Hypothesis Testing, Type I/II & Power

Statistical Hypothesis Testing, Type I/II Error Trade-offs & Power Analysis formalizes the decision-theoretic framework for online A/B experimentation; under null hypothesis $H_0$ (treatment effect $\Delta = 0$) versus alternative hypothesis $H_1$ (treatment effect $\Delta \neq 0$): 1) Type I Error ($\alpha$, False Positive): rejecting true null when no real effect exists, industrially capped at $\alpha = 0.05$; 2) Type II Error ($\beta$, False Negative): failing to detect a genuine effect; 3) Statistical Power ($1 - \beta$): the probability of correctly rejecting false null given true effect size $\delta$, industrially targeted at $\ge 0.80$ ($80\%$); balancing Type I and II risk governs sample allocation and guards against both reckless feature rollouts and missed revenue growth opportunities.

A/B test parameter design, DS foundational statistics screening, and business risk governance.

Eliminates both false-positive feature rollouts that degrade UX and false-negative omissions of winning growth strategies due to undertrained sample sizes.

Draw the dual probability density curves of $H_0$ and $H_1$ highlighting exact geometric areas corresponding to $\alpha/2$, $\beta$, and Power ($1-\beta$)?

Why must product A/B tests enforce Two-Tailed tests even when positive metric lifts are anticipated (protecting against severe regressions)?

Contrast Statistical Significance ($p < 0.05$) vs Practical Business Significance (Cohen's $d$) under big-data sample regimes?

Why does Welch's $t$-test serve as the robust default over Student's $t$-test under unequal group sizes and heteroscedastic variances?

Prove the asymptotic equivalence between the 2-sample proportion $Z$-test and Pearson's Chi-Square Test for binomial ratio metrics?