In a two-factor ANOVA design with replications, there are three hypotheses to be tested; test for factor A, test for factor B, and test for interaction between factors A and B.

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In a two-factor ANOVA with replication, there are indeed three hypotheses tested: one for each of the two factors (A and B) to see if they have significant effects independently, and one for the interaction between factors A and B to see if the effect of one factor depends on the level of the other factor.

In a Two-Factor ANOVA Design with Replications, There Are Three