Bonferroni Correction & Selection Bias

The Multiple Testing Correction (Bonferroni, Benjamini-Hochberg FDR & Selection Bias Mitigation) framework defends statistical evaluations against the catastrophic inflation of false-positive discoveries (P-hacking); Family-Wise Error Rate (FWER) theorem: evaluating $K$ independent model variants at significance level $\alpha=0.05$ causes overall false-positive risk to explode exponentially: $\alpha_{\text{FWER}} = 1 - (1-\alpha)^K$ (when testing $K=20$ random baselines with zero real effect, there is a 64.2% statistical certainty of observing at least one spurious $p < 0.05$ result by pure chance); corrective remedies include: 1) Bonferroni Correction (setting significance threshold to $\alpha' = \frac{\alpha}{K}$); 2) Benjamini-Hochberg False Discovery Rate (FDR) rank scaling; 3) Strict holdout test set locking.

Multi-model benchmark statistical auditing, correcting post-selection optimization bias, and rigorous academic peer-review validation.

Cherry-picking the single best checkpoint out of 200 trials severely inflates reported test performance; multiple testing corrections eliminate spurious false-positive discoveries.

Derive the mathematical proof showing why testing $K=100$ trials yields a $>99.4\%$ probability of generating a spurious false-positive result?

Contrast Bonferroni (controlling FWER) vs Benjamini-Hochberg (controlling FDR) in statistical conservatism and Type-II error power?

Why does repeated model selection on validation sets induce overfitting to the test distribution without clean holdout splits?

How does non-parametric Bootstrap Resampling construct empirical 95% confidence intervals on model performance deltas?

Explain Data Snooping and HARKing pitfalls and how experiment pre-registration enforces scientific integrity?