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

Last updated: Mar 29, 2026

Quick Overview

This question evaluates a data scientist's competency in experimental design and metrics engineering for multi-arm A/B tests, including defining cost-per-conversion metrics, randomization and contamination controls, sample size and power calculations, statistical hypothesis testing, and post-hoc heterogeneity analyses.

  • hard
  • TikTok
  • Analytics & Experimentation
  • Data Scientist

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

Company: TikTok

Role: Data Scientist

Category: Analytics & Experimentation

Difficulty: hard

Interview Round: Onsite

##### Scenario You are the data scientist for a marketing division considering four new acquisition channels—YouTube ads, Google Search ads, Facebook ads, and direct-mail. Leadership wants the marketing budget used in the most cost-efficient way. ##### Question How would you design an A/B (multi-arm) test to compare the cost-per-conversion efficiency of YouTube, Google Search, Facebook, and Direct Mail campaigns? What metric will you optimize and how will you define it precisely? State the null and alternative hypotheses and the statistical test you would apply. How will you determine sample size, budget split, and test duration given desired power and MDE? What post-hoc or follow-up analyses would you conduct after the main test? ##### Hints Discuss cost-per-conversion metric, multi-arm design, power & alpha, ANOVA vs pairwise tests, budget allocation, assumptions, and demographic or creative differences.

Quick Answer: This question evaluates a data scientist's competency in experimental design and metrics engineering for multi-arm A/B tests, including defining cost-per-conversion metrics, randomization and contamination controls, sample size and power calculations, statistical hypothesis testing, and post-hoc heterogeneity analyses.

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TikTok logo
TikTok
Aug 4, 2025, 10:55 AM
Data Scientist
Onsite
Analytics & Experimentation
148
0

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:

  1. Primary metric
    • What exactly will you optimize? Define the metric precisely (including incrementality vs. attribution, unit of analysis, and conversion window).
  2. Experimental design
    • Randomization scheme (units, arms, control), avoiding cross-channel contamination, frequency caps, and deduped conversions.
  3. Hypotheses and statistical test
    • State the null and alternative hypotheses, and specify the appropriate global and pairwise tests.
  4. 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.
  5. 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.

Solution

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