthcare, quantitative analysis is employed for clinical trials, genetic research, and epidemiological studies to name a few areas. It assists in analyzing patient data, evaluating treatment outcomes, and understanding disease spread and its determinants. Meanwhile, in engineering and manufacturing, it's used to optimize processes, improve quality control, and enhance operational efficiency. By analyzing data related to production processes, material properties, and operational performance, engineers can identify bottlenecks, optimize workflows, and ensure the reliability and quality of products. Additionally, in the field of marketing, quantitative analysis is fundamental for market segmentation, advertising effectiveness, and consumer satisfaction studies. It helps marketers understand consumer preferences, the impact of advertising campaigns, and the market potential for new products. Through these diverse applications, quantitative analysis serves as a bedrock for data-driven decision-making, enabling professionals across different fields to derive actionable insights from complex data.

What Is Quantitative Analysis Used for in Finance?

Quantitative analysis is used by governments, investors, and businesses (in areas such as finance, project management, production planning, and marketing) to study a certain situation or event, measure it, predict outcomes, and thus help in decision-making. In finance, it's widely used for assessing investment opportunities and risks. For instance, before venturing into investments, analysts rely on quantitative analysis to understand the performance metrics of different financial instruments such as stocks, bonds, and derivatives. By delving into historical data and employing mathematical and statistical models, they can forecast potential future performance and evaluate the underlying risks. This practice isn't just confined to individual assets; it's also essential for portfolio management. By examining the relationships between different assets and assessing their risk and return profiles, investors can construct portfolios that are optimized for the highest possible returns for a given level of risk.

What Kind of Education Do You Need to Be a Quant?

Individuals pursuing a career in quantitative analysis usually have a strong educational background in quantitative fields like mathematics, statistics, computer science, finance, economics, or engineering. Advanced degrees (Master’s or Ph.D.) in quantitative disciplines are often preferred, and additional coursework or certifications in finance and programming can also be beneficial.

What Is the Difference Between Quantitative Analysis and Fundamental Analysis?

While both rely on the use of math and numbers, fundamental analysis takes a broader approach by examining the intrinsic value of a security. It dives into a company's financial statements, industry position, the competence of the management team, and the economic environment in which it operates. By evaluating factors like earnings, dividends, and the financial health of a company, fundamental analysts aim to ascertain the true value of a security and whether it is undervalued or overvalued in the market. This form of analysis is more holistic and requires a deep understanding of the company and the industry in which it operates.

How Does Artificial Intelligence (AI) Influence Quantitative Analysis?

Quantitative analysis often intersects with machine learning (ML) and other forms of artificial intelligence (AI). ML and AI can be employed to develop predictive models and algorithms based on the quantitative data. These technologies can automate the analysis process, handle large datasets, and uncover complex patterns or trends that might be difficult to detect through traditional quantitative methods.

Quantitative analysis is a mathematical approach that collects and evaluates measurable and verifiable data in order to evaluate performance, make better decisions, and predict trends. Unlike qualitative analysis, quantitative analysis uses numerical data to provide an explanation of "what" happened, but not "why" those events occurred.

DeFusco, R. A., McLeavey, D. W., Pinto, J. E., Runkle, D. E., & Anson, M. J. (2015). Quantitative investment analysis . John Wiley & Sons.

University of Sydney. " On Becoming a Quant ," Page 1

Linsmeier, Thomas J., and Neil D. Pearson. " Value at risk ." Financial analysts journal 56, no. 2 (2000): 47-67.

Fischer, Black, and Myron Scholes, " The Pricing of Options and Corporate Liabilities ." Journal of Political Economy, vol. 81, no. 3, 1974, pp. 637-654.

Francis, J. C., & Kim, D. (2013). Modern portfolio theory: Foundations, analysis, and new developments . John Wiley & Sons.

Kaczynski, D., Salmona, M., & Smith, T. (2014). " Qualitative research in finance ." Australian Journal of Management , 39 (1), 127-135.

• Terms of Service
• Editorial Policy
• Privacy Policy
• Your Privacy Choices

Regression Analysis

Regression analysis is a quantitative research method which is used when the study involves modelling and analysing several variables, where the relationship includes a dependent variable and one or more independent variables. In simple terms, regression analysis is a quantitative method used to test the nature of relationships between a dependent variable and one or more independent variables.

The basic form of regression models includes unknown parameters (β), independent variables (X), and the dependent variable (Y).

Regression model, basically, specifies the relation of dependent variable (Y) to a function combination of independent variables (X) and unknown parameters (β)

                                    Y  ≈  f (X, β)   

Regression equation can be used to predict the values of ‘y’, if the value of ‘x’ is given, and both ‘y’ and ‘x’ are the two sets of measures of a sample size of ‘n’. The formulae for regression equation would be

Do not be intimidated by visual complexity of correlation and regression formulae above. You don’t have to apply the formula manually, and correlation and regression analyses can be run with the application of popular analytical software such as Microsoft Excel, Microsoft Access, SPSS and others.

Linear regression analysis is based on the following set of assumptions:

1. Assumption of linearity . There is a linear relationship between dependent and independent variables.

2. Assumption of homoscedasticity . Data values for dependent and independent variables have equal variances.

3. Assumption of absence of collinearity or multicollinearity . There is no correlation between two or more independent variables.

4. Assumption of normal distribution . The data for the independent variables and dependent variable are normally distributed

My e-book,  The Ultimate Guide to Writing a Dissertation in Business Studies: a step by step assistance  offers practical assistance to complete a dissertation with minimum or no stress. The e-book covers all stages of writing a dissertation starting from the selection to the research area to submitting the completed version of the work within the deadline. John Dudovskiy

Qualitative vs Quantitative Research Methods & Data Analysis

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Learn about our Editorial Process

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

What is the difference between quantitative and qualitative?

The main difference between quantitative and qualitative research is the type of data they collect and analyze.

Quantitative research collects numerical data and analyzes it using statistical methods. The aim is to produce objective, empirical data that can be measured and expressed in numerical terms. Quantitative research is often used to test hypotheses, identify patterns, and make predictions.

Qualitative research , on the other hand, collects non-numerical data such as words, images, and sounds. The focus is on exploring subjective experiences, opinions, and attitudes, often through observation and interviews.

Qualitative research aims to produce rich and detailed descriptions of the phenomenon being studied, and to uncover new insights and meanings.

Quantitative data is information about quantities, and therefore numbers, and qualitative data is descriptive, and regards phenomenon which can be observed but not measured, such as language.

What Is Qualitative Research?

Qualitative research is the process of collecting, analyzing, and interpreting non-numerical data, such as language. Qualitative research can be used to understand how an individual subjectively perceives and gives meaning to their social reality.

Qualitative data is non-numerical data, such as text, video, photographs, or audio recordings. This type of data can be collected using diary accounts or in-depth interviews and analyzed using grounded theory or thematic analysis.

Qualitative research is multimethod in focus, involving an interpretive, naturalistic approach to its subject matter. This means that qualitative researchers study things in their natural settings, attempting to make sense of, or interpret, phenomena in terms of the meanings people bring to them. Denzin and Lincoln (1994, p. 2)

Interest in qualitative data came about as the result of the dissatisfaction of some psychologists (e.g., Carl Rogers) with the scientific study of psychologists such as behaviorists (e.g., Skinner ).

Since psychologists study people, the traditional approach to science is not seen as an appropriate way of carrying out research since it fails to capture the totality of human experience and the essence of being human.  Exploring participants’ experiences is known as a phenomenological approach (re: Humanism ).

Qualitative research is primarily concerned with meaning, subjectivity, and lived experience. The goal is to understand the quality and texture of people’s experiences, how they make sense of them, and the implications for their lives.

Qualitative research aims to understand the social reality of individuals, groups, and cultures as nearly as possible as participants feel or live it. Thus, people and groups are studied in their natural setting.

Some examples of qualitative research questions are provided, such as what an experience feels like, how people talk about something, how they make sense of an experience, and how events unfold for people.

Research following a qualitative approach is exploratory and seeks to explain ‘how’ and ‘why’ a particular phenomenon, or behavior, operates as it does in a particular context. It can be used to generate hypotheses and theories from the data.

Qualitative Methods

There are different types of qualitative research methods, including diary accounts, in-depth interviews , documents, focus groups , case study research , and ethnography.

The results of qualitative methods provide a deep understanding of how people perceive their social realities and in consequence, how they act within the social world.

The researcher has several methods for collecting empirical materials, ranging from the interview to direct observation, to the analysis of artifacts, documents, and cultural records, to the use of visual materials or personal experience. Denzin and Lincoln (1994, p. 14)

Here are some examples of qualitative data:

Interview transcripts : Verbatim records of what participants said during an interview or focus group. They allow researchers to identify common themes and patterns, and draw conclusions based on the data. Interview transcripts can also be useful in providing direct quotes and examples to support research findings.

Observations : The researcher typically takes detailed notes on what they observe, including any contextual information, nonverbal cues, or other relevant details. The resulting observational data can be analyzed to gain insights into social phenomena, such as human behavior, social interactions, and cultural practices.

Unstructured interviews : generate qualitative data through the use of open questions.  This allows the respondent to talk in some depth, choosing their own words.  This helps the researcher develop a real sense of a person’s understanding of a situation.

Diaries or journals : Written accounts of personal experiences or reflections.

Notice that qualitative data could be much more than just words or text. Photographs, videos, sound recordings, and so on, can be considered qualitative data. Visual data can be used to understand behaviors, environments, and social interactions.

Qualitative Data Analysis

Qualitative research is endlessly creative and interpretive. The researcher does not just leave the field with mountains of empirical data and then easily write up his or her findings.

Qualitative interpretations are constructed, and various techniques can be used to make sense of the data, such as content analysis, grounded theory (Glaser & Strauss, 1967), thematic analysis (Braun & Clarke, 2006), or discourse analysis.

For example, thematic analysis is a qualitative approach that involves identifying implicit or explicit ideas within the data. Themes will often emerge once the data has been coded.

Key Features

• Events can be understood adequately only if they are seen in context. Therefore, a qualitative researcher immerses her/himself in the field, in natural surroundings. The contexts of inquiry are not contrived; they are natural. Nothing is predefined or taken for granted.
• Qualitative researchers want those who are studied to speak for themselves, to provide their perspectives in words and other actions. Therefore, qualitative research is an interactive process in which the persons studied teach the researcher about their lives.
• The qualitative researcher is an integral part of the data; without the active participation of the researcher, no data exists.
• The study’s design evolves during the research and can be adjusted or changed as it progresses. For the qualitative researcher, there is no single reality. It is subjective and exists only in reference to the observer.
• The theory is data-driven and emerges as part of the research process, evolving from the data as they are collected.

Limitations of Qualitative Research

• Because of the time and costs involved, qualitative designs do not generally draw samples from large-scale data sets.
• The problem of adequate validity or reliability is a major criticism. Because of the subjective nature of qualitative data and its origin in single contexts, it is difficult to apply conventional standards of reliability and validity. For example, because of the central role played by the researcher in the generation of data, it is not possible to replicate qualitative studies.
• Also, contexts, situations, events, conditions, and interactions cannot be replicated to any extent, nor can generalizations be made to a wider context than the one studied with confidence.
• The time required for data collection, analysis, and interpretation is lengthy. Analysis of qualitative data is difficult, and expert knowledge of an area is necessary to interpret qualitative data. Great care must be taken when doing so, for example, looking for mental illness symptoms.

Advantages of Qualitative Research

• Because of close researcher involvement, the researcher gains an insider’s view of the field. This allows the researcher to find issues that are often missed (such as subtleties and complexities) by the scientific, more positivistic inquiries.
• Qualitative descriptions can be important in suggesting possible relationships, causes, effects, and dynamic processes.
• Qualitative analysis allows for ambiguities/contradictions in the data, which reflect social reality (Denscombe, 2010).
• Qualitative research uses a descriptive, narrative style; this research might be of particular benefit to the practitioner as she or he could turn to qualitative reports to examine forms of knowledge that might otherwise be unavailable, thereby gaining new insight.

What Is Quantitative Research?

Quantitative research involves the process of objectively collecting and analyzing numerical data to describe, predict, or control variables of interest.

The goals of quantitative research are to test causal relationships between variables , make predictions, and generalize results to wider populations.

Quantitative researchers aim to establish general laws of behavior and phenomenon across different settings/contexts. Research is used to test a theory and ultimately support or reject it.

Quantitative Methods

Experiments typically yield quantitative data, as they are concerned with measuring things.  However, other research methods, such as controlled observations and questionnaires , can produce both quantitative information.

For example, a rating scale or closed questions on a questionnaire would generate quantitative data as these produce either numerical data or data that can be put into categories (e.g., “yes,” “no” answers).

Experimental methods limit how research participants react to and express appropriate social behavior.

Findings are, therefore, likely to be context-bound and simply a reflection of the assumptions that the researcher brings to the investigation.

There are numerous examples of quantitative data in psychological research, including mental health. Here are a few examples:

Another example is the Experience in Close Relationships Scale (ECR), a self-report questionnaire widely used to assess adult attachment styles .

The ECR provides quantitative data that can be used to assess attachment styles and predict relationship outcomes.

Neuroimaging data : Neuroimaging techniques, such as MRI and fMRI, provide quantitative data on brain structure and function.

This data can be analyzed to identify brain regions involved in specific mental processes or disorders.

For example, the Beck Depression Inventory (BDI) is a clinician-administered questionnaire widely used to assess the severity of depressive symptoms in individuals.

The BDI consists of 21 questions, each scored on a scale of 0 to 3, with higher scores indicating more severe depressive symptoms. 

Quantitative Data Analysis

Statistics help us turn quantitative data into useful information to help with decision-making. We can use statistics to summarize our data, describing patterns, relationships, and connections. Statistics can be descriptive or inferential.

Descriptive statistics help us to summarize our data. In contrast, inferential statistics are used to identify statistically significant differences between groups of data (such as intervention and control groups in a randomized control study).

• Quantitative researchers try to control extraneous variables by conducting their studies in the lab.
• The research aims for objectivity (i.e., without bias) and is separated from the data.
• The design of the study is determined before it begins.
• For the quantitative researcher, the reality is objective, exists separately from the researcher, and can be seen by anyone.
• Research is used to test a theory and ultimately support or reject it.

Limitations of Quantitative Research

• Context: Quantitative experiments do not take place in natural settings. In addition, they do not allow participants to explain their choices or the meaning of the questions they may have for those participants (Carr, 1994).
• Researcher expertise: Poor knowledge of the application of statistical analysis may negatively affect analysis and subsequent interpretation (Black, 1999).
• Variability of data quantity: Large sample sizes are needed for more accurate analysis. Small-scale quantitative studies may be less reliable because of the low quantity of data (Denscombe, 2010). This also affects the ability to generalize study findings to wider populations.
• Confirmation bias: The researcher might miss observing phenomena because of focus on theory or hypothesis testing rather than on the theory of hypothesis generation.

Advantages of Quantitative Research

• Scientific objectivity: Quantitative data can be interpreted with statistical analysis, and since statistics are based on the principles of mathematics, the quantitative approach is viewed as scientifically objective and rational (Carr, 1994; Denscombe, 2010).
• Useful for testing and validating already constructed theories.
• Rapid analysis: Sophisticated software removes much of the need for prolonged data analysis, especially with large volumes of data involved (Antonius, 2003).
• Replication: Quantitative data is based on measured values and can be checked by others because numerical data is less open to ambiguities of interpretation.
• Hypotheses can also be tested because of statistical analysis (Antonius, 2003).

Antonius, R. (2003). Interpreting quantitative data with SPSS . Sage.

Black, T. R. (1999). Doing quantitative research in the social sciences: An integrated approach to research design, measurement and statistics . Sage.

Braun, V. & Clarke, V. (2006). Using thematic analysis in psychology . Qualitative Research in Psychology , 3, 77–101.

Carr, L. T. (1994). The strengths and weaknesses of quantitative and qualitative research : what method for nursing? Journal of advanced nursing, 20(4) , 716-721.

Denscombe, M. (2010). The Good Research Guide: for small-scale social research. McGraw Hill.

Denzin, N., & Lincoln. Y. (1994). Handbook of Qualitative Research. Thousand Oaks, CA, US: Sage Publications Inc.

Glaser, B. G., Strauss, A. L., & Strutzel, E. (1968). The discovery of grounded theory; strategies for qualitative research. Nursing research, 17(4) , 364.

Minichiello, V. (1990). In-Depth Interviewing: Researching People. Longman Cheshire.

Punch, K. (1998). Introduction to Social Research: Quantitative and Qualitative Approaches. London: Sage

Further Information

• Designing qualitative research
• Methods of data collection and analysis
• Introduction to quantitative and qualitative research
• Checklists for improving rigour in qualitative research: a case of the tail wagging the dog?
• Qualitative research in health care: Analysing qualitative data
• Qualitative data analysis: the framework approach
• Using the framework method for the analysis of
• Qualitative data in multi-disciplinary health research
• Content Analysis
• Grounded Theory
• Thematic Analysis

• Skip to main content
• Skip to primary sidebar
• Skip to footer
• QuestionPro

• Solutions Industries Gaming Automotive Sports and events Education Government Travel & Hospitality Financial Services Healthcare Cannabis Technology Use Case NPS+ Communities Audience Contactless surveys Mobile LivePolls Member Experience GDPR Positive People Science 360 Feedback Surveys
• Resources Blog eBooks Survey Templates Case Studies Training Help center

Home Market Research

10 Quantitative Data Analysis Software for Every Data Scientist

Are you curious about digging into data but not sure where to start? Don’t worry; we’ve got you covered! As a data scientist, you know that having the right tools can make all the difference in the world. When it comes to analyzing quantitative data, having the right quantitative data analysis software can help you extract insights faster and more efficiently. 

From spotting trends to making smart decisions, quantitative analysis helps us unlock the secrets hidden within our data and chart a course for success.

In this blog post, we’ll introduce you to 10 quantitative data analysis software that every data scientist should know about.

What is Quantitative Data Analysis?

Quantitative data analysis refers to the process of systematically examining numerical data to uncover patterns, trends, relationships, and insights. 

Unlike analyzing qualitative data, which deals with non-numeric data like text or images, quantitative research focuses on data that can be quantified, measured, and analyzed using statistical techniques.

What is Quantitative Data Analysis Software?

Quantitative data analysis software refers to specialized computer programs or tools designed to assist researchers, analysts, and professionals in analyzing numerical data. 

These software applications are tailored to handle quantitative data, which consists of measurable quantities, counts, or numerical values. Quantitative data analysis software provides a range of features and functionalities to manage, analyze, visualize, and interpret numerical data effectively.

Key features commonly found in quantitative data analysis software include:

• Data Import and Management: Capability to import data from various sources such as spreadsheets, databases, text files, or online repositories. 
• Descriptive Statistics: Tools for computing basic descriptive statistics such as measures of central tendency (e.g., mean, median, mode) and measures of dispersion (e.g., standard deviation, variance).
• Data Visualization: Functionality to create visual representations of data through charts, graphs, histograms, scatter plots, or heatmaps. 
• Statistical Analysis: Support for conducting a wide range of statistical tests and analyses to explore relationships, test hypotheses, make predictions, or infer population characteristics from sample data.
• Advanced Analytics: Advanced analytical techniques for more complex data exploration and modeling, such as cluster analysis, principal component analysis (PCA), time series analysis, survival analysis, and structural equation modeling (SEM).
• Automation and Reproducibility: Features for automating analysis workflows, scripting repetitive tasks, and ensuring the reproducibility of results. 
• Reporting and Collaboration: Tools for generating customizable reports, summaries, or presentations to communicate analysis results effectively to stakeholders.

Benefits of Quantitative Data Analysis

Quantitative data analysis offers numerous benefits across various fields and disciplines. Here are some of the key advantages:

Making Confident Decisions

Quantitative data analysis provides solid, evidence-based insights that support decision-making. By relying on data rather than intuition, you can reduce the risk of making incorrect decisions. This not only increases confidence in your choices but also fosters buy-in from stakeholders and team members.

Cost Reduction

Analyzing quantitative data helps identify areas where costs can be reduced or optimized. For instance, if certain marketing campaigns yield lower-than-average results, reallocating resources to more effective channels can lead to cost savings and improved ROI.

Personalizing User Experience

Quantitative analysis allows for the mapping of customer journeys and the identification of preferences and behaviors. By understanding these patterns, businesses can tailor their offerings, content, and communication to specific user segments, leading to enhanced user satisfaction and engagement.

Improving User Satisfaction and Delight

Quantitative data analysis highlights areas of success and areas for improvement in products or services. For instance, if a webpage shows high engagement but low conversion rates, further investigation can uncover user pain points or friction in the conversion process. Addressing these issues can lead to improved user satisfaction and increased conversion rates.

Best 10 Quantitative Data Analysis Software

1. questionpro.

Known for its robust survey and research capabilities, QuestionPro is a versatile platform that offers powerful data analysis tools tailored for market research, customer feedback, and academic studies. With features like advanced survey logic, data segmentation, and customizable reports, QuestionPro empowers users to derive actionable insights from their quantitative data.

Features of QuestionPro

• Customizable Surveys
• Advanced Question Types:
• Survey Logic and Branching
• Data Segmentation
• Real-Time Reporting
• Mobile Optimization
• Integration Options
• Multi-Language Support
• Data Export
• User-friendly interface.
• Extensive question types.
• Seamless data export capabilities.
• Limited free version.

Pricing : 

Starts at $99 per month per user.

2. SPSS (Statistical Package for the Social Sciences

SPSS is a venerable software package widely used in the social sciences for statistical analysis. Its intuitive interface and comprehensive range of statistical techniques make it a favorite among researchers and analysts for hypothesis testing, regression analysis, and data visualization tasks.

• Advanced statistical analysis capabilities.
• Data management and manipulation tools.
• Customizable graphs and charts.
• Syntax-based programming for automation.
• Extensive statistical procedures.
• Flexible data handling.
• Integration with other statistical software package
• High cost for the full version.
• Steep learning curve for beginners.

Pricing: 

• Starts at $99 per month.

3. Google Analytics

Primarily used for web analytics, Google Analytics provides invaluable insights into website traffic, user behavior, and conversion metrics. By tracking key performance indicators such as page views, bounce rates, and traffic sources, Google Analytics helps businesses optimize their online presence and maximize their digital marketing efforts.

• Real-time tracking of website visitors.
• Conversion tracking and goal setting.
• Customizable reports and dashboards.
• Integration with Google Ads and other Google products.
• Free version available.
• Easy to set up and use.
• Comprehensive insights into website performance.
• Limited customization options in the free version.
• Free for basic features.

Hotjar is a powerful tool for understanding user behavior on websites and digital platforms. Hotjar enables businesses to visualize how users interact with their websites, identify pain points, and optimize the user experience for better conversion rates and customer satisfaction through features like heatmaps, session recordings, and on-site surveys.

• Heatmaps to visualize user clicks, taps, and scrolling behavior.
• Session recordings for in-depth user interaction analysis.
• Feedback polls and surveys.
• Funnel and form analysis.
• Easy to install and set up.
• Comprehensive insights into user behavior.
• Affordable pricing plans.
• Limited customization options for surveys.

Starts at $39 per month.

While not a dedicated data analysis software, Python is a versatile programming language widely used for data analysis, machine learning, and scientific computing. With libraries such as NumPy, pandas, and matplotlib, Python provides a comprehensive ecosystem for data manipulation, visualization, and statistical analysis, making it a favorite among data scientists and analysts.

• The rich ecosystem of data analysis libraries.
• Flexible and scalable for large datasets.
• Integration with other tools and platforms.
• Open-source with a supportive community.
• Free and open-source.
• High performance and scalability.
• Great for automation and customization.
• Requires programming knowledge.
• It is Free for the beginners.

6. SAS (Statistical Analysis System)

SAS is a comprehensive software suite renowned for its advanced analytics, business intelligence, and data management capabilities. With a wide range of statistical techniques, predictive modeling tools, and data visualization options, SAS is trusted by organizations across industries for complex data analysis tasks and decision support.

• Wide range of statistical procedures.
• Data integration and cleansing tools.
• Advanced analytics and machine learning capabilities.
• Scalable for enterprise-level data analysis.
• Powerful statistical modeling capabilities.
• Excellent support for large datasets.
• Trusted by industries for decades.
• Expensive licensing fees.
• Steep learning curve.
• Contact sales for pricing details.

Despite its simplicity compared to specialized data analysis software, Excel remains popular for basic quantitative analysis and data visualization. With features like pivot tables, functions, and charting tools, Excel provides a familiar and accessible platform for users to perform tasks such as data cleaning, summarization, and exploratory analysis.

• Formulas and functions for calculations.
• Pivot tables and charts for data visualization.
• Data sorting and filtering capabilities.
• Integration with other Microsoft Office applications.
• Widely available and familiar interface.
• Affordable for basic analysis tasks.
• Versatile for various data formats.
• Limited statistical functions compared to specialized software.
• Not suitable for handling large datasets.
• Included in Microsoft 365 subscription plans, starts at $6.99 per month.

8. IBM SPSS Statistics

Building on the foundation of SPSS, IBM SPSS Statistics offers enhanced features and capabilities for advanced statistical analysis and predictive modeling. With modules for data preparation, regression analysis, and survival analysis, IBM SPSS Statistics is well-suited for researchers and analysts tackling complex data analysis challenges.

• Advanced statistical procedures.
• Data preparation and transformation tools.
• Automated model building and deployment.
• Integration with other IBM products.
• Extensive statistical capabilities.
• User-friendly interface for beginners.
• Enterprise-grade security and scalability.
• Limited support for open-source integration.

Minitab is a specialized software package designed for quality improvement and statistical analysis in manufacturing, engineering, and healthcare industries. With tools for experiment design, statistical process control, and reliability analysis, Minitab empowers users to optimize processes, reduce defects, and improve product quality.

• Basic and advanced statistical analysis.
• Graphical analysis tools for data visualization.
• Statistical methods improvement.
• DOE (Design of Experiments) capabilities.
• Streamlined interface for statistical analysis.
• Comprehensive quality improvement tools.
• Excellent customer support.
• Limited flexibility for customization.

Pricing:  

• Starts at $29 per month.

JMP is a dynamic data visualization and statistical analysis tool developed by SAS Institute. Known for its interactive graphics and exploratory data analysis capabilities, JMP enables users to uncover patterns, trends, and relationships in their data, facilitating deeper insights and informed decision-making.

• Interactive data visualization.
• Statistical modeling and analysis.
• Predictive analytics and machine learning.
• Integration with SAS and other data sources.
• Intuitive interface for exploratory data analysis.
• Dynamic graphics for better insights.
• Integration with SAS for advanced analytics.
• Limited scripting capabilities.
• Less customizable compared to other SAS products.

QuestionPro is Your Right Quantitative Data Analysis Software?

QuestionPro offers a range of features specifically designed for quantitative data analysis, making it a suitable choice for various research, survey, and data-driven decision-making needs. Here’s why it might be the right fit for you:

Comprehensive Survey Capabilities

QuestionPro provides extensive tools for creating surveys with quantitative questions, allowing you to gather structured data from respondents. Whether you need Likert scale questions, multiple-choice questions, or numerical input fields, QuestionPro offers the flexibility to design surveys tailored to your research objectives.

Real-Time Data Analysis 

With QuestionPro’s real-time data collection and analysis features, you can access and analyze survey responses as soon as they are submitted. This enables you to quickly identify trends, patterns, and insights without delay, facilitating agile decision-making based on up-to-date information.

Advanced Statistical Analysis

QuestionPro includes advanced statistical analysis tools that allow you to perform in-depth quantitative analysis of survey data. Whether you need to calculate means, medians, standard deviations, correlations, or conduct regression analysis, QuestionPro offers the functionality to derive meaningful insights from your data.

Data Visualization

Visualizing quantitative data is crucial for understanding trends and communicating findings effectively. QuestionPro offers a variety of visualization options, including charts, graphs, and dashboards, to help you visually represent your survey data and make it easier to interpret and share with stakeholders.

Segmentation and Filtering 

QuestionPro enables you to segment and filter survey data based on various criteria, such as demographics, responses to specific questions, or custom variables. This segmentation capability allows you to analyze different subgroups within your dataset separately, gaining deeper insights into specific audience segments or patterns.

Cost-Effective Solutions

QuestionPro offers pricing plans tailored to different user needs and budgets, including options for individuals, businesses, and enterprise-level organizations. Whether conducting a one-time survey or needing ongoing access to advanced features, QuestionPro provides cost-effective solutions to meet your requirements.

Choosing the right quantitative data analysis software depends on your specific needs, budget, and level of expertise. Whether you’re a researcher, marketer, or business analyst, these top 10 software options offer diverse features and capabilities to help you unlock valuable insights from your data.

If you’re looking for a comprehensive, user-friendly, and cost-effective solution for quantitative data analysis, QuestionPro could be the right choice for your research, survey, or data-driven decision-making needs. With its powerful features, intuitive interface, and flexible pricing options, QuestionPro empowers users to derive valuable insights from their survey data efficiently and effectively.

So go ahead, explore QuestionPro, and empower yourself to unlock valuable insights from your data!

LEARN MORE         FREE TRIAL

MORE LIKE THIS

NPS Survey Platform: Types, Tips, 11 Best Platforms & Tools

Apr 26, 2024

User Journey vs User Flow: Differences and Similarities

Best 7 Gap Analysis Tools to Empower Your Business

Apr 25, 2024

12 Best Employee Survey Tools for Organizational Excellence

Other categories.

• Academic Research
• Artificial Intelligence
• Assessments
• Brand Awareness
• Case Studies
• Communities
• Consumer Insights
• Customer effort score
• Customer Engagement
• Customer Experience
• Customer Loyalty
• Customer Research
• Customer Satisfaction
• Employee Benefits
• Employee Engagement
• Employee Retention
• Friday Five
• General Data Protection Regulation
• Insights Hub
• Life@QuestionPro
• Market Research
• Mobile diaries
• Mobile Surveys
• New Features
• Online Communities
• Question Types
• Questionnaire
• QuestionPro Products
• Release Notes
• Research Tools and Apps
• Revenue at Risk
• Survey Templates
• Training Tips
• Uncategorized
• Video Learning Series
• What’s Coming Up
• Workforce Intelligence

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• My Account Login
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Open access
• Published: 24 April 2024

Quantitative analysis and stochastic modeling of osteophyte formation and growth process on human vertebrae based on radiographs: a follow-up study

• Tong Wu 1 ,
• Changxi Wang 1 , 3 &
• Kang Li 1 , 2 , 3  

Scientific Reports volume  14 , Article number:  9393 ( 2024 ) Cite this article

67 Accesses

Metrics details

• Applied mathematics
• Disease prevention
• Musculoskeletal system
• Radiography

Osteophytes are frequently observed in elderly people and most commonly appear at the anterior edge of the cervical and lumbar vertebrae body. The anterior osteophytes keep developing and will lead to neck/back pain over time. In clinical practice, the accurate measurement of the anterior osteophyte length and the understanding of the temporal progression of anterior osteophyte growth are of vital importance to clinicians for effective treatment planning. This study proposes a new measuring method using the osteophyte ratio index to quantify anterior osteophyte length based on lateral radiographs. Moreover, we develop a continuous stochastic degradation model with time-related functions to characterize the anterior osteophyte formation and growth process on cervical and lumbar vertebrae over time. Follow-up data of anterior osteophytes up to 9 years are obtained for measurement and model validation. The agreement test indicates excellent reproducibility for our measuring method. The proposed model accurately fits the osteophyte growth paths. The model predicts the mean time to onset of pain and obtained survival function of the degenerative vertebrae. This research opens the door to future quantification and mathematical modeling of the anterior osteophyte growth on human cervical and lumbar vertebrae. The measured follow-up data is shared for future studies.

Similar content being viewed by others

Analysis of the physiological load on lumbar vertebrae in patients with osteoporosis: a finite-element study

Temporal Trends in Vertebral Dimensions – a case study from Finland

Micro-CT data of early physiological cancellous bone formation in the lumbar spine of female C57BL/6 mice

Introduction.

The spine is a crucial human body component that degenerates over time 1 . One of the most critical indicators of spinal degeneration is osteophyte formation, which is reported to be found in 20–30% of the elderly population and requires proper diagnosis and in-time interventions in clinical practice 2 , 3 , 4 .

Osteophytes most commonly appear at the anterior edges of the cervical and lumbar vertebral bodies 5 , 6 . They are not symptomatic early but would keep growing as the patient ages 7 . The anterior osteophytes that continuously protrude would result in neck/back pain at the point where they mechanically compress the spinal nerve roots or soft tissue structures 8 , 9 . In clinical practice, the oversized anterior osteophyte is a significant concern 2 , 5 . For patients with anterior osteophyte growing on the spine, lateral radiographs are mainly used for osteophyte length evaluation and diagnosis 4 . The accurate measurement of the anterior osteophyte length on lateral radiographs and the understanding of the temporal progression of anterior osteophyte growth are of vital importance to clinicians to develop effective treatment plans.

To date, two categories of measuring methods have been proposed to quantify the anterior osteophyte length on lateral radiographs. The first category 10 , 11 records the measured data directly without processing while the second category 12 uses an index to represent the osteophyte length. Regression models are mainly used to characterize the osteophyte growth process. Watanabe et al. 13 use a linear regression model to describe the relationship between the osteophyte index and age. Gender 14 , weight and BMI 15 , bone mass 16 , etc. are found to be the affecting factors of the osteophyte growth process.

The previous studies contribute to the understanding of the biology of osteophyte growth and may facilitate clinical prevention. However, they have the following three limitations. Firstly, existing methods of measuring anterior osteophyte length are not fully applicable in clinical practices since (i) the measurement steps are not well-defined and (ii) the proposed indicator cannot be applied to radiographs with different scale plates. Secondly, the previously used regression models fail to predict the time-related progression of the osteophyte growth process and the time to onset of pain (TTOOP) under uncertainties. Thirdly, to date, most of the studies on osteophytes are cross-sectional, where data is collected only once for each patient. Few longitudinal studies are available for understanding the temporal progression of osteophyte growth over an extended period.

The osteophyte formation and growth process is subject to uncertainties and may undergo significant variations. The specific degeneration initiation time is not a constant value but rather follows a distribution as it differs among the population due to factors such as incorrect posture and acute spinal injuries 17 . In addition, uncertainties exist during the osteophyte growth process since the biological effects may affect the growth rate of the osteophyte 18 and there are person-to-person variations due to their genetic and lifestyle differences 19 . Compared to the commonly used regression model, stochastic models that incorporate the temporal uncertainties and random factors are suitable for capturing the evolution of osteophyte formation and growth over time 20 .

Currently, a variety of stochastic models have been implemented in degradation analysis 21 . The survival function and the TTOOP can be obtained and the corresponding condition-based maintenance plans are scheduled for the systems subject to degradation to reduce the pain risk 22 . Despite their straightforward physical interpretations and tractable mathematical properties, the applications of stochastic models in characterizing the human spine degeneration process are still at their early stages.

In this study, a robust measuring method for anterior osteophyte length on lateral radiographs is proposed, which can be applied to spine degeneration quantification in clinical studies. Furthermore, we develop a stochastic model to characterize and predict the temporal progression of osteophyte formation and growth with high accuracy, validity and interpretability. Considering that the actual lifetime data are usually censored and aperiodic, the maximum likelihood estimation (MLE) method is used to estimate the parameters. The model is validated using long-term follow-up data. This work contributes not only to the understanding of the osteophyte growth process, but also to the survival assessment and prognostic care for degenerative spinal vertebrae in clinical practice.

Agreement of measurements

In this study, we use the osteophyte ratio index (ORI) to quantify the anterior osteophyte length on lateral radiographs. A robust measuring method is proposed as shown in Fig.  7 b legend. Four observers with different ages and experiences are included in the agreement tests to compare the robustness of the measuring methods proposed in this study and Walraevens et al. 12 ’s study. The results of agreement tests for the two measuring methods are shown in Table 1 .

Validation of the osteophyte formation and growth process model

The results of ORI measurements of the 23 cervical vertebrae samples and 74 lumbar vertebrae samples are shown in Figs.  1 a and 2 a respectively, where the x-axis represents the ages of patients, and the y-axis represents the corresponding ORIs. Based on the MLE functions described in Eq. ( 6 ), the parameters of the Weibull distribution are estimated as \(\left\{ {\hat{a} = {52}{\text{.5216}}, \, \hat{b} = {5}{\text{.7469}}} \right\}\) and \(\left\{ {\hat{a} = {5}4.9779, \, \hat{b} = {2}{\text{.3443}}} \right\}\) for cervical and lumbar vertebrae respectively. The actual osteophytes formation time of samples and the probability density function (PDF) of the fitted Weibull distribution for cervical and lumbar vertebrae are shown in Figs.  1 b and 2 b respectively.

( a ) The osteophyte growth data of the 23 cervical vertebrae. ORI refers to the Osteophyte Ratio Index. ( b ) The validation of the Weibull distribution. The actual cervical osteophyte formation time is compared with the estimated probability density function (PDF). ( c ) The validation of the Wiener process. The actual cervical osteophyte growth paths are compared with the predicted confidence interval (CI). ( d ) The actual and predicted osteophyte formation and growth process of a cervical vertebra. ( e ) The comparison of the theoretical cervical vertebra’s survival function and the Kaplan–Meier (KM) curve of the actual data. ( f ) The comparison of the cervical vertebra’s time to onset of pain and the actual data with the estimated PDF.

( a ) The osteophyte growth data of the 74 lumbar vertebrae. ORI refers to the Osteophyte Ratio Index. ( b ) The validation of the Weibull distribution. The actual lumbar osteophyte formation time is compared with the estimated probability density function (PDF). ( c ) The validation of the Wiener process. The actual lumbar osteophyte growth paths are compared with the predicted confidence interval (CI). ( d ) The actual and predicted osteophyte formation and growth process of a lumbar vertebra. ( e ) The comparison of the theoretical lumbar vertebra’s survival function and the Kaplan–Meier (KM) curve of the actual data. ( f ) The comparison of the lumbar vertebra’s time to onset of pain and the actual data with the estimated PDF.

Based on MLE functions described in Eq. ( 7 ), the parameters of the Wiener process are estimated as \(\left\{ {\hat{\mu } = {0}{\text{.0145553}}, \, \hat{\sigma } = {0}{\text{.0113259}}} \right\}\) and \(\left\{ {\hat{\mu } = {0}{\text{.012836}}, \, \hat{\sigma } = {0}{\text{.024040}}} \right\}\) for cervical and lumbar vertebrae respectively. Based on the parameters, the 95% confidence interval and the mean path of the predicted ORI of cervical and lumbar vertebrae are shown in Figs.  1 c and 2 c respectively, where the x-axis represents the duration since the osteophytes are formed, and the y-axis represents the corresponding ORIs.

Based on Eq. ( 2 ) and the estimated parameters, the mean and 95% confidence interval of the osteophyte length are obtained and shown in Figs.  1 d and 2 d for cervical and lumbar vertebrae respectively. The degeneration data are plotted in blue lines with asterisk markers.

Validation of the survival metrics

To validate the proposed survival metrics, we collected the X-ray image series datasets obtained at discrete time instants during the patients’ follow-up visits, where the ORI value of 0.08 is of the highest count over the 23 cervical vertebrae samples’ ORI series and the value of 0.15 is of the highest count over the 74 lumbar vertebrae samples’ ORI series. For illustration purposes, we assume that the pain threshold values are 0.08 and 0.15, which also conforms to the principles of statistics. The ages when the ORIs reach the pain thresholds are treated as the actual TTOOP values. Compared to other ORI values which only have one or two samples, the counts of 0.08 and 0.15 are higher and thus are more suitable to be used as the pain threshold values. Therefore, without loss of generality, we assume pain thresholds of 0.08 and 0.15 for cervical and lumbar vertebrae respectively to validate the survival metrics.

The theoretical survival curve of cervical/lumbar vertebrae under the pain threshold (i.e., the maximum clinically-acceptable osteophyte size) of 0.08/0.15 is obtained based on Eq. ( 4 ) and shown in Figs.  1 e and 2 e by a blue line. As this study involves survival data, Kaplan–Meier (KM) survival analysis is conducted and the corresponding KM curve of cervical/lumbar vertebrae is shown in Figs.  1 e and 2 e by a red line, which reflects the actual survival probability of cervical/lumbar vertebrae. The shaded pink region represents the 95% confidence interval of the KM curve.

The PDF of the TTOOP of cervical/lumbar vertebrae under the pain threshold of 0.08/0.15 is estimated based on Eq. ( 3 ) and shown in Figs.  1 f and 2 f by a blue line. The actual TTOOP is shown in Figs.  1 f and 2 f with red asterisk markers.

Based on Eq. ( 5 ), the mean time to onset of pain (MTTOOP) of the cervical/lumbar vertebra given the pain threshold of 0.08/0.15 are obtained. The theoretical and actual MTTOOP for cervical vertebra are 54.11 and 53.76 years respectively (percentage difference = 0.65%). The theoretical and actual MTTOOP for the lumbar vertebra are 60.40 and 60.66 years respectively (percentage difference = 0.43%).

Figures  1 b and 2 b indicate that the Weibull distribution can accurately characterize the osteophyte formation time of a cervical and lumbar vertebra. Note that all of the test ORI data of each cervical and lumbar vertebra after the censor time (i.e., the data series on the right of the red line) fall into the predicted confidence intervals in Figs.  1 c and 2 c. It shows that the Wiener process can accurately characterize the osteophyte growth of a cervical and lumbar vertebra. In Figs.  1 d and 2 d, all the actual data fall into the 95% CI. The large CI is due to the large variation and uncertainties of the osteophyte formation time and growth process among the population. It can increase the likelihood that the interval contains the mean response and also contributes to a more accurate and general prediction of the time to onset of pain for the population with large variations in degeneration performance. Figures  1 e and 2 e show that the theoretical survival curve derived from the proposed model accurately matches the actual survival curve under the pain-threshold assumption. It is observed from Figs.  1 f and 2 f that the distribution of the TTOOP obtained from the proposed model accurately characterizes the actual cases. In addition, the theoretical MTTOOP calculated from the proposed model fits the actual data precisely (i.e., The theoretical and actual MTTOOP for cervical vertebra are 54.11 and 53.76 years respectively (percentage difference = 0.65%); The theoretical and actual MTTOOP for the lumbar vertebra are 60.40 and 60.66 years respectively (percentage difference = 0.43%)). Results show that the model is of high accuracy, validity and interpretability.

According to Walraevens et al. 12 , there are no detailed guiding principles for finding the middle point on the irregularly shaped vertebra. As the measurements of osteophyte length are small in magnitude and highly sensitive to noises, measuring methods with ill-defined instructions may result in inaccurate conclusions and low repeatability in clinical practice. Thus, it is urgent to propose a novel robust osteophyte length indicator. In this paper, an indicator ORI (Eq. ( 1 )) with well-defined measuring steps (Fig.  7 b legend) is proposed for the quantification of anterior osteophyte length based on lateral radiographs. In the study of Walraevens et al. 12 , AB and CD (Fig.  7 c) are measured at the middle of the vertebral body to represent the anteroposterior diameter. However, as the anterior and posterior vertebra contour is curved, the determination of midpoints A/B/C/D is subjective. By comparison, parallel and tangent lines are more objective and suitable for measuring curved structures. In addition, since \(h_{0}\) is generally considered as unchanged during the spine degeneration process, the ratio function (Eq. ( 1 )) that divides the \(h_{1}\) by \(h_{0}\) in the same radiographic image can overcome the scale error caused by various generations of medical equipment and be applied to radiographs of different sizes to reflect the osteophyte size. Table 1 shows that the indicator ORI under the proposed well-defined measuring steps has excellent reliability (i.e., with ICC > 0.90 and low PD values). By comparison, the measurement in Walraevens , et al. 12 ’s study has lower ICC scores and higher PD values. This indicates that our method is more robust and can be reliably used in clinical practice and in related research to quantify the anterior osteophyte length.

Without an osteophyte growth prediction model for clinical reference, the current treatment plans for degenerative vertebrae are mainly made by clinicians and the treatment quality highly depends on their experience as shown in Fig.  3 a 9 . The treatment plans made by inexperienced clinicians may fail to provide interventions in time and result in unexpected pain. Studies reported that progressive symptoms caused by anterior osteophytes are easily missed during the early evaluation 25 . When severe and unexpected pain develops due to untimely treatment, surgery is required to remove the osteophyte 26 . The development of accurate and valid mathematical models of osteophyte growth is urgently needed to estimate the osteophyte formation time and growth rate, which can be used as a reference for clinical management in the early stage. In this paper, we develop a stochastic model to characterize and predict the temporal progression of osteophyte formation and growth under uncertainties. Compared to the existing stochastic models such as the Wiener processes 21 , Markov Chains 27 , Gamma processes 28 and Inverse Gaussian processes 29 , we characterize the initiation time of the osteophyte formation by Weibull distribution and incorporate it into the stochastic model by convolution. The proposed model with estimated parameters is especially suitable for characterizing osteophyte formation and growth. Previous studies mainly discuss the prevalence and symptoms of spinal osteophytes rather than quantitative prediction models that would assist prophylactic treatments. In this study, survival metrics can be derived from the stochastic model 20 . As the mean survival time and the pain risk of diseases are major concerns in clinical practice 30 , the derived survival metrics such as MTTOOP and survival function of the degenerated vertebrae can assist clinical decision-making. This study opens the door to the future application of stochastic models to predict degenerative changes in the human spine.

( a ) The existing experienced-based treatment planning framework. ( b ) The proposed quantitative and model-based decision support framework.

Our work has implications for clinical practices. As the proposed models incorporate temporal uncertainties, random factors and person-to-person variation that evolve in the osteophyte formation and growth process, they can provide population-level inferences for insurance companies to develop proper insurance policies accordingly for different populations. In addition, we propose a quantitative and model-based decision support framework with four steps as shown in Fig.  3 b. Step 1: patient A takes a radiographic examination and an osteophyte is detected. Step 2: the indicator ORI is measured to quantify the osteophyte length. Here we assume that the osteophyte is on patient A’s lumbar vertebra and its ORI value is measured to be 0.15 at that time. Step 3: based on the parameters estimated from the population data and the measured initial ORI value, the clinicians can predict how the mean and 95% CI of the patient’s ORI would progress in the future 10 years. Step 4: survival analysis is performed where the survival curve, the PDF plot of the remaining TTOOP and the mean value of the remaining TTOOP are available for the clinician’s reference. For instance, we assume that 80% and 50% are survival probability thresholds for treatment change. The threshold values can be modified by medical professionals. As the survival curve shows that there is an 80% probability of surviving beyond 2.8 years, clinicians can put patient A in observation during the future 0 to 2.8 years. Since the survival probability will decrease to 50% at 5.5 years, frequent follow-up and physical therapy can be scheduled for patient A during the future 2.8–5.5 years. More frequent Follow-up care and medication need to be scheduled during the future 5.5–10 years where the survival probability is under 50%. Note that the treatment plans can be modified in the next follow-up visit based on the patient’s remeasured ORI and the corresponding survival-analysis plots. Compared to the experience-based treatment shown in Fig.  3 a, the proposed quantitative and model-based framework in Fig.  3 b can provide quantitative prediction for clinicians to make more personalized treatment plans. The survival-analysis plots in Fig.  3 b are obtained under the assumed lumbar pain threshold of 0.22. In clinical practice, the pain threshold can be determined based on the criteria provided in the Pain Threshold Definition subsection or modified by the medical professionals. The corresponding survival-analysis plots can be obtained by running the codes in Supplementary B on the MATLAB Platform.

Previous studies are mainly cross-sectional in design and use point datasets to investigate the correlation of osteophyte length with age. For instance, in Chanapa et al. 8 ’s study, five age groups (15–35, 36–60, 61–75, 76–85, and > 85 years old) are used and the mean osteophyte length on the vertebral body of patients in each group is obtained as shown in Fig.  4 a. There is only one data point for each patient that reflects the osteophyte growth level in that group. However, the progressive changes in osteophyte length of the same patient’s vertebrae are unknown. In the study of 31 , 32 , although 2–3 years of follow-up data are collected, they are rather short periods considering the slow and progressive osteophyte growth process. As a result, little change in osteophyte growth is observed during the short periods of the studies 33 . With discrete-time datasets or short-term follow-up data, there is a lack of historical data for model fitting and validation. Long-term follow-up data are crucial for understanding osteophyte growth and developing predictive models. In this study, we obtained long-term time-series follow-up radiographs as illustrated in Fig.  4 b. To the best of the authors' knowledge, it is relatively new to apply time-series osteophyte data for the progression assessment of osteophyte growth. It helps to understand the temporal progression of osteophyte growth over an extended period and to develop models for osteophyte growth prediction.

( a ) Point dataset in Chanapa et al. 8 ’s study. ( b ) Time-series dataset in our study. ( c ) The evolution of the PDFs of the ORI over time, assuming that the ORI at the current state is 0.05 and the pain threshold is 0.15 for illustration purposes. Survival probabilities of the vertebra at the first, third, fifth, seventh, ninth and eleventh year are shown in Figures ( d ), ( e ), ( f ), ( g ), ( h ) and ( i ), respectively.

In previous studies, deterministic models such as linear and logistic regression models are typically used in clinical analysis to predict the development of osteophyte-related diseases 34 , 35 , 36 , 37 . Compared to that, we used the stochastic process model which provides a range of estimates rather than point estimates. The range of estimates that, each of which is associated with a probability, can characterize the randomness and the temporal uncertainties associated with the evolution of the degeneration process. The uncertainties originate from both observable and unobservable factors including the variability of patients, the differences in medicine interventions, etc. The model uses variables to incorporate the random effects of those factors on the osteophyte growth process and therefore, is more appropriate to characterize and predict the osteophyte growth process than the deterministic models that only provide a certain value and neglect the person-to-person variation. Figure  4 c demonstrates the osteophyte growth progression modeled by the stochastic model—the Wiener process. The ORIs at a fixed time instant are normally distributed and the distribution of the ORI keeps evolving over time. The black-dashed line represents the most probable ORI growth path. When the pain threshold is 0.15 (indicated with the red-solid horizontal line in Fig.  4 c, the value is for illustrative purposes), the corresponding survival probability (i.e., survival function), which is the probability that the ORI is smaller than the pain threshold, keeps decreasing over time, as shown in Fig.  4 d–i. The distributions of the ORI in the future can be obtained based on the Wiener process. The medical professionals can provide more reasonable advice regarding the possible consequences and the corresponding probabilities given the current situation. To the best of the authors' knowledge, it is relatively new to apply stochastic models to predict osteophyte growth progression and obtain evaluation metrics that can provide valuable information for clinical decision-making.

Some limitations should be noted in our study. Firstly, the dataset includes the osteophyte formation and growth data of twenty-three cervical vertebrae and seventy-four lumbar vertebrae. Although the sample size is enough for parameter estimation and model validation, a larger quantity of data should be enrolled in future studies for more robust validation and more accurate estimation of the general population parameters. Secondly, this study proposes a basic model where the osteophyte formation and growth process are considered independent and the growth process is homogeneous. However, other behaviors, such as disc height reduction 38 , may occur simultaneously or successively with the osteophytes during the cervical and lumbar vertebrae degeneration and are reported to affect the osteophyte formation time and growth rate 39 . In addition, Gelse et al. 40 proposed that osteophyte growth shows a multi-stage pattern on the cell biological level. Therefore, both its association with other degenerative behaviors and its multi-stage behavior could be quantitatively investigated and enrolled into the future model for a more precise description (e.g., a narrower confidence interval) of osteophyte formation and growth process.

Figure  5 shows the workflow of our study. We develop a measuring method for the anterior osteophyte length and conduct an agreement test to show the robustness of our method. In addition, we develop a stochastic model for characterizing the osteophyte formation and growth process and derive the related survival metrics for clinical application purposes. Time-series radiographic datasets are obtained from the hospital for model validation. Based on the robust measuring method and accurate models, we propose a quantitative and model-based decision support framework for treatment planning of cervical and lumbar osteophytes in clinical practices. The detailed information is found in the subsequent subsections.

The workflow diagram.

Dataset description

This study focuses on the osteophyte formation time and time-dependent osteophyte growth on both cervical and lumbar vertebrae. Radiographic osteophyte formation and growth data collected from September 2009 to September 2021 are obtained from West China Hospital, Sichuan University. As the osteophytes most commonly form on the five cervical vertebrae C3 through C7 and rarely on C1 and C2 41 , we focus on the five levels C3-C7 to investigate the osteophyte formation and growth behavior. For lumbar vertebrae, as osteophytes are frequently reported to form on vertebrae L1 through L5 42 , the five levels are included in the dataset for lumbar osteophyte investigation. Males and females are reported to show similar patterns in osteophyte development 43 , so the gender is not considered in our study.

Figure  6 shows the database organization. Our dataset includes 29 radiographic series of cervical vertebrae from C3 to C7 (23 with osteophytes and 6 without osteophytes) and 103 radiographic series of lumbar vertebrae from L1 to L5 (74 with osteophytes and 29 without osteophytes), where each series corresponds to a vertebra and is collected during the patient’s follow-up visits as shown in Fig.  6 . The radiographic series of cervical and lumbar vertebra osteophytes are collected from 11 (at their first visit: mean age = 49.78 ± 8.72 years, age range = 29.65–61.62 years) and 33 (at their first visit: mean age = 53.07 ± 10.79 years, age range = 38.00–78.63 years) patients, respectively. One radiograph is taken for the vertebra and shows the osteophyte growth level of the vertebra during each visit. To protect the privacy of the patients, the specific dates of the radiographic images are not shown in Fig.  6 . The mean(max) follow-up time-span of patients with cervical and lumbar osteophytes are 4.39(6.71) and 6.77(9.13) years, respectively. Each series consists of over 3 follow-up visits. Radiographs are of high resolution and are viewed by RadiAnt DICOM Viewer.

Database organization diagram.

Measurement of anterior osteophyte length based on lateral radiographs

Measuring methods.

In this study, a new indicator Osteophyte Ratio Index (ORI) is proposed as follows:

where \(h_{1}\) denotes the length of the osteophyte and \(h_{0}\) denotes the width of the cervical or lumbar vertebra body in the lateral view of the radiographic image.

The detailed measuring steps are in the Fig.  7 legend. The measurement is conducted with the RadiAnt DICOM Viewer 44 .

( a ) A normal vertebra (the top one) and a degenerated vertebra (the bottom one) with osteophyte in the anterior side (lower left-hand corner). Points M and N are the anterior edge points of the normal vertebra in the lateral view. Point O is the osteophyte tip in the lateral view. ( b ) Measurement of osteophyte length and vertebra width. An orange dashed line is drawn along the vertebra contour for illustrative purposes. The measurement method includes three steps. First, the points M and N are identified and a yellow line connecting the two points is drawn. A second line (green line) is drawn parallel to the yellow line and tangential to the innermost part of the right vertebra contour. The distance between the yellow and green lines is defined as the vertebra width (white double-sided arrow). A third line (blue dashed line) is drawn parallel to the yellow line and tangential to the osteophyte tip. The distance between the yellow and blue lines is defined as the osteophyte length (white single-sided arrow). ( c ) Measurement of osteophyte length in Walraevens et al. 12 ’s study. The osteophyte length (XY and PQ) is measured with respect to the anteroposterior diameter of the vertebral body (AB and CD, respectively). AB and CD are measured at the middle of the vertebral body.

Agreement test

Inter-observer reproducibility (i.e., the agreement between the measurements of two observers) and intra-observer repeatability (i.e., the agreement between the measurements of the same observer) of ORI are evaluated using the intra-class correlation coefficient (ICC) and percentage difference (PD) 45 . According to 46 , four observers (observers I, II, III and IV) are included to measure the lengths of anterior osteophytes using ORI independently from a subset of 50 randomly selected radiographs. Observers I, II, and III are a 35-year-old radiologic technologist, a 30-year-old orthopedist and a 23-year-old graduate student who majors in medical imaging technology, respectively. Observer IV is a 20-year-old undergraduate student who majors in engineering and has no clinical background. Each observer measures two rounds at a 2-week interval. The interpretation of ICC is based on the previous study 23 where ICC ≤ 0.50, 0.50 < ICC ≤ 0.75, 0.75 < ICC ≤ 0.90 and 0.90 < ICC refers to the poor, moderate, good and excellent agreement, respectively. It is reported that a smaller PD value indicates a lower difference and thus higher agreement 24 . For comparison, the same agreement test is performed by the same four observers on the index proposed in Walraevens et al. 12 ’s study.

Stochastic model development

The assumptions of the osteophyte formation and growth process of a single cervical/lumbar vertebra are made as follows: (1) After a random time, osteophyte forms on one vertebra due to factors such as aging and mechanical stresses; (2) The osteophyte continues to grow after the formation following a stochastic process; (3) Only the largest osteophyte at each vertebra is investigated. (4) The pain occurs when the length of its anterior osteophyte reaches the pain threshold. (5) As the osteophytes on cervical and lumbar spinal vertebrae show similar etiology and growth patterns 47 , their formation and growth are assumed to follow the same stochastic process but with different parameters. The cervical vertebra at different levels (i.e., C3 through C7), are similar in shape and function 48 , 49 and are treated as identical cervical subjects with the same parameters in our model. Likewise, lumbar vertebrae L1 to L5 are considered as identical lumbar subjects with the same parameters in our model as the degenerative behaviors are similar among the lumbar levels (i.e., L1 through L5) 50 .

The schematic diagram of the osteophyte formation and growth process is shown in Fig.  8 . Let \(\tau\) denote the osteophyte formation time of a vertebra. The degeneration status (i.e., osteophyte size) of the vertebra at time \(t\) is denoted as \(X\left( {t|\tau } \right)\) . Note that \(t - \tau\) is the length of time of its degeneration. The pain threshold \(c\) corresponds to the maximum acceptable osteophyte size of the vertebra and \(T\) corresponds to the time to onset of pain (TTOOP) when the degeneration status reaches \(c\) . Take the cervical vertebra as an example, pain occurs when a large anterior osteophyte compresses the pharyngeal wall (as illustrated in Fig.  8 ).

The schematic diagram of the osteophyte formation and growth on a single vertebra and the osteophyte growth data with aperiodic time interval.

Note that \(\tau\) is a random variable that reflects the biological properties of the cervical and lumbar vertebrae influenced by environmental and biological factors, physical activities, etc. In biomedical survival analysis, the two-parameter Weibull distribution is widely used to describe the time to develop a disease and is flexible in characterizing age-related diseases 51 . In this study, the osteophyte formation time since the patients' birthdays (i.e., age in years) is modeled with a Weibull distribution 52 .

In previous studies, a positive correlation has been found between the osteophyte index and age based on the linear regression models 13 . As it is observed that the osteophyte growth process has a linear trend and involves uncertainties, the widely implemented Wiener process 53 is suitable for characterizing the osteophyte growth path. Let \(X\left( {t|\tau } \right)\) denote the conditional osteophyte growth status of a cervical or lumbar vertebra at time \(t\) , given its osteophyte formation time \(\tau\) . For \(\forall t > \tau\) , \(X\left( {t|\tau } \right)\) follows a normal distribution \(N\left( {\mu \left( {t - \tau } \right),\sigma^{2} \left( {t - \tau } \right)} \right)\) .

In an osteophyte formation and growth process, the unconditional probability density function (PDF) of the degeneration status of a cervical or lumbar vertebra at time \(t\) is given by Eq. ( 2 ):

where \(a > 0\) and \(b > 0\) are the scale and shape parameters of the Weibull distribution. \(x\) is the degeneration status of the cervical or lumbar vertebra, the drift parameter \(\mu\) and the diffusion parameter \(\sigma\) correspond to the mean growth rate and the volatility of the osteophyte’s growth respectively.

Pain threshold definition

The anterior osteophyte that grows continuously on the cervical/lumbar vertebra may mechanically compress spinal nerve roots or soft tissue structures and lead to neck/back pain 8 , 9 . The pain threshold refers to the maximum clinically-acceptable osteophyte size. We assume that the patient with an osteophyte on cervical/lumbar vertebra that has an ORI value exceeding the pain threshold will experience neck/back pain. Given the pain threshold value \(c\) , the statistics including the time to onset of pain (TTOOP) distribution, survival function and mean time to onset of pain (MTTOOP) are derived based on the developed model. These statistics predict when the pain will occur and imply the probability that the patient will survive without pain. They can provide references for early intervention before the pain actually occurs.

In clinical practice, the pain thresholds are determined as 0.52 and 0.22 for cervical and lumbar vertebrae, respectively. The determination of the pain thresholds are as follows. According to the literature 54 , the anterior cervical osteophyte with an average length of over 10 mm will cause mechanical compression on the neck. Since the mean anteroposterior (AP) diameter of the cervical vertebral body is 19.13 mm 55 , we recommend the pain threshold \(c_{c} = 10/19.13 = 0.52\) for the cervical vertebra. Likewise, as Kojima et al. 56 propose that the anterior lumbar osteophyte length greater than 10 mm is associated with low back pain and the mean AP diameter of the lumbar vertebral body is 46.31 mm 57 , we recommend the pain threshold \(c_{l} = 10/46.31 = 0.22\) for lumbar vertebra. Note that the 0.52 and 0.22 are population-based recommended values, which are flexible and can be modified accordingly based on patient-specific characteristics. For instance, software or clinicians can measure the patient-specific AP diameter of the cervical/lumbar vertebral body on the patient’s lateral radiograph. The patient-specific pain threshold can be calculated by dividing the literature-recommended osteophyte length of 10 mm by the patient’s AP diameter.

Survival metrics development

Note that as the osteophyte growth follows a Wiener process with drift \(\mu\) and diffusion \(\sigma\) , TTOOP under pain threshold \(c\) after its formation follows an IG distribution \(\left( {T - \tau } \right) \sim IG\left( {\frac{c}{\mu },\frac{{c^{2} }}{{\sigma^{2} }}} \right)\) with a mean of \(\frac{c}{\mu }\) . Accordingly, the MTTOOP given its osteophyte formation time \(\tau\) is \(\frac{c}{\mu } + \tau\) .

The PDF of TTOOP given the pain threshold \(c\) is obtained as shown in Eq. ( 3 ):

where \(g\left( {t|\tau ,c} \right)\) denotes the conditional PDF of TTOOP of a cervical or lumbar vertebra given \(\tau\) is known.

The survival function and MTTOOP for a given threshold \(c\) are obtained in Eqs. ( 4 ) and ( 5 ):

where \(H\left( { \cdot |t,\tau } \right)\) denotes the conditional survival function of a cervical or lumbar vertebra at time \(t\) given \(\tau\) is known, \(\tau\) is the osteopyte formation time, \(E\left( {T|\tau ,c} \right)\) denotes the conditional TTOOP of a cervical or lumbar vertebra given \(\tau\) and \(c\) are known.

The codes for the calculation of Eqs. ( 2 ), ( 3 ), ( 4 ) and ( 5 ) are provided in Supplementary A for clinical application purposes. Clinicians can obtain the corresponding plots by running the program on the MATLAB Platform. In addition, the program can provide personalized prediction and survival analysis based on adjusted versions of the equations. The MATLAB codes are provided in Supplementary B.

Parameters estimation

The maximum likelihood estimation (MLE) algorithm is used to estimate the parameters of the model. The parameters of the proposed model include \(\left\{ {a,b,\mu ,\sigma } \right\}\) , where \(a,b\) are the parameters of the distribution of the osteophyte formation time, and \(\mu ,\sigma\) are the parameters that govern the osteophyte growth since the formation. It is assumed that the osteophyte formation and growth are independent and the likelihood functions for \(\left\{ {a,b} \right\}\) and \(\left\{ {\mu ,\sigma } \right\}\) are obtained independently. Parameters of the proposed model for cervical and lumbar vertebrae are estimated by the same method from separate data sources.

Parameters estimation of the distribution of osteophyte formation time

Assume the radiographic image series of a total of \(M\) cervical vertebrae are available. Among them, \(N\) vertebrae are found to have developed osteophyte over the data-collection period. Let \(\tau_{i}\) , \(1 \le i \le N\) denote the osteophyte formation time of the osteophyte on the \(i^{th}\) cervical vertebra, \(\tau_{k}\) , \(N + 1 \le k \le M\) denote the right-censoring time where the osteophyte has not developed on the cervical vertebra by the time of the last follow-up visit.

Taking the natural logarithm of the joint density:

The MLE estimators of \(a\) and \(b\) for the Weibull distribution are obtained by maximizing Eq. ( 6 ), which can be achieved by using the maxLik package in R.

As the actual radiographic images are not obtained continuously, the exact osteophyte formation time (i.e., the time when ORI begins to exceed zero) is not observed directly. In this study, 23 cervical vertebrae and 74 lumbar vertebrae developed osteophytes over the follow-up period. Since 6 cervical and 29 lumbar vertebrae have not developed osteophytes, the corresponding patient’s age at the last follow-up date is denoted as the right-censored osteophyte formation time 58 . As the overall osteophyte growth process has a linear trend 13 , the actual osteophyte formation time of each cervical/lumbar vertebra is estimated by linear interpolation based on its first and last observations. Both the actual and the right-censored osteophyte formation time are the INPUT for parameter estimation of the Weibull distribution.

Parameters estimation of the osteophyte growth process

The drift \(\mu\) and diffusion \(\sigma\) of the Wiener process are estimated as follows. Assume that a total of \(N\) cervical vertebrae with osteophyte growing on them are available. There are \(n_{i}\) measurements of osteophyte growth increment on the \(i^{th}\) cervical vertebra. Let \(\Delta x_{ij} \left( {1 \le i \le N,1 \le j \le n_{i} } \right)\) denote the \(j^{th}\) osteophyte growth increment on the \(i^{th}\) cervical vertebra and \(\Delta t_{ij} \left( {1 \le i \le N,1 \le j \le n_{i} } \right)\) denote the corresponding time interval for osteophyte growth.

Note that in reality, although periodic follow-up visits are suggested for patients with osteophyte growth on their cervical vertebrae, the follow-up visits are usually aperiodic. Accordingly, the obtained osteophyte growth observations are also aperiodic, as illustrated in Fig.  8 . The corresponding maximum likelihood estimators are obtained as follows.

The likelihood function of \(\mu\) and \(\sigma\) is:

where \(\Delta {\mathbf{x}}\) and \(\Delta {\mathbf{t}}\) are the vectors of the degeneration increments and time increments. The MLE estimators \(\left\{ {\hat{\mu },\hat{\sigma }} \right\}\) are obtained by maximizing the log-likelihood function using the maxLik package in R.

For the actual radiographic image datasets, all vertebrae samples with osteophytes developed are used for parameters estimation of the Wiener process. We censor the osteophyte growth data at time \(t = 4\) for cervical vertebrae and \(t = 6\) for lumbar vertebrae and use the data before the censor time for parameters estimation using MLE.

Ethical approval and consent to participate

This study was approved by the Institutional Review Board of West China Hospital. Written informed consent was obtained from all individual participants included in this study. We confirm that all methods were performed in accordance with the relevant guidelines and regulations.

Data availability

Summarized data have been presented and shared in this manuscript. The raw data that support the findings of this study are available from the West China Hospital but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of West China Hospital. Contact [email protected] to request the data from this study.

Kushchayev, S. V. et al. ABCs of the degenerative spine. Insights Imaging 9 (2), 253–274 (2018).

Article   PubMed   PubMed Central   Google Scholar  

Bone, R. C., Nahum, A. M. & Harris, A. S. Evaluation and correction of dysphagia-producing cervical osteophytosis. Laryngoscope 86 , 1–9 (2014).

Google Scholar  

Klaassen, Z. et al. Vertebral spinal osteophytes. Anat. Sci. Int. 86 , 1–9 (2010).

Article   PubMed   Google Scholar  

Song, A. R. et al. Surgical treatments on patients with anterior cervical hyperostosis-derived dysphagia. Ann. Rehabil. Med. 36 (5), 729–734 (2012).

Chanapa, P., Tohno, Y. & Mahakkanukrauh, P. Distribution and length of osteophytes in the lumbar vertebrae and risk of rupture of abdominal aortic aneurysms: A study of dry bones from Chiang Mai. Thailand. Anat. Cell Biol. 47 , 157–161 (2014).

Karasik, D. et al. Abdominal aortic calcification and exostoses at the hand and lumbar spine: the Framingham Study. Calcif. Tissue Int. 78 (1), 1–8 (2006).

Article   CAS   PubMed   Google Scholar  

Chan, A. Y., Mullin, J. P., Wathen, C. & Benzel, E. C. Degenerative spinal disease (cervical). In Principles of neurological surgery 4th edn 549–553 (Elsevier, Amsterdam, 2018).

Chapter   Google Scholar  

Chanapa, P., Yoshiyuki, T. & Mahakkanukrauh, P. Distribution and length of osteophytes in the lumbar vertebrae and risk of rupture of abdominal aortic aneurysms: A study of dry bones from Chiang Mai Thailand. Anat. Cell Biol. 47 (3), 157–161 (2014).

Al-Jafari, M. et al. Cervical spine osteophyte: A case report of an unusual presentation. Cureus 15 (9), e44762 (2023).

PubMed   PubMed Central   Google Scholar  

Sekiya, I. et al. Medial tibial osteophyte width strongly reflects medial meniscus extrusion distance and medial joint space width moderately reflects cartilage thickness in knee radiographs. JMRI 56 (3), 824–834 (2022).

Moon, Y. et al. Factors correlated with the reducibility of varus deformity in knee osteoarthritis: An analysis using navigation guided TKA. Clin. Orthop. Surg. 5 , 36–43 (2013).

Walraevens, J. et al. Qualitative and quantitative assessment of degeneration of cervical intervertebral discs and facet. Eur. Spine J. Off. Publ. Eur. Spine Soc. Eur Spinal Deform. Soc. Eur. Sect. Cerv. Spine Res. Soc. 18 , 358–369 (2008).

Article   Google Scholar  

Watanabe, S. & Terazawa, K. Age estimation from the degree of osteophyte formation of vertebral columns in Japanese. Leg. Med. 8 (3), 156–160 (2006).

Resnick, D. & Niwayama, G. Degenerative disease of extraspinal locations . Diagnosis of Bone & Joint Disorders , 1263–1371 (1995).

Oishi, Y. et al. Lack of association between lumbar disc degeneration and osteophyte formation in elderly japanese women with back pain. Bone 32 (4), 405–411 (2003).

Hardcastle, S. A. et al. Osteophytes, enthesophytes, and high bone mass: a bone-forming triad with potential relevance in osteoarthritis. Arthritis Rheumatol. 66 (9), 2429–2439 (2014).

Chen, Y.R., Sung, K & Tharin, S. Symptomatic anterior cervical osteophyte causing dysphagia: Case report, imaging, and review of the literature . Cureus (2016).

Pelletier, J.-P. et al. Carprofen simultaneously reduces progression of morphological changes in cartilage and subchondral bone in experimental dog osteoarthritis. J RHEUMATOL. 27 , 2893–2902 (2000).

CAS   PubMed   Google Scholar  

Wong, S., Chiu, K. Y. & Yan, C. H. Review article: Osteophytes. J. Orthop. Surg. 24 (3), 403–410 (2016).

Ye, Z. S. & Chen, N. The inverse Gaussian process as a degradation model. Technometrics 56 (3), 302–311 (2014).

Article   MathSciNet   Google Scholar  

Si, X. S., Wang, W., Hu, C. H., Zhou, D. H. & Pecht, M. G. Remaining useful life estimation based on a nonlinear diffusion degradation process. IEEE Trans. Reliab. 61 (1), 50–67 (2012).

Lin, T. & Pham, H. A two-stage intervened decision system with state-dependent random inspection mechanisms. IEEE Trans. Comput. Soc. Syst. 6 (2), 365–376 (2019).

Koo, T. K. & Li, M. Y. A guideline of selecting and reporting intraclass correlation coefficients for reliability research. J. Chiropr. Med. 15 (2), 155–163 (2016).

Merino-Muñoz, P., Pérez-Contreras, J. & Aedo-Muñoz, E. The percentage change and differences in sport: a practical easy tool to calculate. Sport Perform. Sci. Rep. 118 , 446–450 (2020).

Li, C., Luo, W., Zhang, H., Zhao, J. & Gu, R. Case report: Diffuse idiopathic skeletal hyperostosis with ossification of the posterior longitudinal ligament in the cervical spine: A rare case with dysphagia and neurological deficit and literature review. Front. Surg. 9 , 963399 (2022).

Miyamoto, K. et al. Postsurgical recurrence of osteophytes causing dysphagia in patients with diffuse idiopathic skeletal hyperostosis. Eur. Spine J. 18 (11), 1652–1658 (2009).

Ossai, C. I., Boswell, B. & Davies, I. Markov chain modelling for time evolution of internal pitting corrosion distribution of oil and gas pipelines. Eng. Fail. Anal. 60 , 209–228 (2016).

Article   CAS   Google Scholar  

Zhang, Y. Wiener and gamma processes overview for degradation modelling and prognostic (Norwegian university of science and technology, Trondheim, 2015).

Guo, J., Wang, C., Cabrera, J. & Elsayed, E. A. Improved inverse Gaussian process and bootstrap: Degradation and reliability metrics. Reliab. Eng. Syst. Saf. 178 , 269–277 (2018).

Quraishi, N. et al. Accuracy of the revised Tokuhashi score in predicting survival in patients with metastatic spinal cord compression (MSCC). Eur. Spine J. 22 (1), 21–26 (2013).

Article   PubMed Central   Google Scholar  

Lane, N. E. et al. Running, osteoarthritis, and bone density: Initial 2-year longitudinal study. Am. J. Med. 88 (5), 452–459 (1990).

Felson, D. T. et al. Osteophytes and progression of knee osteoarthritis. Rheumatology (Oxford) 44 (1), 100–104 (2005).

Vilarrasa, N. et al. Evaluation of bone mineral density loss in morbidly obese women after gastric bypass: 3-Year follow-up. Obes. Surg. 21 (4), 465–472 (2011).

Figueiredo, C. P. et al. Quantification and impact of secondary osteoarthritis in patients with anti-citrullinated protein antibody-positive rheumatoid arthritis. A&R 68 (9), 2114–2121 (2016).

CAS   Google Scholar  

Kortekaas, M. C., Kwok, W.-Y., Reijnierse, M., Huizinga, T. W. J. & Kloppenburg, M. Osteophytes and joint space narrowing are independently associated with pain in finger joints in hand osteoarthritis. Ann. Rheum. Dis. 70 (10), 1835–1837 (2011).

Mathiessen, A., Slatkowsky-Christensen, B., Kvien, T. K., Haugen, I. K. & Hammer, H. B. Ultrasound-detected osteophytes predict the development of radiographic and clinical features of hand osteoarthritis in the same finger joints 5 years later. RMD Open 3 (2), e000505 (2017).

Neogi, T., Nevitt, M. C., Ensrud, K. E., Bauer, D. & Felson, D. T. The effect of alendronate on progression of spinal osteophytes and disc-space narrowing. Ann. Rheum. Dis. 67 (10), 1427–1430 (2008).

Harada, G. K. et al. Cervical spine MRI phenotypes and prediction of pain, disability and adjacent segment degeneration/disease after ACDF. J. Orthop. Res. 39 , 657 (2021).

Lipson, S. J. & Muir, H. Vertebral osteophyte formation in experimental disc degeneration. A&R 23 (3), 319–324 (1980).

Gelse, K., Söder, S., Eger, W., Diemtar, T. & Aigner, T. Osteophyte development–molecular characterization of differentiation stages. Osteoarthr. Cartil. 11 (2), 141–148 (2003).

Ezra, D., Hershkovitz, I., Salame, K., Alperovitch-Najenson, D. & Slon, V. Osteophytes in the cervical vertebral bodies (C3–C7)—Demographical perspectives. Anat. Rec. 302 (2), 226–231 (2019).

Kasai, Y., Kawakita, E., Sakakibara, T., Akeda, K. & Uchida, A. Direction of the formation of anterior lumbar vertebral osteophytes. BMC Musculoskelet. Disord. 10 (1), 4 (2009).

Snodgrass, J. J. Sex differences and aging of the vertebral column. J. Forensic Sci. 49 (3), 458–463 (2004).

Brühschwein, A. et al. Free DICOM-viewers for veterinary medicine: Survey and comparison of functionality and user-friendliness of medical imaging PACS-DICOM-viewer freeware for specific use in veterinary medicine practices. J. Dig. Imaging 33 (1), 54–63 (2020).

Ranganathan, P., Pramesh, C. S. & Aggarwal, R. Common pitfalls in statistical analysis: Measures of agreement. Perspect. Clin. Res. 8 (4), 187–191 (2017).

Landis, J. R. & Koch, G. G. The measurement of observer agreement for categorical data. Biometrics 33 (1), 159–174 (1977).

Klaassen, Z. et al. Vertebral spinal osteophytes. Anat. Sci. Int. 86 (1), 1–9 (2011).

Bland, J. H. & Boushey, D. R. Anatomy and physiology of the cervical spine. Semin Arthritis Rheum. 20 (1), 1–20 (1990).

Bazaldúa Cruz, J. J. et al. Morphometric study of cervical vertebrae C3–C7 in a population from Northeastern Mexico. INT. J. MORPHOL. 29 , 325–330 (2011).

Chaimongkhol, T., Thiamkaew, A. & Mahakkanukrauh, P. The characteristics of osteophyte around lumbar vertebral foramina associated with spinal stenosis. Anat. Cell Biol. 52 (2), 143–148 (2019).

Matsushita, S. et al. Lifetime data analysis of disease and aging by the weibull probability distribution. J. Clin. Epidemiol. 45 (10), 1165–1175 (1992).

Almalki, S. J. & Nadarajah, S. Modifications of the Weibull distribution: A review. Reliab. Eng. Syst. Saf. 124 , 32–55 (2014).

Huang, J. et al. Degradation modeling of mid-power white-light LEDs by using Wiener process. Opt. Express 23 (15), A966-978 (2015).

Article   ADS   CAS   PubMed   Google Scholar  

Vodičar, M., Košak, R. & Vengust, R. Long-term results of surgical treatment for symptomatic anterior cervical osteophytes: A case series with review of the literature. Clin. Spine Surg. 29 (9), E482-e487 (2016).

Lu, J., Ebraheim, N. A., Yang, H., Rollins, J. & Yeasting, R. A. Anatomic bases for anterior spinal surgery: Surgical anatomy of the cervical vertebral body and disc space. Surg. Radiol. Anat. SRA 21 (4), 235–239 (1999).

Kojima, S. et al. Associations between degenerative lumbar scoliosis structures and pain distribution in adults with chronic low back pain. Healthcare (Basel, Switzerland) 11 (16), 2357 (2023).

PubMed   Google Scholar  

Shrestha, B. V. & Dhungana, S. P. Measurement of transverse and sagittal diameter of the lumbar vertebral canal in people from Western region of Nepal. Int. J. Infect. 2 , 55–58 (2013).

Klein, J. P. & Moeschberger, M. L. Survival analysis—techniques for censored and truncated data. In Statistics for biology and health 2nd edn 63–70 (Springer, New York, 2003).

Download references

This study was supported by National Natural Science Foundation of China (12201441), Sichuan Science and Technology Program (2023NSFSC1597), Med-X for informatics, Sichuan University (YGJC006), National Key Research and Development Program of China (2020YFB1711500, 2022YFC2407601), the 1·3·5 project for disciplines of excellence, West China Hospital, Sichuan University (ZYYC21004).

Author information

Authors and affiliations.

West China Biomedical Big Data Center, West China Hospital, Sichuan University, Chengdu, 610041, China

Tong Wu, Changxi Wang & Kang Li

Orthopedics Department of West China Hospital, Sichuan University, Chengdu, 610041, China

Sichuan University - Pittsburgh Institute, Sichuan University, Chengdu, 610207, China

Changxi Wang & Kang Li

You can also search for this author in PubMed   Google Scholar

Contributions

Tong Wu contributed to the conception and design, data measurement, data analysis and interpretation and was a major contributor in writing the manuscript. Changxi Wang contributed to the acquisition of data, model construction and drafting/revisions of article. Kang Li contributed to the conception and design as well as final approval of the article. All authors read and approved the final manuscript.

Corresponding authors

Correspondence to Changxi Wang or Kang Li .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Supplementary information., rights and permissions.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and permissions

About this article

Cite this article.

Wu, T., Wang, C. & Li, K. Quantitative analysis and stochastic modeling of osteophyte formation and growth process on human vertebrae based on radiographs: a follow-up study. Sci Rep 14 , 9393 (2024). https://doi.org/10.1038/s41598-024-60212-5

Download citation

Received : 28 June 2023

Accepted : 19 April 2024

Published : 24 April 2024

DOI : https://doi.org/10.1038/s41598-024-60212-5

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

By submitting a comment you agree to abide by our Terms and Community Guidelines . If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

Sign up for the Nature Briefing: AI and Robotics newsletter — what matters in AI and robotics research, free to your inbox weekly.