Chi-square Test

Introduction

• Definition — Chi-square (χ²) is a family of non-parametric inferential tests comparing observed (O) and expected (E) frequencies in categorical data against the χ² sampling distribution.
• Test family — Four named variants — Pearson goodness-of-fit, Pearson independence, χ² of homogeneity, and McNemar (paired) — plus Mantel–Haenszel (stratified), Cochran–Armitage (trend), and the likelihood-ratio G² statistic.
• Historical anchor — Pearson 1900 introduced χ² as the first general goodness-of-fit test; Yates 1934 added the continuity correction; Fisher 1934 defined the exact alternative; McNemar 1947 adapted it for paired binary data.
• MD pharmacology relevance — First-line test for categorical outcomes in pharmacology — drug-vs-placebo response rates, ADR incidence, genotype frequencies, and ordered-category survey responses.
• RGUHS / NMC — Recurring 10-mark RGUHS LAQ (6 verbatim recurrences in the past-question corpus + 3 MPMSU); NMC PG competency PG2.5 — apply appropriate biostatistical tests.