Probability and statistics are foundational to the data scientist role—especially for roles involving A/B testing, causal inference, and experimentation. Companies like Google, Meta, and Airbnb use these questions to test your ability to reason with uncertainty, evaluate experiments, and communicate results clearly.
In this article, we’ll explore the most commonly asked statistics concepts in data interviews and how to answer them with both clarity and business insight.
🎯 Core Topics You Must Know
1. Hypothesis Testing
Understand the framework:
- Null Hypothesis (H₀): No effect or no difference
- Alternative Hypothesis (H₁): There is an effect
- Type I Error: False positive — reject H₀ when it's true
- Type II Error: False negative — fail to reject H₀ when it’s false
- Significance Level (α): Commonly set at 0.05
✅ Tip: Always state your hypotheses clearly in interviews.
2. P-Values
The p-value is the probability of observing a result as extreme or more extreme under the assumption that the null hypothesis is true.
“A p-value of 0.03 means that there’s a 3% chance of observing this result if the null hypothesis were true.”
💡 Common Mistake: P-value ≠ probability the null is true
It’s a measure of evidence against the null—not the probability that the null is false.
3. Confidence Intervals
A 95% confidence interval means that if you repeat the experiment many times, about 95% of the calculated intervals will contain the true parameter.
“We are 95% confident that the true click-through rate is between 1.2% and 1.8%.”
Why it matters:
- It tells you about effect size and uncertainty
- More interpretable than p-values alone
4. Statistical Power
Power = 1 − Type II error rate
It answers: If there is a true effect, how likely are we to detect it?
Use power analysis to:
- Estimate required sample size before A/B tests
- Avoid underpowered tests that produce inconclusive results
5. Bayesian Inference (Optional but Impressive)
Bayesian thinking allows you to:
- Start with a prior belief
- Update it using observed data → posterior belief
“If I believe there's a 20% chance the experiment will work before running it, and the result is positive, how does that change my belief?”
If you mention Bayesian methods like Bayes' Theorem, credible intervals, or priors, be ready to explain intuitively.
🧠 Common Interview Questions
Q1. What does a p-value of 0.04 mean?
- Don't say: “There’s a 4% chance the null is true.”
- Do say: “If the null hypothesis is true, there’s a 4% chance of observing this result or more extreme.”
Q2. You run an A/B test and get p=0.08. What do you do?
Options:
- Check statistical power — was the test underpowered?
- Segment results — is the effect stronger in a specific group?
- Consider business risk — is an 8% p-value still good enough for the decision?
Q3. How would you estimate the sample size for an A/B test?
Key inputs:
- Baseline conversion rate
- Minimum detectable effect (MDE)
- Power (commonly 0.8)
- Significance level (commonly 0.05)
Use a power calculator or formulas to estimate.
⚠️ Common Pitfalls to Avoid
- Interpreting p-values incorrectly
- Focusing only on significance, ignoring effect size
- Neglecting sample size or power in test design
- Ignoring assumptions of the test (e.g., independence, normality)
- Not tying results to business decisions
🧩 Applied Scenarios
Scenario 1: Interpreting Inconclusive Test Results
“Your A/B test didn’t reach statistical significance. What next?”
Answer:
- Check if there was enough power
- Segment results to look for patterns
- Run a follow-up test or switch to Bayesian methods
- Make a decision based on cost-benefit analysis, not just p-values
Scenario 2: Communicating Stats to Non-Technical Stakeholders
“How would you explain a confidence interval to a PM?”
Say:
“We’re 95% confident that the feature improves retention between 1–3%, which gives us confidence to roll it out.”
📌 Tips to Impress
- Bring examples from past tests or analyses
- Explain why the statistical result matters to the business
- Show you understand uncertainty and decision-making trade-offs
- Use visuals or analogies if asked to explain to non-technical people
✅ Conclusion
Excelling at statistics in interviews is about more than memorizing formulas. It’s about showing that you understand the language of uncertainty, and can apply that knowledge to make sound product and business decisions. Master these core ideas and practice applied case studies to gain an edge in your interviews.