The Problem

"How does plant diversity differ between fertilized and control plots?" "Do different ecosystems respond to nitrogen addition in the same way?" These are everyday "compare several groups" questions in ecology. Running pairwise t-tests across many groups is tedious and inflates the probability of a Type I error (a false positive) through multiple comparisons. This is exactly what ANOVA (Analysis of Variance) is built for.

ANOVA uses a single F-test to ask whether all group means are equal, then post-hoc multiple comparisons locate which groups actually differ. Using a "nitrogen addition level × ecosystem type" experiment on plant diversity, this tutorial walks the full workflow: assumption checks, single-factor ANOVA, two-way ANOVA with an interaction effect, and simple effects via emmeans after a significant interaction.

How ANOVA Works

Single-factor ANOVA tests whether one categorical factor (e.g., nitrogen level) affects a continuous response (e.g., the Shannon diversity index).…