The model-based A/B tests: ANOVA for three or more groups, the Chi-square test for categorical data, and the Bonferroni correction, with a chi-squared-distribution and KL-divergence appendix.

The design decisions that make a randomized experiment trustworthy: the causal estimand, the design checklist, and the validity threats (SRM, peeking, clustering, interference).

Prelude: The Central Limit Theorem (CLT) Before diving into null hypotheses and p-values, it is helpful to understand the mathematical phenomenon that underpins large-sample inference: the Central...

This post bridges the probability distributions series to statistical inference. In the realm of statistics, p-values and confidence intervals are fundamental tools that help us make sense of dat...

The Beta distribution models a proportion or probability on [0,1]: how its two shape parameters bend the curve, its role as the Binomial's conjugate prior, a worked Bayesian update, and when it fits.

The Gamma distribution models the waiting time until the k-th constant-rate event: its shape and rate parameters, the Poisson-tail reading of its CDF, how it generalizes the Exponential, and when it fails.

The Laplace distribution: a sharp-centered symmetric model with heavier-than-Normal (still exponential) tails, its median/L1 connections, and where it fits.

The Log-Normal models positive multiplicative variation: median, mode, and mean, why sigma controls the skew, the CDF via the Normal, and why stock-price claims are model-dependent.

The Normal distribution models additive variation around a center: the 68-95-99.7 rule, z-scores, what the CLT does and does not say, and when a bell curve is the wrong model.

The Negative Binomial has two faces: a waiting time for the r-th success, and an overdispersed count arising from a Gamma mixture of Poisson rates.