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Q.1 Roll a fair standard 6−sided die until a 6 appears. Given that the first 6 occurs before the first 5, find the expected number of times the die was rolled.

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dingran/quant-notes

Folders and files, repository files navigation, preparations for ds/ai/ml/quant, what is this.

A short list of resources and topics covering the essential quantitative tools for data scientists, AI/machine learning practitioners, quant developers/researchers and those who are preparing to interview for these roles.

At a high-level we can divide things into 3 main areas:

Machine Learning
Math (calculus, linear algebra, probability, etc)

Depending on the type of roles, the emphasis can be quite different. For example, AI/ML interviews might go deeper into the latest deep learning models, while quant interviews might cast a wide net on various kinds of math puzzles. Interviews for research-oriented roles might be lighter on coding problems or at least emphasize on algorithms instead of software designs or tooling.

List of resources

A minimalist list of the best/most practical ones:

quantitative research interview preparation

Machine Learning:

Course on classic ML: Andrew Ng's CS229 (there are several different versions, the Cousera one is easily accessible. I used this older version )
Book on classic ML: Alpaydin's Intro to ML link
Course with a deep learing focus: CS231 from Stanford, lectures available on Youtube
Book on deep learning: [Deep Leanring] ( https://www.deeplearningbook.org/ ) by Ian Goodfellow et al.
Book on deep laerning NLP: Yoav Goldberg's Neural Network Methods for Natural Language Processing
Hands on exercises on deep learning: Pytorch and MXNet/Gluon are easier to pick up compared to Tensorflow. For anyone of them, you can find plenty of hands on examples online. My biased recommendation is https://d2l.ai/ using MXNet/Gluon created by people at Amazon (it came from mxnet-the-straight-dope )
Course: MIT OCW 6006 link
Book: Cracking the Coding Interview link
SQL tutorial: from Mode Analytics
Practice sites: Leetcode , HackerRank
Calculus and Linear Algebra: undergrad class would be the best, refresher notes from CS229 link
Probability: Harvard Stats110 link ; book from the same professor
Statistics: Shaum's Outline link
Numerical Methods and Optimization: these are two different topics really, college courses are probably the best bet. I have yet to find good online courses for them. But don't worry, most interviews won't really touch on them.

List of topics

Here is a list of topics from which interview questions are often derived. The depth and trickiness of the questions certainly depend on the role and the company.

Under topic I try to add a few bullet points of the key things you should know.

Machine learning

e.g. assumptions, multicollinearity, derive from scratch in linear algebra form
be able to write out everything from scratch: from definitng a classficiation problem to the gradient updates
e.g. how does a tree/forest grow, on a pseudocode level
e.g. K-means, agglomerative clustering
e.g. margin-based loss objectives, how do we use support vectors, prime-dual problem
e.g. Gaussian mixture, Naive Bayes
Anomaly/outlier detection algorithms (DBSCAN, LOF etc)
Matrix factorization based models
Understand momentum, how they work, and what are the diffrences between the popular ones (RMSProp, Adgrad, Adadelta, Adam etc)
Bonus point: when to not use momentum?
Andrew's lecture notes are great, also see this
Gradient boosting
Bias vs variance, regularization
Feature selection
Model validation
Model metrics
Ensemble method, boosting, bagging, bootstraping
Feedforward networks
I really liked the miniflow project Udacity developed
In addition, be absolutely familiar with doing derivatives with matrix and vectors, see Vector, Matrix, and Tensor Derivatives by Erik Learned-Miller and Backpropagation for a Linear Layer by Justin Johnson
CNN, RNN/LSTM/GRU
Regularization in NN, dropout, batch normalization

Coding essentials

The bare minimum of coding concepts you need to know well.

array, dict, link list, tree, heap, graph, ways of representing sparse matrices
see this from brilliant.org
Traversal (BFS, DFS)
Shortest path (two sided BFS, dijkstra)
Recursion and dynamic programming

Just to spell things out

Product rule, chain rule, power rule, L'Hospital's rule,
Partial and total derivative
common function's derivatives
limits and approximations
Applications of derivatives: e.g. this
Power rule, integration by sub, integration by part
Change of coordinates
Single and multiple variables
Taylor/McLauren series for common functions
Derive Newton-Raphson
ODEs, PDEs (common ways to solve them analytically)

Linear algebra

Vector and matrix multiplication
Matrix operations (transpose, determinant, inverse etc)
Types of matrices (symmetric, Hermition, orthogonal etc) and their properties
Eigenvalue and eigenvectors
Matrix calculus (gradients, hessian etc)
Useful theorems
Matrix decomposition
Concrete applications in ML and optimization

Probability

Solving probability interview questions is really all about pattern recognition. To do well, do plenty of exercise from this and this . This topic is particularly heavy in quant interviews and usually quite light in ML/AI/DS interviews.

Event, outcome, random variable, probability and probability distributions
Permutation
Combinations
Inclusion-exclusion
Law of total probability
Expectation and variance equations
Discrete probability and stories
Continuous probability: uniform, gaussian, poisson
solving problems with this theorem and symmetry
Law of total expectation
Covariance and correlation
Independence implies zero correlation
Hash collision probability
Circle problem
Expectation of min and max and random variable
e.g. breaking sticks, meeting at the train station, frog jump (simplex)
Definition, examples (unfair coins, Monte Carlo integration)
Example question
Definition, examples (duplicated draw, near birthday problem)
Poisson from poissons
Various games, introduction of martingale
Z-score, p-value
t-test, F-test, Chi2 test (know when to use which)
Sampling methods

[Optional] Numerical methods and optimization

Computer errors (e.g. float)
Root finding (newton method, bisection, secant etc)
Interpolating
Numerical integration and difference
Solving linear equations, direct methods (understand complexities here) and iterative methods (e.g. conjugate gradient)
Matrix decompositions/transformations (e.g. QR, LU, SVD etc)
Eigenvalue (e.g. power iteration, Arnoldi/Lanczos etc)
ODE solvers (explicit, implicit)
Finite-difference method, finite-element method
Optimization topics: TBA

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Chapter 11: Quantitative Interview Techniques & Considerations

11.1 Conducting Quantitative Interviews

Much of what we learned in the previous chapter on survey research applies to quantitative interviews as well. In fact, quantitative interviews are sometimes referred to as survey interviews because they resemble survey-style question-and-answer formats. They might also be called standardized interviews . The difference between surveys and standardized interviews is that questions and answer options are read to respondents in a standardized interview, rather than having respondents complete a survey on their own. As with surveys, the questions posed in a standardized interview tend to be closed-ended. There are instances in which a quantitative interviewer might pose a few open-ended questions as well. In these cases, the coding process works somewhat differently than coding in-depth interview data. We will describe this process in the following section.

In quantitative interviews, an interview schedule is used to guide the researcher as he or she poses questions and answer options to respondents. An interview schedule is usually more rigid than an interview guide. It contains the list of questions and answer options that the researcher will read to respondents. Whereas qualitative researchers emphasize respondents’ roles in helping to determine how an interview progresses, in a quantitative interview, consistency in the way that questions and answer options are presented is very important. The aim is to pose every question-and-answer option in the very same way to every respondent. This is done to minimize interviewer effect, or possible changes in the way an interviewee responds based on how or when questions and answer options are presented by the interviewer.

Quantitative interviews may be recorded, but because questions tend to be closed-ended, taking notes during the interview is less disruptive than it can be during a qualitative interview. If a quantitative interview contains open-ended questions, recording the interview is advised. It may also be helpful to record quantitative interviews if a researcher wishes to assess possible interview effect. Noticeable differences in responses might be more attributable to interviewer effect than to any real respondent differences. Having a recording of the interview can help a researcher make such determinations.

Quantitative interviewers are usually more concerned with gathering data from a large, representative sample. Collecting data from many people via interviews can be quite laborious. In the past, telephone interviewing was quite common; however, growth in the use of mobile phones has raised concern regarding whether or not traditional landline telephone interviews and surveys are now representative of the general population (Busse & Fuchs, 2012). Indeed, there are other drawbacks to telephone interviews. Aside from the obvious problem that not everyone has a phone (mobile or landline), research shows that phone interview respondents were less cooperative, less engaged in the interview, and more likely to express dissatisfaction with the length of the interview than were face-to-face respondents (Holbrook, Green, & Krosnick, 2003, p. 79). Holbrook et al.’s research also demonstrated that telephone respondents were more suspicious of the interview process and more likely than face-to-face respondents to present themselves in a socially desirable manner.

Research Methods for the Social Sciences: An Introduction Copyright © 2020 by Valerie Sheppard is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Quant Interview Questions: How to Prepare (and What to Ask)

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If you’re an experienced quant applying for a new role in an investment bank, you might presume that you’ll be able to coast through the interview process. Not necessarily.

In the past five years, Dirk Bester, a finance quant with a PhD in Bayesian algorithmic design, has interviewed everywhere from Barclays to Blackrock, to BNP Paribas, Cumulus, G-Research, Goldman Sachs, GSA Capital, J.P. Morgan, Man Group, Oxford Asset Management, RBC, RBS, Squarepoint Capital, Two Sigma, UBS, and Winton Capital. Bester has written a detailed guide to his quant interview experiences and posted it to Github.

Whether you want to become a quant/strat, or you simply want to remain employed as one, Bester’s guide is mandatory reading.

Bester has a job but occasionally still interviews at rival banks. Other recent quant interviewees also send him the questions they’ve recently encountered. He says it’s becoming apparent that the questions being asked in quant interviews are evolving.

“There are more coding questions and coding types of brain teasers,” Bester said. “If you go for a quant finance interview today, you will be required to know a lot about algorithms and data structures. The questions you encounter are similar to the questions you get at Google or Facebook.”

Read full article here.

Common Quantitative Interview Questions

1. how would you validate a statistical model you’ve developed for predicting market trends.

Understanding the validation of a statistical model is essential, particularly when predicting market trends. It’s not just about accuracy but also about the model’s adaptability to changing conditions and the robustness of the underlying data. Candidates should be prepared to discuss their experience with statistical validation techniques and their ability to foresee potential issues.

When responding, highlight your approach to model validation, which might include split-sample testing, cross-validation, or out-of-time validation. Discuss the importance of using relevant and high-quality data, as well as the need to test the model against unseen data to gauge its generalizability. Emphasize your understanding of key performance metrics—like R-squared, RMSE, or MAE—that can help quantify the model’s accuracy. Show that you are also mindful of the model’s limitations and the importance of continuous monitoring and updating to maintain its predictive relevance over time.

Example: “ To validate a statistical model designed for predicting market trends, I would employ a combination of split-sample testing and cross-validation techniques to ensure the model’s robustness and generalizability. Initially, I would partition the dataset into training and testing subsets, using the training set to build the model and the testing set to evaluate its predictive power. This approach helps to mitigate overfitting and provides an initial assessment of the model’s performance on unseen data.

Subsequently, I would implement k-fold cross-validation, which further refines the validation process by averaging the model’s performance across different partitions of the data, offering a more comprehensive view of its predictive capabilities. Throughout this process, I would closely monitor key performance metrics such as R-squared for assessing the proportion of variance explained by the model, and RMSE or MAE for quantifying the prediction errors, adjusting the model accordingly to optimize these metrics.

It’s crucial to recognize that model validation is not a one-time task but an ongoing process. As market conditions evolve, the model should be periodically revalidated using fresh, out-of-time data to ensure its continued relevance. Moreover, I would remain vigilant about the quality of data inputs, as the predictive accuracy of the model is inherently dependent on the relevance and integrity of the data it is trained on. Continuous monitoring and updating of the model are essential to account for new patterns or structural changes in the market, ensuring the model’s long-term predictive validity.”

2. Describe an experience where you had to interpret complex data sets without clear patterns.

For roles that require a high degree of analytical rigor, candidates must be adept at interpreting ambiguous data. This question probes the candidate’s persistence, creativity, and ability to communicate complex findings to non-technical stakeholders.

When responding, candidates should outline the steps they took to analyze the data, including any specific methodologies or tools they employed. They should discuss how they identified variables of interest, dealt with missing or noisy data, and the reasoning behind the particular analytical approaches they chose. It’s also beneficial to explain how they validated their conclusions and the impact of their findings on the decision-making process. A story that conveys the complexity of the situation, the approach taken, and the eventual outcome or learning experience will demonstrate their competence in handling such challenges.

Example: “ In an experience dealing with a multifaceted data set lacking apparent patterns, I approached the analysis through a combination of exploratory data analysis (EDA) and advanced statistical techniques. Initially, I employed EDA methods, such as visualizing the data through histograms, boxplots, and scatter plots, to identify any underlying structures or anomalies. This preliminary step was crucial in formulating hypotheses about potential relationships within the data.

Subsequently, I used dimensionality reduction techniques like Principal Component Analysis (PCA) to distill the data into its most informative components. This was followed by implementing machine learning algorithms, including clustering methods like K-means and DBSCAN, to detect any subtle groupings or trends that were not immediately obvious. To address missing or noisy data, I applied imputation methods and robust statistical measures to minimize bias.

Throughout the analysis, I rigorously validated the findings using cross-validation techniques and sensitivity analysis to ensure the robustness of the results. The insights gained from this comprehensive approach led to the identification of several key drivers that were previously obscured. These findings informed strategic decisions, resulting in optimized processes and a significant improvement in the overall efficiency of the project. The experience underscored the importance of a methodical and iterative approach to data analysis, especially when faced with complex and initially inscrutable data sets.”

3. What metrics would you prioritize when assessing the financial health of a tech startup?

A tech startup’s financial health is not just about current profitability. Candidates should be ready to discuss how they evaluate a startup’s potential for growth, scalability, and other industry-specific KPIs that reflect the unique challenges of the technology sector.

When responding to this question, candidates should focus on a balanced set of metrics such as cash flow, runway, customer acquisition cost (CAC), customer lifetime value (CLV), monthly recurring revenue (MRR), and churn rate. It’s important to articulate why each metric is relevant and how it would influence strategic decisions. For instance, a high CAC relative to CLV could signal unsustainable growth, while a short runway might necessitate immediate fundraising or cost-cutting measures. Demonstrating an understanding of how these metrics interplay can show your analytical skills and your ability to guide a startup towards financial stability and growth.

Example: “ When evaluating the financial health of a tech startup, I would prioritize a mix of liquidity, profitability, and growth metrics. Cash flow is paramount as it indicates the company’s ability to sustain operations and grow without external financing. I would assess the runway by comparing the current burn rate with available cash to estimate the time before additional capital is required. This metric is critical for understanding the immediacy of fundraising needs or the necessity for cost optimization.

Simultaneously, I would analyze customer-centric metrics such as CAC and CLV to gauge the efficiency of the startup’s growth strategies. A lower CAC relative to CLV suggests a sustainable acquisition strategy and a healthy potential for long-term profitability. MRR and churn rate offer insights into the recurring revenue stability and customer retention, respectively. High MRR growth coupled with low churn rates often indicates product-market fit and a loyal customer base, which are strong indicators of a startup’s upward trajectory. These metrics collectively provide a comprehensive view of the startup’s financial performance and can inform strategic decisions to ensure both short-term survival and long-term success.”

4. Outline your process for conducting a Monte Carlo simulation in portfolio risk assessment.

Conducting a Monte Carlo simulation is a key skill for effective portfolio risk assessment. Candidates should be prepared to explain their approach to this stochastic technique and how it helps them understand the impact of risk and uncertainty in financial models.

When responding, you should clearly outline the key steps: defining a domain of possible inputs, generating inputs randomly from a probability distribution that reflects the risk or uncertainty being modeled, running a deterministic computation with those inputs, and aggregating the results to get a probability distribution of the output. It’s important to detail your experience with relevant software or programming languages, explain how you ensure the accuracy and reliability of the data, and discuss how you interpret the results to inform risk management decisions. Demonstrating an understanding of the limitations and assumptions of the model will also show depth of knowledge.

Example: “ In conducting a Monte Carlo simulation for portfolio risk assessment, I begin by defining the domain of possible inputs, which typically includes historical return distributions for each asset class, correlations, and volatilities. I ensure these inputs are based on robust statistical analysis and are reflective of current market conditions. Using these distributions, I generate a large number of random scenarios for future returns, employing a pseudo-random number generator or a quasi-random sequence for better convergence properties.

Next, I run deterministic computations for each scenario, which involves calculating the portfolio returns and risk metrics such as VaR (Value at Risk) or CVaR (Conditional Value at Risk). This is done through a simulation engine that I either code in a language like Python or R, or by using specialized software such as @RISK or Crystal Ball, depending on the complexity and the specific requirements of the task.

The aggregation of results is critical; I analyze the output distribution to assess the risk profile of the portfolio, looking at the range of outcomes and the likelihood of extreme losses. I interpret these results within the context of the portfolio’s investment strategy and risk tolerance, providing actionable insights for risk management decisions.

Throughout the process, I am mindful of the assumptions and limitations inherent in the model, such as the assumption of a static correlation structure or the potential for model risk due to input uncertainty. I conduct sensitivity analyses to understand how changes in the inputs affect the outcomes, ensuring that the final recommendations are robust and account for a range of possible market conditions.”

5. In what ways have you utilized machine learning algorithms to enhance quantitative analysis?

In modern finance, marketing, or data science, machine learning is increasingly important. Candidates should be able to discuss how they use machine learning algorithms to enhance decision-making and drive innovation.

When responding to this question, a candidate should highlight specific projects or experiences where machine learning algorithms directly impacted the analysis. Discuss the type of algorithms used—such as decision trees, neural networks, or clustering techniques—and the outcomes they achieved. Explain the problem-solving process, including how the algorithm was selected, the data preparation involved, and how the results were validated and interpreted. It’s essential to articulate the value added through these techniques, such as increased accuracy of predictions, time saved, or improved profitability.

Example: “ In a recent project, I leveraged Random Forest algorithms to enhance the predictive accuracy of a quantitative trading strategy. By integrating a multitude of decision trees, the model was trained on historical market data to identify complex patterns and interactions between various financial indicators. The ensemble approach not only improved the robustness of the predictions against overfitting but also increased the out-of-sample Sharpe ratio significantly, leading to a more profitable and risk-adjusted return profile.

Furthermore, I employed neural networks for time-series forecasting, specifically LSTM (Long Short-Term Memory) models, to capture the temporal dependencies in asset price movements. The LSTM’s ability to remember information over extended periods was crucial for understanding the momentum and mean-reversion effects in the markets. The model’s forecasts were instrumental in optimizing trade execution and managing dynamic portfolio allocations, resulting in a marked decrease in slippage costs and enhanced overall portfolio performance. Validation of the models’ effectiveness was conducted through rigorous backtesting and forward performance monitoring, ensuring that the machine learning applications provided tangible benefits to the quantitative analysis framework.”

6. Detail a scenario where you significantly improved a model’s accuracy; what changes did you make?

Model improvement is a critical skill in quantitative roles. Candidates should be ready to showcase their problem-solving skills and their ability to enhance existing systems, demonstrating a deep understanding of data science methodologies.

When responding, candidates should outline the situation clearly, describing the model in question, the specific issues with its accuracy, and the steps taken to address them. They should discuss the data analysis performed, any algorithm adjustments, feature engineering, or cross-validation techniques employed. Articulating the reasoning behind each change and how it contributed to the overall improvement in accuracy will show a thoughtful and methodical approach to model optimization.

Example: “ In one scenario, the model’s performance was hindered by overfitting due to a high dimensionality of features relative to the number of observations. To address this, I implemented a combination of feature selection and regularization techniques. I started by applying a variance threshold to remove features with minimal variance, as they were unlikely to contribute significantly to the model’s predictive power. Then, I used a recursive feature elimination process with cross-validation (RFECV) to identify and retain the most impactful features.

Subsequently, I incorporated L1 regularization (Lasso) into the model to penalize the magnitude of the coefficients and encourage sparsity, effectively reducing the complexity of the model. This regularization technique not only helped in feature selection but also improved the model’s generalization by discouraging overfitting. The changes led to a more parsimonious model with a better balance between bias and variance, resulting in a significant uplift in out-of-sample accuracy, as confirmed by a stratified K-fold cross-validation approach.”

7. Walk us through a time when you had to explain quantitative findings to a non-technical audience.

Translating complex quantitative data into digestible insights is a valuable skill. Candidates should be prepared to discuss how they make complex numerical information accessible and actionable for those without a technical background.

When responding, begin by outlining the context of the quantitative findings you were dealing with, emphasizing the audience’s lack of technical expertise. Describe the steps you took to simplify the data, such as using analogies, visual aids, or breaking down the methodology into layman’s terms. Highlight your ability to engage with the audience, asking questions to gauge their understanding, and adjusting your explanation accordingly. Conclude by reflecting on the outcome—how your communication facilitated a better understanding and led to informed decisions or actions.

Example: “ In a recent project, I was tasked with presenting the results of a complex regression analysis that identified key factors affecting customer retention rates. The audience comprised department heads with varied backgrounds, most of whom lacked statistical training. To bridge the gap, I distilled the findings into the core message: which factors were most influential and by how much. I used a simple analogy, comparing the statistical model to a recipe where each ingredient’s quantity affects the final taste, to convey the idea of coefficients impacting the outcome.

I supplemented this with a clear, intuitive visualization—a bar chart showing the relative importance of each factor, avoiding technical jargon like “p-values” or “confidence intervals.” During the presentation, I engaged with the audience by asking if the visual representation made sense and if they could relate the findings to their experiences. This interaction helped me tailor the explanation further, ensuring clarity.

The outcome was a productive discussion that led to actionable strategies. The department heads grasped the key takeaways and were able to brainstorm targeted initiatives to improve customer retention, demonstrating that the quantitative findings had been successfully communicated and understood.”

8. Which quantitative research publication has most influenced your work and why?

The influence of quantitative research on your work can demonstrate scholarly rigor and breadth of knowledge. Candidates should be ready to discuss how they integrate complex data from research publications into their thought process.

To respond effectively, you should select a publication that is not only reputable but also closely related to your field of work or the position you are applying for. Discuss the publication’s findings or methodologies and clearly articulate how it has shaped your approach to data analysis or problem-solving. Be prepared to explain the publication’s impact on your thought process or professional practices, providing concrete examples of how you have applied its insights to your work.

Example: “ The publication that has most influenced my work is “The Econometrics of Financial Markets” by John Y. Campbell, Andrew W. Lo, and A. Craig MacKinlay. This seminal work provided a comprehensive framework for analyzing financial markets using econometric methods, which has been invaluable in both my approach to modeling market behaviors and in developing predictive analytics for asset pricing.

The rigorous treatment of topics such as time-series analysis, the Capital Asset Pricing Model (CAPM), and the Efficient Market Hypothesis (EMH) within this text has been particularly impactful. It has honed my ability to critically evaluate model assumptions and to integrate econometric techniques with machine learning algorithms for enhanced forecasting accuracy. For instance, leveraging the concepts from this publication, I’ve successfully implemented vector autoregression models to predict stock prices, accounting for the dynamic interplay between multiple economic indicators. The book’s empirical focus also encouraged a data-driven mindset that ensures the robustness and validity of my analyses, a principle that I’ve upheld in all my quantitative endeavors.”

9. What approach do you take to ensure compliance with data protection regulations during analysis?

Data protection is a critical concern, especially when handling sensitive information. Candidates should be prepared to discuss their knowledge of data protection laws and how they incorporate compliance into their daily work processes.

To respond effectively, outline specific steps you take to ensure compliance, such as anonymizing data, implementing access controls, and conducting regular audits. You may also mention staying updated on the latest regulations, attending training sessions, and collaborating with legal or compliance teams. It’s essential to demonstrate a proactive approach to data protection, showcasing that you prioritize ethical considerations alongside analytical rigor.

Example: “ In ensuring compliance with data protection regulations during analysis, my approach is both proactive and systematic. Initially, I conduct a thorough data inventory to classify the sensitivity of the data sets and understand the specific compliance requirements associated with each. Following this, I employ data minimization techniques, ensuring that only the necessary data for the analysis is processed, and anonymize or pseudonymize personal data to mitigate any privacy risks.

I implement robust access controls, restricting data access to authorized personnel and applying the principle of least privilege. To maintain the integrity of these measures, I regularly perform audits and monitor data access logs to detect any unauthorized attempts or non-compliance issues. Furthermore, I stay abreast of the evolving regulatory landscape by attending advanced training sessions and actively engaging with legal or compliance teams to ensure that my analysis practices are aligned with the latest data protection standards. This ongoing dialogue allows for the anticipation of regulatory changes and the seamless integration of new compliance requirements into the analytical workflow.”

10. Share an example of how you’ve used hypothesis testing to inform a business decision.

Hypothesis testing is a fundamental statistical method in decision-making. Candidates should be ready to explain how they conduct hypothesis tests and how they use the results to inform business strategies.

When responding to this question, articulate a clear scenario where hypothesis testing was central to resolving a business question or challenge. Describe the hypothesis you tested, the data you used, and the statistical method you employed. Most importantly, discuss the results of the test and how you interpreted them to make a well-informed business decision. Highlight how your analysis had a tangible impact on the business, such as improving a product, optimizing a process, or enhancing customer satisfaction. This will showcase your ability to bridge the gap between data analysis and practical business outcomes.

Example: “ In a recent project, we were faced with the challenge of optimizing the pricing strategy for a new product line. The hypothesis was that by increasing the price point by 10%, we would not significantly affect the sales volume, aiming to increase overall revenue without deterring customers. To test this hypothesis, we conducted an A/B test, where Group A was exposed to the current pricing and Group B to the increased price.

Utilizing a t-test for the difference in means between the two groups, we analyzed sales data over a four-week period. The results indicated that there was no statistically significant difference in sales volume (p > 0.05), suggesting that the price increase did not negatively impact sales. Based on this analysis, we advised the business to implement the new pricing strategy across all markets, which ultimately led to a 9% rise in revenue without a drop in sales volume. This decision was further supported by monitoring post-implementation sales data, confirming the sustainability of the new pricing model.”

11. When building predictive models, how do you address multicollinearity in your independent variables?

Multicollinearity can complicate the interpretation of predictive models. Candidates should be prepared to discuss how they diagnose and resolve issues of multicollinearity to ensure the accuracy of their models.

When responding to this question, you should demonstrate a clear understanding of the concept of multicollinearity and its implications for predictive modeling. Outline the methods you employ to detect multicollinearity, such as examining correlation matrices or variance inflation factors (VIF). Then, explain the strategies you apply to address it, which might include removing highly correlated predictors, combining them into a single variable, or using regularization techniques like Lasso or Ridge regression that can penalize coefficients for correlated variables and reduce overfitting. Your answer should convey a methodical and informed approach to maintaining the integrity of your predictive models.

Example: “ To address multicollinearity among independent variables in predictive modeling, I first employ diagnostic tools like correlation matrices and Variance Inflation Factor (VIF) thresholds to detect the presence and severity of multicollinearity. A VIF above 5 or 10, depending on the context and domain-specific thresholds, usually signals a multicollinearity issue that needs to be addressed.

Once identified, I tackle multicollinearity using a combination of domain knowledge and statistical techniques. If two variables are highly correlated and one is deemed less important based on domain knowledge, I might remove it to reduce redundancy. Alternatively, I might combine correlated variables into a single feature through principal component analysis or factor analysis, which preserves the information while mitigating the multicollinearity effect. In situations where variable selection is crucial, I might apply regularization methods like Lasso regression, which is designed to perform both variable selection and parameter shrinkage, effectively handling multicollinearity by penalizing the coefficients of correlated predictors and driving some to zero. This approach ensures the model remains robust and generalizable without compromising the predictive power.”

12. Describe a situation where you integrated qualitative insights into your quantitative analysis.

Blending quantitative and qualitative insights can lead to more effective analysis. Candidates should be ready to discuss how they incorporate qualitative factors like consumer behavior and market trends into their data analysis.

When responding, candidates should recount a specific scenario where they identified the need for qualitative input to complement their quantitative findings. They might discuss how they gathered qualitative data, such as customer feedback or expert opinions, and the methods used to integrate this information with quantitative results. The aim is to illustrate their thought process, the challenges they faced, and how the integration of both data types led to a more informed decision or recommendation. It’s important to convey adaptability, analytical depth, and a recognition that numbers tell a part of the story, but not the whole.

Example: “ In a recent analysis of customer churn, I recognized that while the quantitative data highlighted trends in cancellations, it didn’t provide the underlying reasons for customer dissatisfaction. To address this gap, I conducted a series of in-depth interviews and focus groups to gain qualitative insights. I used thematic analysis to identify common reasons for churn that weren’t apparent in the numerical data, such as perceived value and customer service interactions.

Integrating these qualitative insights with the quantitative data involved creating a framework that allowed for a holistic view of the factors influencing churn. By overlaying sentiment analysis on the churn rate across different customer segments, I was able to pinpoint specific service touchpoints that required improvement. This mixed-methods approach not only enriched the analysis but also led to targeted strategies that reduced churn by 15% over the next quarter. The process highlighted the importance of blending qualitative nuances with quantitative rigor to derive actionable intelligence.”

13. How do you determine the right sample size for a statistically significant survey study?

Determining the right sample size is crucial for survey studies. Candidates should be prepared to discuss their approach to calculating sample size and ensuring the reliability and validity of their research findings.

When responding to this question, one should discuss the factors that influence sample size determination, such as the desired confidence level, the margin of error, the population size, and the expected effect size or variability in the data. It’s important to articulate a systematic approach to sample size calculation, perhaps referencing specific statistical formulas or software used to make these estimations. Offering an example from past experience where you determined sample size for a study can showcase your practical application of these concepts, along with any lessons learned from the outcome of that research.

Example: “ Determining the right sample size for a statistically significant survey study hinges on balancing precision and practicality. Initially, I establish the desired confidence level, typically 95% for conventional standards, which sets the Z-score used in calculations. The margin of error, reflecting the maximum expected difference between the sample statistic and the population parameter, is chosen based on the level of precision required for the study’s objectives. For a general population survey, a 5% margin is common, but this might be tightened for more sensitive analyses.

I then consider the population size, especially relevant when dealing with finite populations, to apply the finite population correction if necessary. The expected effect size or variability in the data, informed by prior research or pilot studies, guides my estimation of the standard deviation, which is crucial for calculating the required sample size. Utilizing formulas for sample size calculation or software like G*Power or nQuery, I incorporate these parameters to yield a sample size that balances statistical rigor with resource constraints. For instance, in a previous study estimating the prevalence of a health behavior, I used a conservative estimate of variability to ensure the sample size was sufficient to detect even small prevalence rates, which was vital for the subsequent health intervention planning. The study’s success underscored the importance of meticulous sample size calculation in achieving meaningful and actionable results.”

14. What is your strategy for staying current with advancements in quantitative methods and tools?

Keeping up with the latest trends and tools is essential in the quantitative field. Candidates should be ready to discuss their commitment to continuous learning and how they stay current with new technologies and methodologies.

When responding to this question, a candidate should highlight their proactive approach to professional development. This could include subscribing to industry journals, attending workshops and conferences, participating in online courses, or being part of professional forums and networks. Demonstrating a systematic approach to integrating new knowledge and tools into one’s work routine will reassure employers that the candidate is both technically proficient and strategically prepared to contribute to the organization’s success.

Example: “ To stay abreast of the latest advancements in quantitative methods and tools, I maintain a disciplined approach to continuous learning and professional development. I regularly subscribe to and read key industry journals such as the “Journal of Quantitative Analysis” and “Quantitative Finance,” which provide insights into cutting-edge research and applications. Additionally, I leverage online platforms like Coursera and edX to enroll in relevant courses that sharpen my skills and deepen my understanding of new techniques.

I also prioritize attending annual conferences and workshops, which not only offer exposure to innovative methodologies but also provide opportunities to engage with thought leaders and practitioners in the field. This engagement is complemented by active participation in professional forums and networks, such as the Quantitative Finance Professional Group on LinkedIn, where I can exchange ideas and discuss practical challenges with peers. By systematically integrating new knowledge into my existing framework, I ensure that my quantitative analysis remains robust, relevant, and aligned with the state-of-the-art in the field.”

15. Provide an instance where you had to adapt your analytical approach due to unexpected data limitations.

Agility in problem-solving is key when data is incomplete or unexpected. Candidates should be prepared to discuss how they handle such challenges while maintaining data integrity and accuracy.

When responding, recount a specific scenario where you encountered data limitations, emphasizing how you evaluated the situation, identified the constraints, and decided on an alternative approach. Outline the steps you took to ensure the new approach still provided valuable insights, and if possible, share the outcome of your analysis. This will illustrate your adaptability, problem-solving skills, and commitment to delivering results despite challenges.

Example: “ In a project where I was modeling customer churn, I encountered a situation where the historical data was far less comprehensive than initially anticipated. The data lacked granularity on customer interactions and product usage, which were critical for building a robust predictive model. I quickly realized that traditional regression techniques would not yield the predictive power needed due to the sparsity of data.

To adapt, I pivoted to a survival analysis approach, leveraging what we did have—customer tenure and churn events. This allowed me to model churn risk over time without the need for detailed interaction data. I also employed bootstrapping methods to enhance the stability of the model given the limited dataset. By focusing on the time-to-event aspect, I could still provide the business with meaningful insights into customer retention patterns and identify key time intervals for intervention. The outcome was a strategic shift in customer engagement, informed by the survival model, which ultimately led to a measurable reduction in churn.”

16. In your view, what is the biggest challenge facing quantitative analysts in the finance sector today?

The finance sector’s constant evolution requires quantitative analysts to be adaptable. Candidates should be ready to discuss how they integrate new data sources and technologies into their financial models.

When responding to this question, candidates should articulate their understanding of the current financial landscape, highlighting specific challenges such as the need for real-time data analysis, cybersecurity threats, or the implications of global economic events. They should also discuss their approach to continuous learning and adaptation, perhaps by mentioning their engagement with new analytical tools, professional development courses, or forums that discuss emerging trends in finance. Demonstrating awareness of these challenges and a proactive approach to overcoming them will show interviewers that the candidate is both informed and forward-thinking.

Example: “ The most pressing challenge for quantitative analysts in the finance sector today is the rapid evolution of machine learning and artificial intelligence technologies. These advancements are constantly reshaping the landscape of data analysis and predictive modeling. The integration of AI into quantitative finance not only requires analysts to maintain a robust understanding of new algorithms and computational methods but also to ensure that these tools are employed without introducing systemic risk. As financial markets become increasingly complex and automated, the potential for AI-driven strategies to create feedback loops or unforeseen market dynamics grows, necessitating a deep understanding of both the financial instruments involved and the underlying technology.

To navigate this challenge, I actively engage with the latest research and developments in AI and machine learning, applying a critical eye to how these innovations can be leveraged responsibly in financial contexts. This involves not only staying abreast of the technical aspects but also understanding the broader economic implications and regulatory frameworks. By maintaining a dialogue with industry peers through forums and professional development opportunities, I ensure that my approach to quantitative analysis is both cutting-edge and grounded in a risk-aware perspective.”

17. How do you balance the need for timely results with the rigor of thorough quantitative analysis?

Delivering accurate data analysis promptly is essential in quantitative roles. Candidates should be prepared to discuss how they balance the need for speed with the need for precision in their work.

When responding to this question, candidates should articulate a structured approach to quantitative tasks that showcases their time management skills. They could mention specific methodologies or tools they use to streamline analysis, such as automating repetitive tasks, employing statistical software, or breaking projects into phases to allow for preliminary insights to be shared in advance of full analysis completion. It’s also important to communicate an understanding of when depth is crucial versus when an executive summary will suffice, and to provide examples from past experiences where this balance was successfully achieved.

Example: “ Balancing timeliness with rigor in quantitative analysis is a matter of prioritizing efficiency without compromising on the integrity of the results. I employ a phased approach, where I initially focus on exploratory data analysis to quickly identify patterns, outliers, and potential areas of interest. This allows for the generation of preliminary insights that can guide subsequent, more detailed investigations. I leverage statistical software and scripting to automate routine data processing tasks, which significantly cuts down on the time required for data cleaning and manipulation.

When deeper analysis is necessary, I judiciously apply sampling techniques or model-based approaches to extrapolate findings without having to crunch every data point, which can be time-consuming. I’m always conscious of the trade-off between accuracy and speed, and I communicate these considerations transparently with stakeholders. For instance, in a past project involving predictive modeling, I used ensemble methods to quickly generate a robust model, then iteratively refined it as time allowed, ensuring that stakeholders had a functional tool at their disposal while I worked on enhancing its precision.”

18. Illustrate how you would conduct a cost-benefit analysis on implementing new technology within an organization.

Conducting a cost-benefit analysis requires strategic thinking. Candidates should be ready to discuss how they evaluate the tangible and intangible factors that contribute to an organization’s ROI.

To respond, you should outline a structured approach, starting with defining the scope of the analysis and identifying all associated costs, such as purchase price, implementation expenses, training, and maintenance. Next, articulate how you would measure the anticipated benefits, which might include increased efficiency, revenue growth, or improved customer satisfaction. Explain how you would consider the time value of money in your analysis, possibly utilizing net present value (NPV) or internal rate of return (IRR) calculations. Then, discuss how you would weigh these factors against each other, possibly including a scenario analysis to account for uncertainty. Finally, describe how you would present your findings, emphasizing clear communication of the potential risks and rewards to stakeholders.

Example: “ In conducting a cost-benefit analysis for new technology implementation, I would begin by meticulously defining the scope and identifying all relevant costs, including upfront capital expenditure, operational costs, and any indirect costs such as potential downtime during the transition. I would then forecast the tangible benefits, such as productivity gains and cost savings, as well as intangible benefits like customer satisfaction and competitive advantage, quantifying these where possible.

To assess the financial viability, I would calculate the net present value (NPV) of the project, ensuring that future cash flows are discounted appropriately to reflect the time value of money. I would also consider the internal rate of return (IRR) to understand the project’s profitability relative to the cost of capital. To address uncertainty, I would perform sensitivity and scenario analyses, varying key assumptions to gauge the robustness of the project under different conditions. My findings would be synthesized into a clear, data-driven recommendation, articulating the strategic rationale and potential impact on the organization’s bottom line, ensuring that decision-makers are fully informed of the risks and potential returns.”

19. What techniques do you apply to forecast demand for a product with little historical data available?

Forecasting demand with limited historical data is challenging. Candidates should be prepared to discuss their approach to making informed predictions in such scenarios.

When responding, emphasize your systematic approach to the problem. You might start by explaining how you gather qualitative insights from market research, expert opinions, and competitive analysis to form initial hypotheses. Then, detail how you use quantitative methods such as time series analysis, regression models, or even newer techniques like machine learning to extrapolate from available data. Highlight any specific tools or software you are proficient with, and describe a past scenario where you successfully forecasted under similar constraints, focusing on the process and the outcome.

Example: “ To forecast demand for a product with limited historical data, I employ a combination of qualitative assessments and exploratory quantitative methods. Initially, I gather insights through market research, including customer surveys, focus groups, and Delphi method sessions with industry experts to establish a foundational understanding of potential demand drivers and market dynamics. Concurrently, I perform a competitive analysis to benchmark against similar products or services, which can provide valuable clues about the market’s response to analogous offerings.

Quantitatively, I lean towards employing Bayesian methods that allow for the incorporation of prior knowledge and expert opinion into the statistical model, which is particularly useful when data is scarce. This approach, coupled with bootstrapping techniques, helps in constructing confidence intervals around forecasts even with small datasets. Additionally, I utilize machine learning algorithms, such as random forests or gradient boosting machines, which can capture complex nonlinear relationships and interactions between variables, even when historical data is not robust. Tools like R or Python, with their extensive libraries for statistical and machine learning methods, are instrumental in this process.

A specific instance where this approach proved successful was when forecasting the demand for a niche technological product entering a new market. By synthesizing market research insights with a Bayesian model that integrated expert assessments, I was able to provide a demand estimate that was later validated to be within 10% of actual sales in the first quarter post-launch. This accuracy was pivotal in optimizing the supply chain and marketing strategy, ultimately contributing to a successful product introduction.”

20. Tell us about a project where you leveraged network analysis to uncover insights into customer behavior.

Network analysis can reveal strategic business insights. Candidates should be ready to discuss how they use network analysis to inform decisions on marketing, product development, and customer engagement.

When responding to this question, candidates should outline a specific project they worked on, detailing the objectives, the nature of the data, the network analysis techniques employed, and the software or tools used. It’s crucial to articulate the unique customer behavior insights gained from the analysis and how these insights led to actionable strategies or decisions within the project. Quantify the impact whenever possible, such as increased customer retention rates or improved product recommendations, to underscore the value of your analytical contributions.

Example: “ In a recent project, the objective was to understand the interconnectedness of customers within a subscription-based service to identify influential users and predict churn. Utilizing a combination of transactional data and social interaction metrics, I constructed a weighted undirected graph where nodes represented customers and edges signified the frequency and quality of interactions between them.

Employing network analysis techniques such as centrality measures and community detection algorithms, I identified clusters of highly interconnected users and pinpointed those with high eigenvector centrality as potential influencers. These insights were instrumental in developing targeted retention strategies. By engaging these key influencers with personalized incentives, we observed a 15% reduction in churn rate within their respective clusters. Additionally, the analysis of structural holes within the network revealed opportunities for cross-selling, leading to a 10% increase in uptake of additional services among identified bridging users. The project leveraged Python’s NetworkX library for the analysis, which facilitated a robust and scalable examination of the network’s properties.”

1) Heard on The Street: Quantitative Questions from Wall Street Job Interviews - Timothy Falcon Crack

Heard on the Street is a classic Wall Street interview Q&A book. Many of the questions you will hear in real interviews will have been "borrowed" or modified from this book. In fact, many interviewers want to see that you've done the necessary "grunt work" just by reading through it! The book contains five main sections - Quantitative/Logical Questions, Derivatives Questions, Financial Economics Questions, Statistics Questions and Non-Quantitative Questions. Each of these five areas is incredibly important for the aspiring quant. The questions are by no means straightforward - there are some particularly challenging statistics and quantitative questions. Make sure to study this book thoroughly before taking an interview on the 'Street.

2) Frequently Asked Questions in Quantitative Finance - Paul Wilmott

Paul Wilmott is known for his stimulating, engaging and humourous works on quantitative finance. He has also applied his talents to writing an interview Q&A book, in Frequently Asked Questions in Quantitative Finance . So, what does the book cover and is it worth an investment, especially if you already own Paul Wilmott on Quantitative Finance ? Its main advantage is that it provides both a short and long version of an answer to a particular 'FAQ'. This means that the book can be scanned rapidly, if you wish to gain a quick insight into certain topics. Talking of topics, the book covers predominantly Stochastic Calculus, Geometric Brownian Motion, Black-Scholes as well as Volatility Modelling and the CAPM. This book is definitely one for the shelf at home, prior to heading into the interview room.

3) Quant Job Interview Questions And Answers - Mark S. Joshi, Nick Denson, Andrew Downes

Some time ago, Mark Joshi wrote a fantastic PDF article about getting a job in quantitative finance and what to expect prior to, and during, an interview. This book is a significant expansion and elaboration on that article, with the inclusion of more technical questions and further discussions on the "soft" questions. The book covers the interview process, options pricing, probability, rates, numerical methods, general mathematics, C++ and brainteasers. It contains many questions not seen before in other books and is significantly more up to date than some. It was Joshi's first attempt at self-publishing and the experiment worked very well. Pick this up if you're looking for help with different technical questions or more insight into what the interview, and subsequent job, will be like.

4) A Practical Guide To Quantitative Finance Interviews - Xinfeng Zhou

Zhou's book is another self-published work (in the vein of Joshi). Be aware that it has been criticised on the basis of less-than-professional editing and formatting. However, leaving those quirks aside, it does contain more than 200 fantastic questions on topics that a quant will likely be asked about in interview. The book covers a broad range of categories such as calculus/linear algebra, brainteasers (many varieties here!), probability and combinatorics, stochastic processes, finance/options and numerical methods. If you still think you need more practice after the aforementioned works by Crack, Wilmott and Joshi, Zhou will provide that practice!

5) Starting Your Career as a Wall Street Quant: A Practical, No-BS Guide to Getting a Job in Quantitative Finance - Brett Jiu

Dr Jiu's book is a little different from the four mentioned above. It contains a more philosophical approach to obtaining a quantitative role. He is keen to stress that the market has changed significantly since the 2007/2008 crisis, with more roles now being available in funds and less from banks. The other major shift described is that of the necessity to have extremely strong programming skills, particularly C++. The first four chapters discuss a quant career as well as how to begin hunting for one, finally concluding with tips for interview. The next set of chapters encourage one to self-learn and provide detail on how to go about achieving that, while at different stages of your career. Finally, Dr Jiu discusses "real world" skills, such as internship opportunities or networking. This is a great book to complement the other four and QuantStart highly recommends purchasing a copy.

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Career Advice

Common Interview Questions for Quantitative Analysts

Quantitative analysts develop high-level trading and risk management strategies using complex algorithms and mathematical equations. This is a career for the top 1% in numerical proficiency. If you were always the math whiz in class, even at the post-graduate level, a lucrative career in quantitative analysis could be in your future.

Most quantitative analysts have at least a master's degrees, with many carrying doctorates in fields like mathematics or statistics. Indeed, quants' most common college majors are mathematics, economics and statistics, with strong academic performance paramount for getting a foot in the door.

Assuming you have the credentials to get an interview, you need to shine, because your competition is going to be elite. Anticipating the most likely questions lets you practice delivering winning responses with confidence.

Key Takeaways

Quantitative analysts, or 'quants', perform the number crunching and statistical analysis for companies in all sectors of the economy.
Computer skills are a key, and you should know your way around several of the popular and current programming languages.
You should also know how to build and evaluate statistical models as well as have a good handle on your math skills.
In a job interview, be prepared to be quizzed on your background and qualifications in each of these domains.

Computer Skills and Programming Languages

Apart from math skills, computer skills are the next most important thing to have as a quantitative analyst. Trading operations, in particular, need quantitative analysts who can program complex algorithms into their trading software. Algorithm-based computerized trading, in particular high-frequency trading (HFT), in which securities are bought and sold electronically at a frenetic pace, has replaced much of the manual trading on Wall Street. The firms with the fastest, most effective algorithms reap the most profits.

As of 2022, the most valuable computer language to have mastered is Python. However, expertise in SQL, Java, C++, and even advanced Excel can add value, so highlight all of the computer knowledge you possess.

The interviewer wants to see that you have applied your knowledge not only in theory but in practice. He also wants to assess your models themselves and determine whether your thought process aligns with what the company is looking for. Even if you have a different trading philosophy than your interviewer, this is not always a bad thing, particularly if you can demonstrate where your models have enjoyed a track record of producing big gains.

When you get this question, the most important thing is how clearly and confidently you explain your past accomplishments. A bit of salesmanship goes a long way. Before your interview, prepare by making a list of your biggest modeling and forecasting accomplishments, and then practice describing them to an interviewer.

Mastery of statistical software packages like Stata, SPSS, and/or R will be helpful.

At some point during the interview, you are going to feel like you are back in school. Expect an impromptu math question. The interviewer wants to see you employ your high-level quantitative skills to reason through it as quickly as possible. They might ask you a probability question about a stock trade, or possibly a variation of the old handshake riddle: How many people are at a party if 100 handshakes take place and everyone shakes hands with everyone else?

The possibilities for questions are almost endless, making it difficult to prepare for anything specific. Get plenty of sleep the night before your interview, and go in focused and ready to think on your feet. Trust that since you qualified to interview for a quantitative analyst position, your math skills are good enough to handle whatever the interviewer might throw your way.

Quantitative analyst is a high-level job, so ask high-level questions when the interviewer prompts you. Probe the company's trading philosophy, ask about the technology it employs, and determine what tools you will have at your disposal. Show the interviewer that you mean business and that you want to be equipped to make a difference for your new employer from day one.

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Quantitative Interview Preparation Guide

5 minute read

May 05, 2018 5 minute read

What is this

A short list of resources and topics covering the essential quantitative tools for Data Scientists, Machine Learning Engineers/Scientists, Quant Developers/Researchers and those who are preparing to interview for these roles.

At a high-level we can divide things into 3 main areas:

Machine Learning
Math (calculus, linear algebra, probability, etc)

List of resources

A minimalist list of the best/most practical ones:

Machine Learning:

Course on classic ML: Andrew Ng’s CS229 (there are several different versions, the Cousera one is easily accessible. There is also an older version recorded at Stanford)
Book on classic ML: Alpaydin’s Intro to ML link
Course with a deep learing focus: CS231 from Stanford, lectures available on Youtube.

If you are just breaking into the field I think the above are enough, stop there and move on to other areas of preparation. Here are a few very optional items, mostly on deep learning, in case you have more time: Overview book on deep learning: Neural Networks and Deep Learning by Michael Nielson. Amazing book on deep laerning for NLP: Neural Network Methods for Natural Language Processing by Yoav Goldberg Pick one of those Udacity nanodegrees on deep learning / self-driving cars to get some hands on experience with deep learning frameworks (Tensorflow, Pytorch, MXNet)

Course: MIT OCW 6006 link
Book: Cracking the Coding Interview link
Practice sites: Leetcode , HackerRank
SQL tutorial: from Mode Analytics
Calculus and Linear Algebra: undergrad class would be the best, refresher notes from CS229 link
Probability: Harvard Stats110 link ; book from the same professor.
Statistics: Shaum’s Outline link .
[Optional] Numerical Methods and Optimization: these are two different topics really, college courses are probably the best bet. I have yet to find good online courses for them. But don’t worry, most interviews won’t really touch on them.

List of topics

Here is a list of topics from which interview questions are often derived. The depth and trickiness of the questions certainly depend on the role and the company.

Under topic I try to add a few bullet points of the key things you should know.

Machine learning

Linear regression - e.g. assumptions, multicollinearity, derive from scratch in linear algebra form
be able to write out everything from scratch: from definitng a classficiation problem to the gradient updates
Decision trees/forest - e.g. how does a tree/forest grow, on a pseudocode level
e.g. K-means, agglomerative clustering
e.g. margin-based loss objectives, how do we use support vectors, prime-dual problem
e.g. Gaussian mixture, Naive Bayes
Anomaly/outlier detection algorithms (DBSCAN, LOF etc)
Matrix factorization based models
Gradient descent, SGD and other popular variants - Understand momentum, how they work, and what are the diffrences between the popular ones (RMSProp, Adgrad, Adadelta, Adam etc) - Bonus point: when to not use momentum?
EM algorithm - Andrew’s lecture notes are great, also see this
Gradient boosting
Bias vs variance, regularization
Feature selection
Model validation
Model metrics
Ensemble method, boosting, bagging, bootstraping
Feedforward networks
I really liked the miniflow project Udacity developed
In addition, be absolutely familiar with doing derivatives with matrix and vectors, see Vector, Matrix, and Tensor Derivatives by Erik Learned-Miller and Backpropagation for a Linear Layer by Justin Johnson
CNN, RNN/LSTM/GRU
Regularization in NN, dropout, batch normalization

Coding essentials

There are a lot of resources online on how to prepare for this, some are already listed in the resources section. I think the key thing is to pick a language and know it really well. For example, for Python, if you claim you know it well and have used in some non-trivial code base. I’ll assume you know why abstract base class exists, how decorator works in general and what @property means along with a few language-specific data structures (like OrderedDict , deque , defaultdict and etc).

The bare minimum of coding concepts you need to know well.

array, dict, link list, tree, heap, graph, ways of representing sparse matrices
see this from brilliant.org
I think in real life you’ll most likely never implement a sorting algorithm, but I think quick sort is very cool and quick select / partition is used in many other places, so take a look.
Traversal (BFS, DFS)
Shortest path (two sided BFS, dijkstra)

Just to spell things out

Product rule, chain rule, power rule, L’Hospital’s rule,
Partial and total derivative
common function’s derivatives
limits and approximations
Applications of derivatives: e.g. this
Power rule, integration by sub, integration by part
Change of coordinates
Single and multiple variables
Taylor/McLauren series for common functions
Derive Newton-Raphson
ODEs, PDEs (common ways to solve them analytically)

Linear algebra

Vector and matrix multiplication
Matrix operations (transpose, determinant, inverse etc)
Types of matrices (symmetric, Hermition, orthogonal etc) and their properties
Eigenvalue and eigenvectors
Matrix calculus (gradients, hessian etc)
Useful theorems
Matrix decomposition
Concrete applications in ML and optimization

Probability

Event, outcome, random variable, probability and probability distributions
Permutation
Combinations
Inclusion-exclusion
Law of total probability
Expectation and variance equations
Discrete probability and stories
Continuous probability: uniform, gaussian, poisson
solving problems with this theorem and symmetry
Law of total expectation
Covariance and correlation
Independence implies zero correlation
Hash collision probability
Circle problem
Expectation of min and max and random variable
e.g. breaking sticks, meeting at the train station, frog jump (simplex)
Definition, examples (unfair coins, Monte Carlo integration)
Example question
Definition, examples (duplicated draw, near birthday problem)
Poisson from poissons
Various games, introduction of martingale
Z-score, p-value
t-test, F-test, Chi2 test (know when to use which)
Sampling methods

[Optional] Numerical methods and optimization

Computer errors (e.g. float)
Basic root finding (newton method, bisection, secant etc)
Interpolating
Numerical integration and difference
Solving linear equations, direct methods (understand complexities here) and iterative methods (e.g. conjugate gradient), maybe BFGS
Matrix decompositions/transformations (e.g. QR, Givens, LU, SVD etc)
Eigenvalue solvers (e.g. power iteration, Arnoldi/Lanczos etc)
ODE solvers (explicit, implicit)
Finite-difference method, finite-element method
Optimization topics: linear programming (and convex opt in general), calculus of variations

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Quant Interview Questions

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Quantitative Research Analyst Interview Preparation

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Read this free guide below with common Quantitative Research Analyst interview questions

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Pay attention to your body language.

Positive body language can convey confidence and enthusiasm. Remember to sit up straight, smile, and maintain good eye contact.

1. What knowledge and experience do you have in regression analysis?

Regression analysis refers to a statistical technique used to identify the relationship between variables. Here, the interviewer wants to know if you have knowledge about the regression analysis techniques and its applications. You can explain the statistical models you are familiar with and provide an example of how you apply regression analysis to solve problems.

2. How do you handle missing data in a data set?

When dealing with quantitative data, missing data is not uncommon. It is essential to have a strategy in place for handling missing data effectively. You can discuss techniques such as mean imputation, maximum likelihood, and Expectation-Maximization (EM) method for handling missing data.

3. What is your experience in data visualization tools such as Tableau and Excel?

As a quantitative research analyst, you must have knowledge of data visualization and dashboarding tools. Your knowledge on data visualization tools is essential when presenting insights to decision-making teams visually. You can explain your experience using data visualization tools and provide an example of how you have used visualization to present your findings.

4. Can you discuss a quantitative research project you have worked on in the past?

The interviewer may want to know about a quantitative research project you have worked on in the past to understand your experience and approach to problem-solving. You can provide a brief overview of a project you worked on, discuss how you approached the project, and what techniques you used to analyze the data.

5. How do you stay up-to-date with new statistical modeling techniques?

As a quantitative research analyst, you need to keep up-to-date with new statistical modeling techniques that will help you improve your analysis. You can discuss your methods of staying up-to-date with industry news and publications such as academic journals, e-books, and webinars.

6. Can you explain statistical concepts such as mean, median, and standard deviation?

The interviewer may ask a question on statistical concepts such as mean, median, and standard deviation to test your knowledge of basic statistics. You can explain each concept in simple terms, provide an example of how you have used each concept in the past, and the context in which you would use them.

7. Can you discuss a time when you had to solve a complex quantitative problem?

The interviewer may want to know your approach to problem-solving when dealing with quantitative data. You can describe how you approached a complex quantitative problem, the challenges you faced, and how you overcame them.

8. Can you discuss your experience working with large data sets?

Large data sets can be challenging to work with, and the interviewer may want to know about your experience working with them. You can discuss the tools and techniques you have used to handle large data sets, such as Hadoop, Spark, and other Big Data technologies.

9. How do you ensure data privacy and security in your analysis?

Data security and privacy are critical when working with quantitative data. The interviewer may want to know your approach to data protection. You can explain your methods of ensuring data privacy and discuss the role of the General Data Protection Regulation (GDPR) in data privacy.

10. Can you discuss your experience working collaboratively on a quantitative research project?

The interviewer may want to know about your experience working collaboratively with others on a quantitative research project. You can discuss any collaborative projects you've worked on in the past and how you approached working with a team.

Preparing for a quantitative research analyst interview can be challenging, but these top 10 interview questions and answers should help you feel more confident and prepared for your interview.

How to Prepare for Quantitative Research Analyst Interview

Quantitative research analysts play an essential role in the financial industry. They provide data-driven insights, conduct market research, and help develop investment strategies. If you're pursuing a career in quantitative research analysis, you'll need to prepare for the interview process to showcase your skills and experience. Here are some tips on how to prepare for a quantitative research analyst interview:

1. Understand the Job Description

To prepare for a quantitative research analyst interview, you need to understand the job description completely. Analyze the job requirements and responsibilities to make sure that your skills and experience match the job description. You should also have an in-depth understanding of the company culture, mission, and vision.

2. Brush up on Your Technical Skills

Quantitative research analysts need to have strong mathematical and technical skills. Make sure that you brush up on your knowledge of statistics, data analysis, and programming languages such as Python and R. Additionally, get comfortable with Excel and other data analysis tools that you may need to use on the job.

3. Prepare for Behavioral-Based Questions

While technical skills are essential for a quantitative research analyst position, soft skills such as communication, teamwork, and problem-solving abilities are equally critical. Employers often ask behavioral-based questions to assess your soft skills, so it's essential to prepare for these types of questions. Think about situations where you demonstrated leadership, teamwork, adaptability, or effective communication and how you dealt with problems or conflicts.

4. Research the Company

Before attending the interview, research the company's background, current projects, and future goals. Look for articles, press releases, and other relevant information to demonstrate your interest and preparation for the role. Additionally, understand how the company fits within the larger financial industry and any trends or challenges that may impact the company's business.

5. Be Prepared for Technical Questions

Quantitative research analyst interviews often involve technical questions to assess your skills and experience. Prepare for questions related to data analysis, statistics, or programming languages. Additionally, be ready to present any previous research projects or case studies that you worked on to demonstrate your skills and experience.

6. Practice, Practice, Practice

Finally, practice is key to preparing for a quantitative research analyst interview. Take as many practice interviews as you can with friends, family, or mentors to practice answering technical and behavioral questions. Additionally, practice presenting your previous research projects or case studies to make sure that you can explain them clearly and concisely.

Preparing for a quantitative research analyst interview requires careful preparation and attention to detail. By understanding the job description, brushing up on your technical skills, preparing for behavioral-based questions, researching the company, being prepared for technical questions, and practicing, you'll be well on your way to success! Good luck!

Common Interview Mistake

Not selling your skills.

An interview is your chance to demonstrate your skills and value. If you're too modest, you might fail to convince the interviewer that you're the right candidate for the job.

Interview prep information you may interested

16 Quantitative Research Analyst Interview Questions (With Example Answers)

It's important to prepare for an interview in order to improve your chances of getting the job. Researching questions beforehand can help you give better answers during the interview. Most interviews will include questions about your personality, qualifications, experience and how well you would fit the job. In this article, we review examples of various quantitative research analyst interview questions and sample answers to some of the most common questions.

Quantitative Research Analyst Resume Example

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Common Quantitative Research Analyst Interview Questions

What motivated you to choose quantitative research as your area of focus, what do you think sets quantitative research apart from other research disciplines, what would you say is the most challenging aspect of quantitative research, what do you think is the most rewarding aspect of quantitative research, what do you think is the most important skill for a quantitative researcher to possess, what do you think is the most important attribute of successful quantitative research projects, what do you think is the most important factor to consider when designing a quantitative research study, what do you think is the most important element of data analysis in quantitative research, what do you think is the most important consideration when interpreting results from quantitative research studies, what do you think is the most important thing to remember when writing a report on quantitative research findings, what do you think is the most important advice you would give to someone who is new to conducting quantitative research, what do you think is the most important thing to keep in mind when working with clients or sponsors on quantitative research projects, what do you think is the most important factor to consider when planning a career in quantitative research, what do you think is the most important attribute of successful quantitative researchers, what do you think sets quantitative research apart from other types of research, what do you think is the most rewarding aspect of a career in quantitative research.

There are a few reasons why an interviewer might ask this question. First, they may be trying to gauge your interest in the field of quantitative research. Second, they may be trying to determine if you have the necessary skills and knowledge to be successful in this field. Finally, they may be trying to get a sense of your long-term career goals and how quantitative research fits into those goals.

It is important for the interviewer to know your motivation for choosing quantitative research as your area of focus because it will help them understand your level of commitment to the field and whether or not you are likely to stick with it for the long haul. Additionally, this question can give the interviewer some insight into your thought process and how you go about making decisions.

Example: “ I was motivated to choose quantitative research as my area of focus because it is a highly analytical and detail-oriented field that allows me to use my critical thinking skills to solve complex problems. Additionally, I am interested in the mathematical and statistical aspects of quantitative research, which makes this field even more appealing to me. ”

There are a few reasons why an interviewer might ask this question to a quantitative research analyst. First, it allows the interviewer to gauge the analyst's understanding of quantitative research methods. Second, it allows the interviewer to determine whether the analyst is familiar with the key differences between quantitative and other research disciplines. Finally, this question can help the interviewer to understand the analyst's thoughts on the strengths and weaknesses of quantitative research methods.

Quantitative research is a scientific approach to data collection and analysis that focuses on measuring and quantifying variables of interest. In contrast, qualitative research is a more exploratory and open-ended approach that emphasizes understanding and describing phenomena rather than measuring and quantifying them.

The key difference between quantitative and qualitative research lies in their respective goals. Quantitative research is typically used to test hypotheses or to answer questions about cause-and-effect relationships, while qualitative research is used to explore phenomena or to generate new hypotheses. Qualitative research is often more flexible and allows for more detailed data collection than quantitative methods, but it can be more difficult to draw clear and definitive conclusions from qualitative data.

Both quantitative and qualitative research play important roles in the scientific process, and each has its own strengths and weaknesses. Quantitative methods are often seen as more objective and rigorous, while qualitative methods are seen as more flexible and responsive to the complexities of real-world phenomena. Ultimately, the choice of which research method to use depends on the specific question being asked and the resources available.

Example: “ There are a few key things that set quantitative research apart from other research disciplines: 1. The focus on data and numbers. Quantitative researchers are interested in understanding relationships between variables using numerical data. This data can be collected through surveys, experiments, or other means. 2. The use of statistical methods. In order to analyze this data, quantitative researchers use statistical methods to identify patterns and relationships. 3. The use of formal models. Formal models are used to describe the relationships between variables and to make predictions about future behavior. 4. The focus on generalizability. One of the goals of quantitative research is to be able to generalize findings to a larger population. This requires careful design and analysis of data. ”

There are a few reasons why an interviewer might ask this question. First, they want to see if you are able to identify the challenges of quantitative research. This is important because it shows that you understand the limitations of this type of research and that you are aware of the potential difficulties that can arise. Second, they want to see how you would address these challenges if you were to encounter them in your work. This is important because it shows that you are proactive and that you have a plan for dealing with difficult situations. Finally, they want to see if you have a good understanding of the statistical methods that are used in quantitative research. This is important because it shows that you are knowledgeable about the topic and that you are able to apply these methods in a real-world setting.

Example: “ There are many challenges that can be faced when conducting quantitative research, but one of the most challenging is ensuring the data collected is accurate and representative of the population being studied. This can be difficult to achieve if the sample size is small or if there is a lot of variability in the data. Another challenge is designing experiments or surveys that accurately measure the phenomena being studied. This can be difficult if the phenomena are complex or if there are many variables that need to be considered. ”

There are a few reasons why an interviewer might ask this question to a quantitative research analyst. First, it allows the interviewer to gauge the analyst's understanding of the field of quantitative research. Second, it allows the interviewer to gauge the analyst's understanding of the benefits of quantitative research. Finally, it allows the interviewer to gauge the analyst's motivation for pursuing a career in quantitative research.

The most rewarding aspect of quantitative research is that it allows analysts to use their skills to help organizations make better decisions. Quantitative research provides organizations with data that can be used to improve policies, make more informed decisions, and allocate resources more effectively. By conducting quantitative research, analysts can have a direct and positive impact on the lives of people and organizations.

Example: “ There are many rewarding aspects of quantitative research, but I think the most rewarding is the ability to see the impact of your work on real-world problems. When you can see that your research is making a difference in the world, it is a very gratifying feeling. ”

Some possible reasons an interviewer might ask this question are to better understand the candidate's views on the role of a quantitative researcher, to gauge the candidate's level of experience, or to get a sense for how the candidate would approach problem-solving in this role. The most important skill for a quantitative researcher depends on the specific field or industry, but some essential skills might include the ability to effectively collect and analyze data, to develop hypotheses and test them using statistical methods, and to communicate findings clearly.

Example: “ There are many important skills that a quantitative researcher should possess, but some of the most important ones include: 1. Strong analytical and critical thinking skills: A quantitative researcher needs to be able to analyze data and identify patterns and trends. They also need to be able to think critically about the data and come up with hypotheses about what it might mean. 2. Strong math skills: A quantitative researcher needs to be able to understand and work with complex mathematical concepts. They need to be able to use statistical software to analyze data and draw conclusions from it. 3. Strong communication skills: A quantitative researcher needs to be able to communicate their findings clearly and concisely, both in writing and verbally. They need to be able to explain their findings to those who may not be familiar with the concepts involved. ”

There are many important attributes of successful quantitative research projects, but the most important attribute is probably methodological rigor. A rigorous quantitative research project is one that is carefully designed and executed, and which uses sound statistical methods to analyze the data. A rigorous quantitative research project can provide valuable insights into a wide variety of topics, and can help to improve decision-making in many different fields.

Example: “ There are a number of attributes that can contribute to the success of quantitative research projects, but some of the most important include: 1. A clear and concise research question that can be answered using quantitative methods. 2. A well-designed research plan that includes a detailed methodology and robust data collection and analysis procedures. 3. A commitment to rigorously following the research plan and ensuring that data is of high quality. 4. A willingness to iterate and refine the research design as needed in order to obtain accurate and meaningful results. 5. A thorough understanding of statistical methods and their application to the data at hand. 6. The ability to effectively communicate findings to both academic and non-academic audiences. ”

There are many factors to consider when designing a quantitative research study, but the most important factor is the research question. The research question should be clear and concise, and it should be possible to answer it with the data that is collected. Other important factors to consider include the population of interest, the sample size, and the type of data that is collected.

Example: “ The most important factor to consider when designing a quantitative research study is the research question. The research question should be clear and concise, and should be able to be answered by the data that is collected. Other important factors to consider when designing a quantitative research study include the population of interest, the sampling method, and the type of data that is collected. ”

The interviewer is likely looking for qualities that are important in a quantitative research analyst, such as attention to detail, strong mathematical skills, and the ability to draw conclusions from data. This question allows the interviewer to gauge the interviewee's understanding of the role of data analysis in quantitative research and their ability to articulate why it is important.

Example: “ There are many elements of data analysis in quantitative research, but I believe the most important element is accuracy. In order to produce accurate results, quantitative researchers need to have a strong understanding of statistics and be able to apply the proper statistical techniques to their data. They also need to be able to effectively communicate their findings to others. ”

There are a few reasons why an interviewer might ask this question to a quantitative research analyst. First, it is important to understand the limitations of quantitative research studies in order to properly interpret their results. Second, analysts need to be aware of potential sources of bias that can distort results. Finally, analysts need to understand how to effectively communicate results to those who may not be familiar with the technical details of the study.

The most important consideration when interpreting results from quantitative research studies is understanding the limitations of the study. Quantitative research studies are often limited in scope and cannot provide a complete picture of a phenomenon. For example, a quantitative study might only be able to measure a limited number of variables, or it might only be able to observe a phenomenon over a short period of time. As a result, analysts need to be careful not to overinterpret the results of a quantitative study.

Another important consideration when interpreting results from quantitative research studies is potential sources of bias. There are many potential sources of bias that can distort results, such as selection bias, measurement bias, and self-reporting bias. analysts need to be aware of these potential sources of bias and take them into account when interpreting results.

Finally, analysts need to understand how to effectively communicate results to those who may not be familiar with the technical details of the study. When presenting results from a quantitative study, analysts need to clearly explain the methodology used and the limitations of the study. They also need to provide context for the results, such as how the results compare to other studies on the same topic.

Example: “ There are a number of important considerations to take into account when interpreting results from quantitative research studies. Perhaps the most important consideration is the study's methodological quality. This includes factors such as the study's design, sample size, and statistical analysis. If a study has flaws in any of these areas, its results may not be accurate or reliable. Another important consideration is the context in which the study was conducted. This includes factors such as the population being studied, the setting in which the data was collected, and the specific research question that was being addressed. All of these factors can affect the results of a quantitative study and how they should be interpreted. Finally, it is also important to consider the implications of the results before drawing any conclusions. What do the results mean in terms of real-world applications? Are there any potential risks or benefits associated with implementing the findings? These are just some of the questions that need to be considered before making any decisions based on quantitative research results. ”

There are a few reasons why an interviewer might ask this question to a quantitative research analyst. First, it is important to remember that when writing a report on quantitative research findings, it is important to be clear and concise. The report should be easy to read and understand, and should not contain any superfluous information. Second, it is important to remember that the report should be objective and unbiased. The report should not be swayed by the researcher's personal opinions or biases. Third, the report should be accurate. All of the data and information included in the report should be accurate and up-to-date. Finally, the report should be well-organized. The information should be presented in a logical and easy-to-follow manner.

Example: “ There are a few things to keep in mind when writing a report on quantitative research findings: 1. Make sure to clearly state the research question that was being addressed in the study. 2. Present the data in a clear and concise manner, using tables and graphs as needed. 3. Be sure to discuss the implications of the findings and how they relate to the research question. 4. Finally, make sure to proofread the report carefully before submitting it. ”

There are a few reasons why an interviewer would ask this question to a quantitative research analyst. First, it allows the interviewer to gauge the analyst's level of experience and expertise in conducting quantitative research. Second, it allows the interviewer to understand the analyst's process for conducting quantitative research and how they go about acquiring data and analyzing it. Finally, it allows the interviewer to get a sense for the analyst's personal philosophies or methods for conducting research, which can be helpful in determining if they would be a good fit for the position.

Example: “ There are a few things to keep in mind when conducting quantitative research: 1. Make sure your data is of high quality. This means that it should be accurate, reliable, and representative of the population you are studying. 2. Choose the right statistical methods for your data and research question. There are many different statistical methods, and it is important to choose the one that is most appropriate for your data and question. 3. Be careful when interpreting results. Quantitative research is often complex, and it is easy to make mistakes when interpreting results. Make sure to carefully review your results before drawing any conclusions. ”

There are a few reasons why an interviewer might ask this question to a quantitative research analyst. Firstly, the interviewer wants to know if the analyst is aware of the importance of working closely with clients or sponsors on quantitative research projects. Secondly, the interviewer wants to know if the analyst has the ability to think critically about the project and identify the most important aspects that need to be considered. Finally, the interviewer wants to gauge the analyst's level of experience and knowledge in this area.

Quantitative research projects can be extremely complex, and it is crucial that analysts work closely with clients or sponsors in order to ensure that all of the necessary data is collected and analyzed correctly. Furthermore, analysts need to be able to identify the most important factors that will impact the results of the research in order to ensure that the project is successful. Therefore, it is essential that analysts have a strong understanding of both the quantitative research process and the specific needs of their clients or sponsors.

Example: “ There are a few things that are important to keep in mind when working with clients or sponsors on quantitative research projects: 1. It is important to clearly define the goals and objectives of the project from the outset. This will help to ensure that everyone is on the same page and that the project stays focused. 2. It is also important to be clear about who the target audience is for the research. This will help to ensure that the data collected is relevant and can be used to answer the research questions. 3. Another thing to keep in mind is that quantitative research can be expensive, so it is important to work with a budget in mind. This will help to ensure that the project stays within its financial constraints. 4. Finally, it is also important to keep in mind that quantitative research takes time. This means that it is important to plan for adequate time to collect and analyze data before presenting results. ”

There are many factors to consider when planning a career in quantitative research, but the most important factor is probably experience. The more experience you have in the field, the better equipped you will be to handle the challenges that come with it. Additionally, it is important to stay current on the latest methods and techniques used in quantitative research.

Example: “ There are many factors to consider when planning a career in quantitative research, but the most important factor is probably your own skills and interests. If you're not interested in the subject matter, it will be very difficult to succeed in this field. Likewise, if you don't have strong mathematical and analytical skills, you'll likely find it difficult to progress in this career. So, it's important to consider your own skills and interests when planning a career in quantitative research. ”

There are many important attributes of successful quantitative researchers, but some attributes are more important than others. The most important attribute of successful quantitative researchers is the ability to think critically and solve problems. Quantitative research is all about finding solutions to problems, so it is essential that quantitative researchers be able to think critically and solve problems. Other important attributes of successful quantitative researchers include the ability to communicate effectively, the ability to work independently, and the ability to work in a team.

Example: “ There are a few attributes that are important for successful quantitative researchers. Firstly, they need to be excellent at math and statistics. Secondly, they need to be able to think logically and solve problems efficiently. Thirdly, they need to be able to communicate their findings clearly and concisely. Lastly, they need to be able to work well under pressure and meet deadlines. ”

There are a few reasons why an interviewer might ask this question. First, it allows them to gauge the interviewee's understanding of quantitative research. Second, it allows them to see how the interviewee would explain the concept of quantitative research to someone who is not familiar with it. Finally, it allows the interviewer to get a sense of the interviewee's thought process and how they approach problem solving.

It is important for the interviewer to ask this question because it allows them to get a better understanding of the interviewee's skills and abilities. Additionally, it allows the interviewer to get a better sense of the interviewee's personality and whether or not they would be a good fit for the position.

Example: “ Quantitative research is a type of scientific research that focuses on the collection and analysis of numerical data. This data can be collected through surveys, experiments, or other methods of observation. Once collected, this data can be used to answer questions about the relationships between different variables, or to test hypotheses about how these variables interact with each other. One of the main things that sets quantitative research apart from other types of research is its focus on data. This data can be collected in a number of ways, but it must be numerical in order to be analyzed. This means that quantitative research is often more rigorous and objective than other types of research, as it relies on hard evidence rather than personal opinions or anecdotal evidence. Another thing that sets quantitative research apart is its focus on relationships between variables. This type of research is often used to test hypotheses about how different variables interact with each other. For example, a researcher might want to know if there is a relationship between income and happiness. By collecting data on both income and happiness levels, the researcher can test their hypothesis and see if there is a statistically significant relationship between the two variables. Overall, quantitative research is a powerful tool for understanding the world around us. By collecting and analyzing numerical data, we can ”

An interviewer might ask this question to gain insight into what motivates the research analyst and what they consider to be the most important part of their job. This can help the interviewer understand if the analyst is likely to be satisfied with the position and if they are likely to stay in the role for the long term. Additionally, this question can give the interviewer a sense of the research analyst's priorities and how they might approach their work.

Example: “ The most rewarding aspect of a career in quantitative research is the ability to make a real difference in the world. With the help of data and analysis, quantitative researchers are able to provide insights that can lead to positive change. They can help decision-makers understand complex problems and identify potential solutions. In addition, quantitative researchers often have the opportunity to work on cutting-edge projects that can have a real impact on people’s lives. ”

Ace Your Next Quant Interview

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Which industry are you most interested in? If you don't know yet, pick one and we will tell you a bit about it.

Great choice! Asset management firms offer lots of exciting opportunities for quants and Quant Questions can help you get there. Roles can vary from portfolio management, portfolio construction and optimization, transaction cost analysis, finding alpha generating strategies, beta market research or market risk management.

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Great choice! Most quants don't think about private equity as a career path. But as this traditionally non-quant industry becomes more quantitative, this is a very viable option. Roles can vary from portfolio construction and optimization, to residential credit modeling and to general analytics.

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Which firm are you most interested in working for? If you don't know yet, pick one and we will tell you a bit about the firm.

Great choice! BlackRock is the largest asset manager with $6.5 trillion in AUM and offers lots quant opportunities. Quants can find themselves at home in various investment divisions such as Scientific Active Equities or Model-Based Fixed Income, or in roles in Portfolio Analytics or Risk & Quantitative Analytics.

Great choice! State Street is based in Boston and manages $2.5 trillion in AUM. Quants can find interesting roles in groups such as Fixed Income and Currencies, Active Quantitative Equities, Enterprise Risk Management or Model Validation.

Great choice! Pimco is the biggest bond manager based in Newport Beach, California. Quants can find roles within the Client Solution and Analytics or on the Trade Support team on one of their many trading desks.

Great choice! Wellington Management is a $1.1 trillion AUM asset manager. Quants can find technical roles within the Fixed Income, Trading Data & Analytics or Derivative Analytics and Valuations.

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Great choice! Morgan Stanley is a multinational investment bank with over 50,000 employees and over $800 billion in total assets. You can find opportunities as a Desk Strategist, on a modeling team or in the Electronic Market Making Group.

Great choice! JP Morgan is a multinational investment bank based in NYC with over $2.5 trillion in total assets. You can find positions in the Quantitative Research division or in the Data Analytics team.

Great choice! Citi has over 200,000 employees and over $1.9 trillion in total assets. You can find quant opportunities in their trading, asset management or investment banking divisions.

Great choice! Wells Fargo has over $1.8 tillion in total assets and over 250,000 employees. You can find quant opportunities in their trading, asset management or investment banking divisions.

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Great choice! Two Sigma has over $30 billion in AUM and is at the forefront of quantitative investment hiring scientists, academics and engineers. Quants can find intellectually stimulating roles in Data Science & Analytics, Quantitative Research & Modeling or Execution & Trading.

Great choice! AQR is an $80 billion investment management firm based in Greenwich, Connecticut. You can find quant roles within Global Asset Allocation, Global Stock Selection, Risk Management or Trading.

Great choice! Balyasny is based out of Chicago and has over $7 billion in AUM. You can find roles of interest in the following divisions: Financial Engineering, Risk, Quantitative Research or Investment & Trading.

Great choice! D.E. Shaw is based in NYC and has over $30 billion in AUM. You can find quant jobs in their Investment Analysis, Quantitative Strategies or Trading divisions.

Great choice! Citadel is based out of Chicago and has over $30 billion in AUM. You can find quant jobs in their Global Quantitative Strategies, Global Fixed Income or Portfolio Constructions division.

Great choice! Cidatel Securities is the largest market maker in the US. You can find interesting roles in their Information Technology, Engineering or Finance & Accounting teams.

Great choice! Jane Street was founded in 2000 and has about 900 employees. You can find interesting roles in their Quantitative Trading, Quantitative Resarch or Institutional Services divisions.

Great choice! Hudson River Trading is based in NYC and was founded in 2002. They can trade up to 5% of all US stock trading any given day. They have many quant roles in Strategy Development, Software Engineering or Trade Operations.

Great choice! Optiver was founded 1986 and now has over 1,000 employees. Optiver makes markets in options and delta1 products. You can find interesting quant roles in their risk, technology or trading divisions.

Great choice! SIG was founded in 1987 and is based out of Philadelphia. They make markets in equity options and index options. You can find interesting roles in their Trading, Quantitative Research, Machine Learning or Operations teams.

Great choice! Bloomberg was founded in 1981 and now has over 19,000 employees. Bloomberg has great opportunities for quants in Multi-Asset Risk System (MARS), Enterprise Data, Quant Analytics and Desktop Build Group (DBG).

Great choice! Moody's Analytics was founded in 2007 and now has over 10,000 employees. They offers opportunities for quant in their Enterprise Risk Solutions, Credit Analysis & Research or Strategy & Analytics groups.

Great choice! MSCI is based out of NYC and has over 3,000 employees. They have opportunities in Multi-Asset Class Research, Risk Analytical QA and Analytics Platform Development teams.

Great choice! Numerix was founded in 1996 and is based out of NYC. You can find interesting quant roles in their Financial Engineering, Client Solutions Group or Global Operations groups.

Great choice! HSBC is headquartered in London and has over 230,000 employees. They have quant opportunities in Traded Risk Management, Risk Analytics and Modeling or Data Analytics teams.

Great choice! Santander is headquartered in Santander, Spain and has over 200,000 employees worldwide. They offer quant opportunities in Risk Modeling, Operational Risk and Technology divisions.

Great choice! US Bank is the 5th largest bank in the US. They have quantitative positions within their Enterprise Research and Insights teams, Data Analytics and AI/ML & Data Platform teams.

Great choice! CIT Group has over $50 billion in total assets. CIT has quant opportunities in the Quantitative Strategies (QS) or Analytics teams within Audit or Information Technology.

Great choice! Deloitte has over is headquartered in London and has over 280,000 employees world wide. Deloitte has quant roles in their Analytics & Cognitive, Managed Analytics or Risk and Financial Advisory (RFA) groups.

Great choice! PwC is headquartered in London and has over 250,000 employees. They have opportunities in their Valuations or Financial Markets Business Advisory groups.

Great choice! EY was founded in 1989 and is headquartered in London. They has over 270,000 employees and you can find roles in the Quantitative Advisory Services (QAS) or Risk Technology teams.

Great choice! Bain is headquartered in Boston and has over 8,000 employees. Bain has lots quant opportunities within their Advanced Analytics Group (AAG), including data science, engineering, marketing science, operations research.

Great choice! KPMG has over was founded in 1987 and now has over 200,000 employees. has quant positions in Economic and Valuation Services, groups, Technology Enablement, Risk Strategy & Compliance and Data & Analytics groups

Great choice! Quantopian

Great choice! Lending Club was founded in 2007 and is based in San Francisco. You can find quant roles in their Data Technology, Risk or Engineering teams.

Great choice! Affirm was founded in 2012 and is based out of San Francisco. They offer quant positions in their Strategy & Analytics, Data/Risk and Finance divisions.

Great choice! Square is headquartered in San Francisco and was founded in 2009. Square has quantitative opporuntities in Marketing Analytics, Data Engineering, Data Science and Product Analytics.

Great choice! Coinbase is a digital currency exchange based out of San Francisco. Coinbase has quant opportunities in Operations & Technology, Data and Engineering.

Great choice! You may have heard of IEX Group from Michael Lewis's book Flash Boys. IEX is based in NYC and you can find interesting roles in Quantitative Research, Development or Finance teams.

Great choice! KKR has over $150 billion in AUM and is headquartered in NYC.

Great choice! TPG has over $100 billion in AUM and is headquartered in Fort Worth and San Francisco.

Great choice! The Carlyle Group is based out of Washington D.C. and has over $220 billion in AUM. You can find quantitative roles on the Enterprise Data team or Analytics team.

Great choice! Apollo is based out of NYC and has over $303 billion in AUM. You can find quant roles on the Risk Management and Quantitative Business Modeling team.

Great choice! Blackstone is based out of NYC and has over $450 billion in AUM. You can find quant jobs as part of the Blackstone Innovations, Blackstone Alternative Asset Management or Portfolio Management Program teams.

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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 .

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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.

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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.

Student Assistant (HiWi) (f/m/d)

Job Code: Stu_53

The vision of the Organizational Leadership and Diversity at the Max Planck Institute for Intelligent Systems group is to support leaders in using artificial intelligence to contribute to more tolerant, diverse, and inclusive organizations.

We are looking for a Student Assistant (HiWi) (f/m/d) to support a Grassroots research project “Harnessing the Power of AI to Recognize Microaggressions in the Workplace”

About the project

"Wow, you did such a great job on that project! I never expected you to be so competent at this." If you heard anything similar addressed to you or your peer, you were exposed to microaggression. Together with the Optics & Sensing Laboratory (MPI IS, Tübingen), we conduct research that aims to harness the power of artificial intelligence to tackle the pervasive issue of microaggressions in the workplace. A far-reaching aim of our research is to foster a more inclusive work climate: We strive to supply senders of microaggression and third parties in the microaggressive conversations with knowledge and tools to detect and address non-verbal/verbal microaggressions in physical, virtual, and hybrid workplaces.

For further information please see our websites OLG and OSLab .

Roles & Responsibilities

The student assistant position will allow the student to gain hands-on experience in designing and conducting qualitative research (interviews).

Tasks include:

Preparation of the interview questionnaire
Organization of meetings with interviewees
Conducting semi-structured interviews and debriefing the interviewees after the interviews
Coding of the interviews according to the established methodology using coding software

Education & Experience

Currently be pursuing a Master's degree in Social Sciences (e.g., Management, Psychology, Education) or Economics or related fields
Have high motivation
Be currently enrolled in a German university
Want to work in an international and interdisciplinary research group
Have good oral and written communication skills in German and English
Be able to work on site at the Max-Planck Institute for Intelligent Systems in Stuttgart, Germany, at least for a part-time employment

We are especially interested in applicants who have:

experience in conducting qualitative research
critical thinking skills combined with prominent empathy
social psychology
cognitive psychology
topics of diversity and inclusion
communication
Master students holding a Bachelor’s degree will be paid €13,03 per hour.
Max. 83 hours per month, up to 3 months.
Workplace: A modernly equipped workplace, an international working environment.
Starting date: as soon as possible

Application

Please, upload your application including a CV in English or German, a short motivation letter in English (why you are interested in this position/research), and optionally other documentation helpful to evaluate your background.

Please upload your application via our application portal .

Closing date: 17.05.2024

Questions about the position should be addressed via email to Dr. Ksenia Keplinger at [email protected] .

The Max Planck Society is committed to increasing the number of individuals with disabilities in its workforce and therefore encourages applications from such qualified individuals. The Max Planck Society strives for gender equality and diversity. Furthermore, the Max Planck Society seeks to increase the number of women in its workforce in those areas where they are underrepresented and therefore explicitly encourages women to apply.

Notification Settings

Open access
Published: 24 April 2024

Access to family planning services and associated factors among young people in Lira city northern Uganda

Eustes Kigongo 1 ,
Raymond Tumwesigye 1 ,
Maxson Kenneth Anyolitho 1 ,
Marvin Musinguzi 1 ,
Gad Kwizera 3 ,
Everlyne Achan 1 ,
Caroline Kambugu Nabasirye 2 ,
Samson Udho 2 ,
Amir Kabunga 4 &
Bernard Omech 1

BMC Public Health volume 24 , Article number: 1146 ( 2024 ) Cite this article

Metrics details

Access to family planning services among young people is crucial for reproductive health. This study explores the access and associated factors among young people in Lira City, Northern Uganda.

Methods and materials

A mixed-methods study was conducted in March to April 2022. Quantitative data were collected using a structured questionnaire from 553 participants aged 15–24 years. Qualitative data were obtained through in-depth interviews and focus group discussions. Data analysis included univariate, bivariate, and multivariate analyses for quantitative data, while interpretative phenomenological analysis was used for qualitative data.

Overall, 31.7% of the respondents had a good perceived access to family planning services, with 64.6% reporting perceived availability of FP methods. Challenges included lack of privacy (57.7%), fear of mistreatment (77.2%), and decision-making difficulties (66.2%). Among females, good perceived access to FP services was less likely among urban residents (AOR: 0.22, 95% CI: 0.09–0.53), Christian respondents (AOR: 0.51, 95% CI: 0.01–0.36), Muslim respondents (AOR: 0.07, 95% CI: 0.01–0.55) and respondents with poor attitude to FP services (AOR: 0.39, 95% CI: 0.24–0.64), but more likely among respondents with a sexual a partner (AOR: 4.48, 95% CI: 2.60–7.75). Among males, good perceived access to FP services was less likely among respondents living with parents (AOR: 0.19, 95% CI: 0.05–0.67) but more likely among respondents with good knowledge of FP services (AOR: 2.28, 95% CI: 1.02–5.32). Qualitative findings showed that three themes emerged; knowledge of family planning methods, beliefs about youth contraception and, friendliness of family planning services.

The study revealed a substantial gap in perceived access to family planning services among young people in Lira City. Barriers include privacy concerns, fear of mistreatment, and decision-making difficulties. Tailored interventions addressing urban access, religious beliefs for females, and knowledge enhancement for males are essential. Positive aspects like diverse FP methods and physical accessibility provide a foundation for targeted interventions. Youth-friendly services, comprehensive sexual education, and further research are emphasized for a nuanced understanding and effective interventions in Northern Uganda.

Peer Review reports

Globally, approximately 16 million girls aged 15–19 give birth each year, with 95% of these births occurring in developing countries [ 1 ]. Additionally, annually, 14 million unsafe abortions take place among adolescents, who face various sexual and reproductive health challenges, including early pregnancy, unsafe abortions, sexually transmitted infections (STIs), and sexual abuse, particularly in Sub-Saharan Africa (SSA) [ 2 ]. Family planning (FP) is a critical aspect of global public health, recognized for its impact on maternal and child health, gender equality, and socioeconomic development [ 3 ]. The international community, as reflected in various global health initiatives and sustainable development goals, acknowledges the importance of ensuring universal access to FP services for all individuals, including young people [ 4 ]. This global perspective emphasizes the interconnectedness of reproductive health and broader efforts to achieve sustainable development [ 4 ]. Access to these services is particularly pertinent among young people, who constitute a significant demographic in many Low-and Middle-income Countries (LMICs).

Uganda, boasting one of the world’s youngest and fastest-growing populations, has nearly half (48%) of its estimated 46 million people under the age of 15, significantly surpassing the averages for SSA (43%) and the world (26%) [ 5 ]. Uganda, as a signatory to global health agendas, has made significant strides in promoting FP services [ 6 ]. The National Population Policy, coupled with the National Reproductive Health Policy, reflects the government’s commitment to ensuring access to FP for all citizens [ 7 ]. However, challenges persist, especially in urban areas. An examination of the national context provides insights into the policy circumstances, healthcare infrastructure, and societal norms that shape family planning services’ availability and utilization among young people in Northern Uganda.

According to the Uganda Demographic and Health Survey (UDHS) 2016, 25% of women aged 15–19 and 1% below 15 had initiated childbearing, with the incidence of unplanned pregnancies significantly rising following the shutdown of schools during the COVID-19 pandemic [ 8 , 9 ]. Reported underlying causes of teenage pregnancy include gender inequality, restricted freedom for girls to voice their concerns, school dropout, and limited access to contraception and knowledge [ 10 ]. Unintended teenage pregnancies can have severe adverse effects on well-being, leading to maternal morbidity and mortality related to childbirth and unsafe abortion [ 11 ]. Moreover, these pregnancies contribute to social consequences such as stigma and discrimination, accounting for 59% of school dropouts in Uganda in 2012, potentially hindering education and future employment opportunities [ 12 , 13 ]. Reports by the World Bank and the World Health Organization (WHO) emphasize the association of adolescents-childbearing with social stigma, lifelong poverty, and health risks, necessitating a comprehensive approach to address these issues [ 14 , 15 ].

Uganda’s current health sector strategy aims to expand youth-friendly health services (YFHS) and promote adolescent sexual and reproductive health and rights information in schools, ensuring access to FP information and services irrespective of age, marital status, or school status [ 16 ]. The country plans to increase access to modern contraceptive use and reduce unmet need for contraception in the coming years [ 17 ]. According to WHO guidelines, addressing the underlying factors, including the timing of first sex and marriage, effective contraceptive use, and the socio-cultural and economic environment, is crucial for delaying childbearing and expanding FP access to adolescents [ 18 ].

Notably, northern Uganda bears one of the highest burdens of adolescent pregnancies, with reports indicating a significant percentage of unintended pregnancies in Lira district in 2019 (33.3%) and a notable number of teenage girls visiting antenatal clinics in Lango sub-region in 2021 [ 19 ]. A recent study in Oyam district reported a high percentage of unintended pregnancies among adolescent girls [ 8 ]. In the context of Lira City in northern Uganda, unintended pregnancies represent a significant challenge affecting various aspects of young people’s lives, including education and economic prospects [ 20 ]. Despite the recognized importance of FP, there is a need for a comprehensive understanding of the factors hindering or facilitating youth access to FP services in Lira City. Existing literature primarily focuses on the prevalence of unintended pregnancies and associated outcomes, emphasizing challenges in accessing reliable information, contraceptives, and quality reproductive health services [ 20 ]. However, there is limited research examining the factors contributing to these challenges, such as cultural norms, stigma, and structural barriers specific to Lira City. Moreover, the evolving circumstances of youth perspectives, preferences, and behaviors related to FP require an updated understanding, considering rapid socio-cultural changes and advancements in technology [ 21 ]. To develop evidence-based intervention strategies, our assessment focused on the knowledge, perceptions, and factors influencing access to contraceptive services among young people in the specific context of northern Uganda.

Study design

This was an explanatory-sequential mixed methods study [ 22 ] conducted in Lira city, northern Uganda between March and April 2023. The mixed-methods approach was adopted so as to generate a more holistic understanding and a stronger inference with two approaches complementing each other [ 23 ].

Study setting

Lira City is among the newly created cities, located approximately 375 km by road north of the capital city of Kampala via Karuma-Kamdini. Lira City is the central business hub for Northern Uganda and comprises the west and east divisions. According to projections by the Uganda Bureau of Statistics (UBOS) in 2014, the population of 2020 for the Lira district was 474,200 people, and it is traditionally inhabited by the Lango tribe, who are farmers and cattle keepers. The urban centers of the district also have people engaged in many small-scale businesses, such as produce businesses and trading.

Study population

The study was among young people aged 15 to 24 years, residing in Lira city. Inclusion into the study was based on being a young person of 15 to 24 years of age who has lived in Lira city for at least six months. Additionally, being present at the selected household during data collection, and those who consented to participate were included in the study. In households where more than one persons were eligible, simple random sampling by lottery method was employed to select one. Exclusion was based on being critically ill to participate, or refusing to participate in the interviews.

Sample size determination

The sample size of the study was estimated using Kish Leslie (1965) as follows:

In the equation above, n is the sample size for the study, Z is the Z score at the 95% confidence interval (1.96), p is the proportion of perceived access to FP services (50%), d is the desired precision of the study (5%), and deff is the design effect due to multistage random sampling. A factor of 1.5 has been used to adjust the sample size based on what previous studies have used [ 24 , 25 ]. A design effect of 1.5 was employed to increase the homogeneity of the participants following the use of a multistage random sampling procedure. Therefore, the final sample size obtained was 577.

Interpretative phenomenological analysis (IPA) was employed for qualitative research to delve into individual experiences, progressing towards an examination of shared and contrasting aspects within a limited sample [ 26 ]. This approach facilitated the identification of thematic connections. Adhering to IPA guidelines advocating for a compact and homogenous sample, purposive sampling was used to recruit 5 participants. This sample size aligns with the recommended number for an IPA study [ 27 ], and was considered sufficient to capture a distinct range of experiences related to the phenomenon under investigation.

Sampling technique

A multistage sampling procedure was employed to select the 577 study participants. The study was conducted in both divisions of Lira City, East and West. From each of the divisions, five wards were selected, making a total of ten wards. This was done by simple random sampling using the lottery method, where the names of wards were written on small papers, folded, mixed in a container, and shaken well, and then five were picked at random without replacement. From each of the wards, two cells were selected using the same procedure, which generated a total of 20 cells. From each of the cells, Village Health Teams (VHTs) were used to obtain lists of households with young people aged 15 to 24 years, and these were used as sampling frames per cell. The number of participants to be selected from each cell was determined by the sample size proportionate to the cell size. In each of the cells, participants were selected through simple random sampling using computer-generated random numbers. Purposive sampling was used to select participants for qualitative interviews [ 28 ]. While purposive sampling guided our selection process, we also sought to include a diverse range of perspectives by engaging with individuals from various backgrounds, including community health workers, educators, and youth leaders. Our rationale for selecting community peer educators stems from their unique position as trusted intermediaries within their communities, often serving as frontline advocates for reproductive health education and services. Similarly, the inclusion of university leaders was motivated by their influence and role in shaping policies and programs related to youth reproductive health within academic settings.

Study variables

Dependent variable.

The dependent variable for the study is perceived access to FP services. Access to healthcare means “the timely use of personal health services to achieve the best health outcomes” [ 29 ]. Many frameworks have been proposed to measure access to family planning services but have all proved not sufficient [ 30 ]. This study adopted one of the common frameworks, Penchansky and Thomas (1981) framework that reflects the fit between characteristics and expectations of the providers and the clients. These characteristics (5As of access) are availability, accessibility, acceptability, accommodation, and affordability [ 31 ]. This conceptualization of access has been adopted because it describes the broad dimensions and determinants that integrate demand and supply-side factors [ 32 ]. According to the model, the five As of access form a chain that is no stronger than its weakest link. For example, improving affordability by providing health insurance will not significantly improve access and utilization if the other four dimensions have not also been addressed. The perception of access to FP services index composed of five questions of yes or no response. For all the questions “yes” was coded 2 and “no” coded 1. The percentage of respondents that perceived access to be good on all five variables had good perceived access to FP services.

Availability: Are the family planning commodities available when you need them, and meet your FP needs?

Accessibility: Is the location of the facilities that provide family planning services convenient for you?

Acceptability: Are the characteristics of the FP service providers (including attitudes and attributes such as age, sex and religion) comfortable for you?

Accommodation: Do health providers organize FP services in ways (including appointment system, hours of operation and facility environment) that suit your needs and preferences?

Affordability: Do you have to pay for family planning services?

All the access questions were asked as yes and no questions and coded 1 and 2, respectively. To measure the index of perceived access, only participants who answered Yes to all the access questions were labeled as having good perceived access to FP services.

Independent variables

The independent variables included sociodemographic characteristics (age, sex, education, religion, marital status, living with parents), sexual-related characteristics (having a child, sexually active, sexual partners), knowledge, and attitudes. The knowledge of the participants was assessed based on a total of nine questions about family planning. Each of the questions was binary coded as 1(Yes) and 0(No). Overall knowledge was therefore measured as a composite score ranging from 0 to 9. The mean score was taken as a cut-off with individuals above the mean score categorized as having good knowledge and those below the mean as having poor knowledge. This measurement was adopted from a recent study [ 33 ]. The overall attitudes of the young people regarding actual use of family planning commodities, which includes the misconceptions, fears, cultural and religious beliefs about family planning commodities such as condoms were assessed based on a total of eight questions with a favorable response coded as Yes (0) and unfavorable response coded as No [ 1 ]. The responses were computed into an overall attitude to FP services score with a total of eight. Similarly, the cut-off was set as the mean with individuals above the mean classified as having a poor perception and those below the mean with a good perception, as from a recent related study [ 33 ]. The knowledge items had a scale reliability coefficient of 0.78 whereas the perception items had 0.70, all these are within the acceptable limits [ 34 ].

Participant recruitment and informed consent processes

After obtaining ethical approval and clearance, five research assistants from the city were recruited and trained on the study protocol and data collection procedures. A pretest of the questionnaire was carried out among 58 youths from Lira district to refine the questions for simplicity and comprehension and to assess validity and reliability using the Statistical Package for Social Sciences (SPSS) software. Lists of households with young people aged 15 to 24 years were obtained by Village Health Teams (VHTs). Sampling was then conducted, and eligible participants were approached for data collection after providing informed consent and, for minors, informed assent. During this process, the study objectives, procedures, benefits, risks, and voluntarism were explained. Interviews took place in a private space within the participants’ homes. In cases where the parent or guardian was absent during data collection, the household was skipped.

Data collection instruments

Quantitative data was collected using a pretested interviewer-administered questionnaire developed by the researcher (Supplementary file 1 ). The questionnaire consisted of four sections: sociodemographic characteristics (age, sex, education, religion, marital status, residence, and parent’s education), sexually related information (ever had a child, engaged in sexual relationships, number of sexual partners, sexual risks encountered), access questions (availability, accessibility, acceptability, accommodation, and affordability), knowledge of family planning services, and attitudes regarding family planning services. This was administered in approximately 15 min. Qualitative data was collected through in-depth interviews and focus group discussions using guides (Supplementary file 2 ). This was done after obtaining insights from quantitative data. Interviews with participants were done at proposed times and places deemed convenient to the participants themselves. During collection, audio recordings were made together with extended field notes to complement the audios. Data collection was done in Lango, verbatim transcribed, and then translated to English for analysis. Data collection was conducted through five in-depth interviews and four focus group discussions all from young people aged 15 to 24 years. A sample of 10 were from the University and 30 were from the community with equal proportions of males and females. These participants were community adolescent peer-educators and University reproductive health leaders. Some were picked after quantitative interviews while others based on their roles regarding reproductive health for the young people.

Statistical analysis

Quantitative data analysis.

The collected data was entered into SPSS software, where it was cleaned and coded, then exported to STATA version 17 software for final analysis. The analysis was conducted at three levels. At the univariate level, data was summarized as frequencies and proportions, means and standard deviations, or median with interquartile range, and presented in frequency tables. In bivariate analysis, perception of access to SRHR services was cross-tabulated with the independent variables one at a time to assess relationships. A crude odd ratio (COR) and a 95% confidence interval were reported. At this level, associations were considered at p < 0.25 in order to consider all possible predictors [ 35 ], and all those associated factors were taken into multivariate analysis. In multivariate analysis, binary logistic regression was used to estimate the predictors of the primary outcome. The backward elimination method was used to build a predictive model. Results were reported as adjusted odds ratios and 95% confidence intervals. A p -value of < 0.05 was considered statistically significant for variables.

Qualitative data analysis

The data analysis adhered to the seven-stage IPA process outline, derived from Smith and colleagues, as outlined by Brown and colleagues [ 36 ]. Each interview underwent verbatim transcription and was entered into a customized IPA analysis framework. Multiple re-readings of the interviews were conducted, applying in-method triangulation by integrating field notes with observations and commentary from the fieldwork [ 37 ]. This triangulation process enhanced confidence in the outcomes post data analysis. Following the verbatim transcription of the audio data and thorough review of the text, initial notes were made, leading to the development of emerging themes. Connections across these emergent themes were sought to identify subordinate themes. Subsequently, a search for patterns across the cases was conducted to reveal the major themes.

We employed research assistants who are social scientists trained in qualitative study and interview techniques to assure the validity of our study. Data from diverse sources, including field notes and audio recordings, were independently analyzed by two researchers. The newly emerging themes were routinely compared to the original transcribed text, and the writers frequently convened for debriefings to make sure that the subjects were at the center of the data analysis and interpretation. The results of the data analysis were examined and discussed until a consensus was achieved in order to increase the dependability and accuracy of the results. To demonstrate confirmability (the degree to which the findings are shaped by participants and the context rather than the perspectives of the research), the researchers used participants’ narratives and words as noted in the transcripts. Additionally, the researchers dwelled on their previous experiences to reduce their influence on the findings. To ensure that the processes of data collecting and analysis could be traced back to the initial interviews, we have preserved all audit trails from data collection to analysis.

Quantitative findings

Sociodemographic characteristics.

Recruitment into the study was between March and April 2022. Out of a total of 577 participants, 553 were included generating a response rate of 95.8%. Table 1 shows that the majority of the respondents, 65.3% were female, with a mean age of 17 (± 2.1) years and 90.8% aged between 15 and 19 years. Most of the youth, 45.2% were in secondary school, 40.7% were Anglican, and 71.4% were living with their parents. The majority of the youths, 46.8% were sexually active and had had sex in the past 4 months.

Perceived access to family planning services

The mean score for perception of access to family planning services was 1.91 with a standard deviation of ± 0.29. Figure 1 shows that the percentage of respondents that perceived access to be good for all the five variables was 31.7% (95% CI: 28%, 36%). The majority of the young people, 64.6% reported that different FP methods were available at the health facilities. Most of the young people, 79.3%% also reported that the health facilities were within their reach, and 61.3% reported that attitudes and personal characteristics of FP service providers were comfortable for them. The majority of the young people, 66.7% also reported that the manner in which FP services are organized, including facility’s operating and environment, suited their needs and preferences. Additionally, females had overall favorable responses compared to their male counterparts.

Percentage of young people reporting a good response to variables on the perceived access index in Lira district, Northern Uganda

Knowledge and attitudes regarding perceived access to family planning services

Table 2 presents questions used to assess both knowledge and perceptions regarding family planning services. questions 1 to 9 were designed to measure knowledge and 10 to 17 were aimed at capturing perceptions regarding use of family planning commodities. The majority of the young people, 69.4% were aware that FP, 75.6% knew the facility that offers FP services, 89.3% knew how to prevent pregnancy and 75.8% knew about sexual rights. Table 3 also shows that the majority of the young people, 58.1% perceived that FP services were not for young people, 80.5% could access FP whenever they wanted and 90.4% knew that information at the health facility was always kept confidential. However, the majority of the young people, 66.2% cannot decide on using a FP method, 57.7% also reported that there is not enough privacy at the health facilities, and 77.2% fear being mistreated by the staff at the health facilities.

Factors associated with perceived access to family planning services among young people

The bivariate analysis was performed stratified by sex to prevent introduction of bias arising from differencing sample sizes because males were close to a third of the entire sample. Table 3 indicates that among the females, being aged 20–24 years, having a child, being sexually active and having a sexual partner was associated with a higher perceived access to FP services at p value less than 0.25. On the other hand, having primary and secondary education, urban residence, Christians, Muslims, not in a marital relationship, secondary education of a mother, primary, secondary and tertiary education of father, and good attitude towards FP services were associated with a lower perceived access to FP services at p value less than 0.25. Table 3 also shows that among males, living with parents, mother’s secondary education level, and good attitude towards FP services had a lower perceived access to FP, where as being sexually active and good overall knowledge of FP services had higher perceived access to FP services with p value of less than 0.25.

Multivariate analysis was performed to assess the predictors of perceived access to family planning services for males and females, presented as two separate models for females and males. Table 4 show among females, residence, religion, sexual partners and perception regarding use of family planning methods had significant associations. Females respondents who were less likely to consider access to family planning services as good were urban residents (AOR: 0.22, 95% CI: 0.09–0.53, p = 0.001), those who were Christian (AOR: 0.51, 95% CI: 0.01–0.36, p = 0.003) and Muslim (AOR: 0.07, 95% CI: 0.01–0.55, p = 0.012), and those who had a poor attitude towards family planning services (AOR: 0.39, 95% CI: 0.24–0.64, p < 0.001). Female respondents who had a sexual partner were more likely to consider access to family planning services as good (AOR: 4.48, 95% CI: 2.60–7.75, p < 0.001). Table 4 also shows that among males, living with parents and overall knowledge about family planning services were significantly associated with perceive access to family planning services. Male respondents that were less likely to consider access to family planning as good were those who lived with their parents (AOR: 0.19, 95% CI: 0.05–0.67, p = 0.010), and those that were more likely to consider access to family planning as good were those that had good overall knowledge about family planning methods (AOR: 2.28, 95% CI: 1.02–5.32, p = 0.050).

Qualitative findings

Characteristics of participants.

A total of 5 in-depth interviews and 4 FGDs were conducted with a total of 30 young people; 10 were university students, whereas 20 were from the community. The focus groups were homogeneous in nature, for males and females separated. Two focus groups of 10 participants for males and females were conducted in the community, and two groups of five males and females were conducted from the University youths. The participants were young people aged 15 to 24 years. Themes were obtained through finding similar texts, patterns, and insights. We generated 8 different codes, 7 subthemes, and 3 themes.

Theme 1: knowledge of family planning methods

Majority of the young people did not have adequate knowledge regarding access and use of FP services. This was evidenced as most participants from the community reported that many young people used off label benefits of paracetamol and traditional herbal medicines for contraception. Additionally, many reported their source of information to be friends who seemed not to have adequate knowledge as well. Here are some of the verbatim comments to support the results:

“After having sex today, you can take 4 Panadol tablets immediately after having sex or 6 tablets, though it depends, you can also take it a day after having the sexual intercourse, taking on the third day will be late for it to work well in preventing the pregnancy”. (Female, 22 years, Lira Town, Feb 2023) “When I was in Primary six class. I was living with my sister and she had maids who told me about Panadol use”. (Female, 21 years, Junior quarters, Feb 2023) “Some girls use paw paw leaves, others mixing diclofenac drug with herbs which can also cause abortion. But these procedures can also either lead to incomplete abortion, death or even over bleeding” (Male, 24 years, Barapwo, Feb 2023) . “There is no proper sexual information. In the past, parents called children to prepare for education but today nowhere it’s practiced. Now it is only in schools to ensure that people know that sex is good but has challenges” (Female, 23 years, LU, Feb 2023) .

Theme 2: beliefs about youth contraception

The majority of the participants also reported negative perceptions regarding family planning services. However, this appears to stem from the common narrative that frames sexual health for young people as taboo. To continue, many young people and the community reported distancing themselves from reproductive health programs, citing that their motives are not entirely transparent. Here are some of the quotes that were recorded to emphasize the narrative:

“I see no meaning in engaging in such because they are just avenues for disseminating homosexuality and encouraging the youths to abort. They come in the sense of advocating for rights but instead teach that abortion and homosexuality is okay and a human right” (Female, 24 years, LU, Feb 2023) . “Family planning services are for big people. But there is need for a comprehensive guidance in matters of Sexual health for adolescents and adults about hygiene and opposite sex interaction” (Male, 16 years, Lira town, Feb 2023) .

Theme 3: friendliness of family planning services

Most of the participants reported that reproductive health services for young people are not friendly. The services are provided in environments that do not guarantee privacy and confidentiality, as well as during inflexible hours. To emphasize the narrative, here are a few verbatim comments:

It’s very difficult to go and access family planning services like pills from the teaching hospital…, can you imagine being served by your own lecturer who discourages having sex before marriage……Hmmm it’s funny! (Female, 24 years, LU, Feb 2023) A friend can help buy contraceptives if the user is known to the health worker who is selling. The seller might inform the buyer’s parents when one goes to buy condoms. (Male, 18 years, Amuca, Feb 2023)

The study aimed to assess perceived access to FP services and associated factors among young people in Lira City, Northern Uganda. Though many models have been suggested to measure access, they have all showed deficiencies in measuring actual access to family planning methods [ 30 ]. This study adopted the Penchansky and Thomas (1981) framework that measures perception of access through a 5-item index to explore the level of perceived access in this study. Findings of the current study showed that good perceived access to FP services was among 31.7% of respondents, with 64.6% reporting availability, 76.5% accessibility, 61.3% acceptability, 66.7% accommodative and 87.9% affordability of FP methods at health facilities. Our study indicates a low perceived access to FP services. Among the various components, availability, acceptability and accommodation pose significant obstacles to contraceptive access. A similar study in South Africa also reported the accommodation component as the greatest obstacle for accessing FP services due to integrated care, long waiting hours, and limited operational hours [ 38 ]. Additionally, the study reported that community were less concerned about the availability of trained service providers and a variety of contraceptive methods [ 38 ]. These possibly explain the low perceived access in the current study. In line with the current study, a recent study on utilization of sexual and reproductive services including family planning among young people in Lira city also reported a low level of 42% [ 39 ].

The overall perceived access to FP services at 31.7% suggests a substantial gap in service availability, indicating the need for targeted interventions to enhance accessibility. The presence of different FP methods at health facilities (64.6%) is a positive aspect, but the study unveils underlying challenges that contribute to the overall low perceived access. One of the key positive findings is the proximity of health facilities for 79.3% of participants, emphasizing the importance of physical accessibility. Additionally, positive perceptions towards use of family planning commodities, such as acceptability of FP use by the young people (61.3%) and a conducive environment at health facilities (66.7%), indicate a foundation upon which interventions can build. However, challenges identified, particularly for females, including a lack of privacy (57.7%), fear of mistreatment by staff (77.2%), and difficulties in decision-making regarding FP use (66.2%), highlight the nature of barriers to access. These challenges align with existing literature on the importance of privacy [ 40 ], quality of service [ 41 ], and decision-making autonomy in shaping individuals’ willingness to utilize FP services [ 42 ].

Quantitative findings revealed significant associations between perceived access to FP services and various sociodemographic factors, emphasizing the complexity of the issue. For females, urban residence, religion, having sexual partners, and perception were identified as influencing factors, while for males, living with parents and overall knowledge played a significant role. These associations underline the necessity for tailored interventions that consider the specific challenges faced by each gender. Qualitative findings highlighted insufficient knowledge, negative perceptions, and unfriendly FP services. These findings provide a deeper understanding of the barriers, emphasizing inadequate knowledge of FP methods, negative cultural and societal perceptions about youth contraception, and unfriendly service environments. These findings are consistent with existing literature, highlighting the role of cultural perceptions, knowledge gaps, and service quality in shaping young people’s access to FP services [ 43 ]. In agreement with previous studies, the study underscores the importance of comprehensive sexual education programs and youth-friendly service initiatives [ 44 ]. Our study shows a notable link between Islam and Catholicism and perceived access to FP services, aligning with previous research on religious influences that notes that the use of contraception is not promoted by any of the two religions [ 45 ]. Further exploration and comparative analysis with other studies may help elucidate these discrepancies and provide a more nuanced understanding of the factors influencing access to FP services among young people in Northern Uganda.

Strength and limitations

The study benefits from a mixed-methods approach, which integrates both qualitative and quantitative data to offer a comprehensive understanding of the factors influencing young people’s perceived access to family planning services. However, the cross-sectional design presents a limitation as it hinders the establishment of causality, providing only a snapshot of the situation at a specific moment and limiting exploration of temporal relationships over time. Acknowledging the small sample size and the potential bias introduced by selecting individuals with extensive knowledge on the topic, we recognize the limitation on the generalizability of our findings only to Lira City. The selection of individuals for IDIs may have inadvertently limited the diversity of perspectives represented in our study. Furthermore, participants may exhibit social desirability bias, particularly in studies addressing sensitive topics like sexual and reproductive health. Recall bias among participants, particularly when recalling past experiences related to sensitive topics or events that occurred some time ago, is also a possibility. Lastly, the quantitative sample was skewed towards females and those aged 15–19 years, potentially affecting the representativeness of the findings.

Our study reveals a substantial gap in perceived access to family planning services among young people. Despite high awareness, barriers like privacy concerns and fear of mistreatment contribute to low access. Tailored interventions are needed, focusing on urban service access, religious beliefs for females, and knowledge enhancement for males. Positive aspects, such as diverse FP methods and physical accessibility, form a foundation for interventions. The study emphasizes the importance of youth-friendly services, comprehensive sexual education, and further research for a nuanced understanding and targeted interventions in Northern Uganda.

Data availability

The data for the study is not publicly available due to restrictions from the Research Ethics Committee (REC) for posting of public data. However, can be accessed from the principal investigator on a reasonable request ([email protected]).

Abbreviations

Sexual Reproductive Health and Rights

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Village Health Team

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Acknowledgements

Pre-Publication Support Service (PREPSS) supported the development of this manuscript by providing author training, as well as pre-publication peer-review and copy editing.

The authors want to acknowledge all the young people who took part in the study. In a special way, we also want to thank Dr. Marc Sam Opollo of Faculty of Public Health Lira University for reviewing and guiding our results presentation for the annual sexual and reproductive symposium presentation in 2023.

This research work was supported by a seed grant from the Center for International Reproductive Health Training at the University of Michigan (CIRHT-UM). The content is solely the responsibility of the authors and does not necessarily represent the official views of CIRHT-UM. The funders had no role in study design, data collection and analysis, the decision to publish, or the preparation of the manuscript.

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Eustes Kigongo, Raymond Tumwesigye, Maxson Kenneth Anyolitho, Marvin Musinguzi, Everlyne Achan & Bernard Omech

Faculty of Nursing , Mbarara University of Science and Technology, Mbarara, Uganda

Caroline Kambugu Nabasirye & Samson Udho

Faculty of Education, Lira University, Lira, Uganda

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Faculty of Medicine, Lira University, Lira, Uganda

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Contributions

All authors made significant contributions to the conceptualization, design, data collection, curation, manuscript writing, and editing. EK, MKA and RT conceptualized and designed the study. EA, MM, GK, CKN, and SU designed the data collection tools and conducted the study. AK and BO gave overall guidance for the study. All the authors gave final approval to the manuscript for journal submission and are responsible for the content of the manuscript.

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Correspondence to Eustes Kigongo .

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Kigongo, E., Tumwesigye, R., Anyolitho, M.K. et al. Access to family planning services and associated factors among young people in Lira city northern Uganda. BMC Public Health 24 , 1146 (2024). https://doi.org/10.1186/s12889-024-18605-8

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