Design A/B Test for Cost-Per-Conversion Efficiency Analysis

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Question

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:

Primary metric
- What exactly will you optimize? Define the metric precisely (including incrementality vs. attribution, unit of analysis, and conversion window).
Experimental design
- Randomization scheme (units, arms, control), avoiding cross-channel contamination, frequency caps, and deduped conversions.
Hypotheses and statistical test
- State the null and alternative hypotheses, and specify the appropriate global and pairwise tests.
Sample size, budget split, and duration
- How will you determine these given desired power and minimum detectable effect (MDE)? Include how per-user costs differ by channel.
Post-hoc / follow-up analyses
- 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.

Clarifying Questions to Ask Guidance

Clarify the business objective, unit of analysis, time window, exposure definition, and primary metric.
State assumptions about instrumentation, randomization, sample size, and data quality.
Separate descriptive analysis from causal claims.

What a Strong Answer Covers Guidance

A metric framework with primary, guardrail, and diagnostic metrics.
A credible analysis or experiment design with clear assumptions and bias checks.
SQL/statistical logic for segmentation, variance, confidence, and data validation where relevant.
An actionable recommendation that explains trade-offs and next steps.

Follow-up Questions Guidance

What sanity checks would you run before trusting the result?
How would you handle novelty effects, seasonality, or selection bias?
What decision would you make if metrics disagree?

Design A/B Test for Cost-Per-Conversion Efficiency Analysis

Quick Overview

Design A/B Test for Cost-Per-Conversion Efficiency Analysis

Design A/B Test for Cost-Per-Conversion Efficiency Analysis

Multi-Arm A/B Test: Comparing Cost-Per-Conversion Across Channels

Scenario

Task

Clarifying Questions to Ask Guidance

What a Strong Answer Covers Guidance

Follow-up Questions Guidance

Write your answer