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Hypothesis tests that make up two-factor ANOVA

The structure of a two-factor study can be presented as a matrix with the levels of one factor determining the rows and the levels of the second factor determining the columns. With this structure in mind, how can one describe the mean differences that are evaluated by each of the three hypotheses tests that make up a two-factor ANOVA?

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In a two-factor ANOVA, we have three hypotheses as follows:

(1) Ho: The means are the same for all the levels of Factor A

Ha: At least one level of Factor A has a mean different from the rest

(2) Ho: The means are the same for all the levels of Factor B

Ha: At least one level of Factor B has a mean ...

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