Skill Guide

Statistical hypothesis testing and multiple testing correction (BH, FDR)

Statistical hypothesis testing is the formal procedure of using sample data to decide whether to reject a null hypothesis, while multiple testing correction (like Benjamini-Hochberg/BH and False Discovery Rate/FDR) adjusts the significance threshold to control the expected proportion of false positives when performing numerous simultaneous tests.

It enables data-driven decision-making with quantifiable confidence, preventing costly false conclusions in A/B testing, genomics, and risk modeling. Mastering it directly protects revenue and reputation by ensuring findings are statistically robust, not random noise.

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How to Learn Statistical hypothesis testing and multiple testing correction (BH, FDR)

1. Master core concepts: p-values, Type I/II errors, null/alternative hypotheses, significance level (alpha). 2. Understand the multiple testing problem: why running thousands of t-tests inflates false positives. 3. Learn the BH procedure step-by-step: sorting p-values, calculating adjusted thresholds, and applying the FDR control.

Apply to real datasets: run A/B test analysis with >10 metrics, perform genomic differential expression analysis. Common mistake: applying BH without checking test assumptions (e.g., independence). Use permutation tests or bootstrap methods when distributional assumptions fail. Practice interpreting Q-values (FDR-adjusted p-values) in tools like R or Python.

Design and oversee enterprise-scale experimentation platforms (e.g., feature rollouts with 100+ metrics). Implement hierarchical testing procedures (e.g., gatekeeping) for correlated endpoints. Mentor teams on aligning statistical thresholds with business risk tolerance and operationalizing FDR control in automated pipelines.

Practice Projects

Beginner

Project

A/B Test Metric Analysis with BH Correction

Scenario

You have click-through data for 20 different webpage elements from an A/B test. Naively, 1 out of 20 will appear significant by chance at α=0.05.

How to Execute

1. Simulate data with no true effect (null) for 20 metrics. 2. Perform individual t-tests or proportion tests for each metric. 3. Implement the BH procedure manually or with `statsmodels.stats.multitest.multipletests()` in Python. 4. Compare the number of 'significant' results before and after correction.

Intermediate

Case Study/Exercise

Genomics Differential Expression Pipeline

Scenario

Analyze RNA-seq data with ~20,000 gene expression levels to identify genes differentially expressed between two cell types. Control the FDR at 5%.

How to Execute

1. Use DESeq2/edgeR in R to compute per-gene p-values. 2. Apply BH correction. 3. Filter genes with adjusted p-value (q-value) < 0.05. 4. Validate top hits against known biological pathways and assess the impact of correlation between genes on FDR control.

Advanced

Project

Enterprise Experimentation Platform Audit

Scenario

Audit a platform running 500+ concurrent experiments with 50+ metrics each. Reports show a suspiciously high number of 'wins'.

How to Execute

1. Analyze historical data to estimate the proportion of true nulls (π₀). 2. Evaluate if BH or Storey's q-value is more appropriate. 3. Design a two-stage gatekeeping procedure to control family-wise error rate (FWER) for primary metrics and FDR for secondary exploratory metrics. 4. Present a cost-benefit analysis of stricter vs. looser FDR thresholds to stakeholders.

Tools & Frameworks

Software & Platforms

R (stats::p.adjust, multtest, qvalue packages)Python (statsmodels.stats.multitest, scipy.stats)JMP/SAS (Fit Y by X, Multivariate Methods)Genomics: DESeq2, edgeR, limma

Use R/Python for custom analysis pipelines and reproducibility. JMP/SAS for interactive, GUI-driven exploration. Specialized genomics packages incorporate model-based p-value adjustments with BH.

Mental Models & Methodologies

Benjamini-Hochberg ProcedureBonferroni Correction (FWER)Storey's Q-Value / π₀ EstimationHierarchical Testing / Gatekeeping

BH is the standard FDR control method. Bonferroni is overly conservative for large-scale testing. Storey's method improves power when many nulls are true. Gatekeeping is used for structured hypothesis families (e.g., primary/secondary endpoints).

Interview Questions

Answer Strategy

Diagnose the multiple testing problem immediately. Explain the inflated family-wise error rate (>50% chance of at least one false positive). Propose BH correction to control the False Discovery Rate at 5%, ensuring that among declared successes, only 5% are expected to be false. Provide a concrete implementation plan using their analytics stack.

Answer Strategy

Test understanding of statistical vs. practical significance and large sample sizes. The answer must pivot from statistical significance to effect size and business impact. Mention visualization (volcano plot) and setting a higher threshold for action.