One Test, Many Means: Why ANOVA Exists

T-tests shine when there are two groups. Add a third and you’re tilting at windmills… each pairwise test inflates your error, turning “maybe” into “must be.” ANOVA reframes the question: is between-group variation meaningfully larger than within-group noise? One gatekeeping test protects your alpha, then (if warranted) planned contrasts or honest post-hocs tell you where differences live. The deeper lesson: structure beats scavenging. Pre-register the one big question. Specify which follow-ups you’d run if the omnibus is significant. Commit to reporting effect sizes (η²/ω²) and intervals, not just stars. Models aren’t decorations; they are guardrails. Use them.

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