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I went with conversion rate as the primary metric, which felt obvious, and then listed unsubscribe rate and spam complaint rate as guardrails.
Start by clarifying the business goal of the A/B test and how it maps to a measurable primary success metric that directly reflects the intended impact. Then select at least two guardrail metrics that capture potential negative side effects on long-term health, such as customer satisfaction or retention. Justify each metric by linking it to the company's strategic objectives and explaining how it balances short-term gains with long-term sustainability.
Pro tip: Choose guardrail metrics that are leading indicators of long-term value, not just lagging ones, and explicitly state thresholds for acceptable degradation to show you understand risk management in experimentation.
Restate the hypothesis and the specific change being tested to ensure alignment on what success looks like. Identify the key business outcome the test aims to influence.
Select a metric that directly measures the intended impact and is sensitive to the change. Justify why it is the best proxy for the business goal, considering factors like measurability and alignment with strategic KPIs.
Choose at least two metrics that could be negatively affected by the change and are critical to long-term program health. Examples include customer retention, satisfaction (e.g., NPS), or operational efficiency.
Explain how each guardrail protects against unintended consequences and why it matters for long-term success. Link them to potential trade-offs and the company's risk tolerance.
Recap how the primary and guardrail metrics together provide a balanced view of success. Mention any statistical considerations, such as power or minimum detectable effect, to show rigor.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the parameters: baseline conversion rate (p1=0.05), relative lift of 10% gives p2=0.055. Then, use the standard formula for sample size per arm for a two-proportion z-test: n = ( (z_{α/2} + z_β)^2 * (p1(1-p1) + p2(1-p2)) ) / (p2 - p1)^2. Plug in z_{α/2}=1.96, z_β=0.84, and compute the result, rounding up to the next integer.
Pro tip: Mention that this is a simplified calculation assuming no continuity correction and equal arm sizes; in practice, you might adjust for unequal allocation or use exact methods, but this is standard for quick sizing.
Identify baseline conversion rate (p1=0.05), relative lift (10%), so p2 = p1 * 1.10 = 0.055. Also note significance level (α=0.05, two-sided) and power (1-β=0.80).
For two-sided test at 95% confidence, z_{α/2} = 1.96. For 80% power, z_β = 0.84 (or 0.8416).
Use n = ( (z_{α/2} + z_β)^2 * (p1(1-p1) + p2(1-p2)) ) / (p2 - p1)^2. Compute numerator and denominator separately.
Plug in values: (1.96+0.84)^2 = 7.84; p1(1-p1)=0.0475; p2(1-p2)=0.051975; sum=0.099475; difference=0.005; squared=0.000025. n = (7.84 * 0.099475) / 0.000025 ≈ 31,195. Round up to 31,196 per arm.
State that approximately 31,196 users per arm are needed. Mention assumptions: independent observations, no continuity correction, equal variance approximation.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
I brought up Bonferroni as the simple answer, then mentioned that hierarchical modeling lets you borrow strength across tiers which is more appropriate when segments are small.
Start by acknowledging the multiple testing problem when segmenting by donor tier, then propose a hierarchical Bayesian model that partially pools information across tiers to control false positives. Alternatively, discuss pre-registering tier-based hypotheses with appropriate corrections like Bonferroni or FDR, and emphasize the trade-off between power and false discovery. Conclude with how you'd validate results via simulation or holdout.
Pro tip: Mention that hierarchical models are especially useful when tier sizes are imbalanced—high-value donors are few, so borrowing strength from the overall population reduces variance without inflating false positives. Also, note that pre-registration of tier hypotheses is key to avoid p-hacking.
Explain that segmenting by donor tier creates multiple comparisons (e.g., high vs. low), increasing family-wise error rate. Emphasize the need to control false positives.
Present options: frequentist corrections (Bonferroni, Holm, FDR) or hierarchical Bayesian models. Discuss when each is appropriate, noting hierarchical models are better for small subgroups.
Describe how partial pooling across tiers estimates tier-specific effects while shrinking extreme estimates toward the overall mean, reducing false positives. Mention priors and hyperpriors.
Propose simulating data under the null to check false positive rates, or using a holdout set to confirm findings. This demonstrates rigor.
Summarize how the chosen method balances false positives and power, and how it informs decisions about donor tiers. Highlight interpretability for stakeholders.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Peeking question is pretty standard and I handled it fine.
Start by defining a stopping rule based on statistical power and business constraints, then explain the risks of peeking (inflated Type I error, biased estimates). Finally, address uneven email deliverability by proposing segment-level analysis and adjustments like stratification or weighted metrics.
Pro tip: Mention sequential testing or alpha-spending as a rigorous alternative to fixed-horizon tests if stakeholders insist on early looks, and emphasize pre-registration of the stopping rule to avoid p-hacking.
Specify a fixed sample size or duration based on power analysis, and state that the experiment will stop only when that criterion is met. Optionally, mention sequential testing methods if early stopping is required.
Describe how repeated looks at accumulating data inflate the false positive rate and lead to biased effect estimates. Emphasize that peeking without correction undermines the validity of the test.
Acknowledge that deliverability differences across segments can confound results. Propose analyzing results within segments, using stratification, or weighting to ensure balanced comparisons.
Suggest techniques like inverse probability weighting, propensity score adjustment, or running separate experiments per segment if deliverability issues are severe.
Tie the technical solutions back to reliable decision-making, ensuring that conclusions are valid and actionable for the business.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This was my favorite part of the whole case because it forced you to stop treating conversion rate as the end goal.
Reframe the decision by calculating net revenue per reached recipient for both variants, incorporating the conversion rate and average gift size. Compare the net revenue per recipient to determine which variant yields higher overall revenue, considering the trade-off between conversion and gift size. Show the calculation clearly and discuss implications for statistical significance and business goals.
Pro tip: Always tie the metric back to the business objective—here, net revenue per recipient directly aligns with profitability. Also, mention that you'd validate the result with a confidence interval to ensure the difference isn't due to chance.
Net revenue per reached recipient = conversion rate × average gift size. This metric captures both the likelihood of conversion and the value of each conversion.
Assume baseline values for Variant A (e.g., conversion rate = c, average gift = g). For Variant B, conversion rate increases by some percentage (e.g., +x%), and average gift decreases by 5% (so new gift = 0.95g).
For Variant A: R_A = c × g. For Variant B: R_B = (c × (1 + x/100)) × (0.95g). Simplify to R_B = 0.95 × (1 + x/100) × c × g.
Compare R_B to R_A. Variant B is better if 0.95 × (1 + x/100) > 1, i.e., if the conversion lift exceeds approximately 5.26% (since 1/0.95 ≈ 1.0526). Otherwise, Variant A yields higher net revenue per recipient.
Even if R_B > R_A, check if the difference is statistically significant and practically meaningful. Consider confidence intervals and potential long-term effects on customer lifetime value.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.