ANOVA (Analysis of Variance)

Introduction

• Definition — Analysis of variance (ANOVA) is the family of techniques that tests the null hypothesis that the means of two or more populations (groups/treatments) are equal, by partitioning the total variability in the data into identifiable components and comparing them.
• Why the name — A hypothesis about means is tested by analysing variances — comparing the variance between group means against the variance within groups. If groups truly differ, the between-group variance is inflated relative to the within-group variance.
• Extends the t-test — ANOVA is the natural extension of the two-sample t-test to ≥3 groups. With exactly 2 groups, one-way ANOVA is algebraically equivalent to the two-sample t-test and F = t² (the F-statistic on 1 numerator df equals the square of the t-statistic).
• Why not many t-tests — Running all pairwise t-tests across several groups inflates the overall (familywise) Type I error far above α — the multiple-comparisons problem. ANOVA gives a single omnibus test of "are any means different?" at a controlled α before any pairwise probing.
• Omnibus only — A significant F says at least one mean differs — but not which; locating the difference requires post-hoc / multiple-comparison procedures.
• Pharmacology relevance — The default analysis whenever a continuous outcome (BP fall, enzyme concentration, AUC, pain score, receptor density, % inhibition) is compared across ≥3 treatment arms — multi-dose comparisons, dose–response designs, several actives vs placebo, multi-group preclinical experiments, and repeated-measures pharmacodynamic time-courses.
• RGUHS / NMC — Recurring 10-mark question (2 RGUHS recurrences plus DNB, MUHS, MPMSU); maps to the NMC PG competency — apply appropriate biostatistical tests.