A one-way analysis of variance on two independent groups generally requires follow-up (i.e., post hoc) tests.

Name: A one-way analysis of variance on two independent groups generally requires follow-up (i.e., post hoc) tests.
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A one-way ANOVA on two groups does not require post hoc tests because it is equivalent to a t-test, which directly compares the two groups. Post hoc tests are needed when there are more than two groups to determine which specific groups differ.

A One-Way Analysis of Variance on Two Independent Groups Generally