Design A/B Test for Cost-Per-Conversion Efficiency Analysis
Multi-Arm A/B Test: Comparing Cost-Per-Conversion Across Channels
Scenario
You need to compare four new acquisition channels—YouTube ads, Google Search ads, Facebook ads, and Direct Mail—to choose the most cost-efficient option for driving conversions given a fixed budget.
Task
Design a rigorous multi-arm A/B test to evaluate cost-per-conversion efficiency across these channels.
Address the following:
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Primary metric
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What exactly will you optimize? Define the metric precisely (including incrementality vs. attribution, unit of analysis, and conversion window).
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Experimental design
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Randomization scheme (units, arms, control), avoiding cross-channel contamination, frequency caps, and deduped conversions.
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Hypotheses and statistical test
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State the null and alternative hypotheses, and specify the appropriate global and pairwise tests.
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Sample size, budget split, and duration
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How will you determine these given desired power and minimum detectable effect (MDE)? Include how per-user costs differ by channel.
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Post-hoc / follow-up analyses
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What analyses will you run after the main test (e.g., multiple comparisons, heterogeneity, creative, response curves)?
Hints: Discuss cost-per-conversion metric, multi-arm design, power/alpha, ANOVA vs. pairwise tests, budget allocation, assumptions, and demographic/creative differences.
Constraints & Assumptions
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Preserve the scope, facts, inputs, and requested outputs from the prompt above.
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If the prompt leaves a detail unspecified, state a reasonable assumption before relying on it.
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Keep the answer interview-ready: concise enough to present, but concrete enough to implement or evaluate.
Clarifying Questions to Ask
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Clarify the business objective, unit of analysis, time window, exposure definition, and primary metric.
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State assumptions about instrumentation, randomization, sample size, and data quality.
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Separate descriptive analysis from causal claims.
What a Strong Answer Covers
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A metric framework with primary, guardrail, and diagnostic metrics.
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A credible analysis or experiment design with clear assumptions and bias checks.
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SQL/statistical logic for segmentation, variance, confidence, and data validation where relevant.
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An actionable recommendation that explains trade-offs and next steps.
Follow-up Questions
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What sanity checks would you run before trusting the result?
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How would you handle novelty effects, seasonality, or selection bias?
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What decision would you make if metrics disagree?