Explain P-value, Confidence Interval, and Multiple Testing Adjustments
Overview
This question evaluates a data scientist's mastery of inferential statistics for A/B testing, encompassing p-values and confidence intervals, multiple-testing adjustments (Bonferroni vs Tukey’s HSD), Type I/II error interpretation, selection of Z versus t tests, and the practical implications of the Central Limit Theorem versus the Law of Large Numbers. It is commonly asked in the Statistics & Math domain to evaluate interpretation of experimental results, control of false positives across comparisons, and both conceptual understanding and practical application of hypothesis-testing assumptions in production experiments.
A/B Testing and Inferential Statistics for a New Product Launch
You are running online A/B experiments to evaluate a new product launch. Assume standard randomized assignment, independent users/sessions, and a binary primary metric (e.g., conversion), unless otherwise noted.
Answer the following:
- Define the p-value and a confidence interval (CI), and explain their relationship.
- How do you adjust for multiple testing? Briefly describe and contrast Bonferroni and Tukey’s HSD, and note when you would use each.
- Explain Type I and Type II errors with concrete A/B testing examples.
- When would you use a Z-test versus a t-test? State assumptions and typical A/B testing choices.
- Compare the Central Limit Theorem (CLT) with the Law of Large Numbers (LLN), including practical implications for experiment analysis.
Solution
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