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When a one-way ANOVA results in rejecting the null hypothesis, it indicates that not all population group means are equal, but it does not specify which ones differ. To pinpoint these specific differences, researchers conduct post hoc comparisons. These are follow-up statistical analyses that compare selected pairs of group means to determine exactly which groups are significantly different from each other.

Post Hoc Comparisons

Conducting multiple independent-samples $$t$$-tests to compare every pair of group means in an experiment creates a statistical problem. While a single $$t$$-test has a $$5\%$$ chance of mistakenly rejecting a true null hypothesis (a Type I error), conducting several $$t$$-tests simultaneously causes this risk to compound. As more tests are run, the overall probability of mistakenly rejecting at least one true null hypothesis becomes unacceptably high, necessitating specialized statistical procedures to control the error rate.

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