The structure of a twofactor study can be presented as a mat

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, which of the following are mean differences that are evaluated by the three hypothesis tests that make up a two-factor ANOVA? Check all that apply. Mean differences between cells Mean differences between samples Mean differences not explained by row or column differences Mean differences between rows Mean differences between columns Mean differences along diagonals

Solution

answers

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 different from the rest

(3) Ho: There is no interaction between the factors

Ha: There is a significant interaction between the factors

Once we run the ANOVA, we get three p- values (one each for the three hypotheses)

(a) If the p- value for Factor A is < alpha, then we reject Ho and accept Ha, and

conclude that Factor A is significant.

Else, we fail to reject Ho and say that there is no sufficient evidence that Factor A is

significant

(b) If the p- value for Factor B is < alpha, then we reject Ho and accept Ha, and

conclude that Factor B is significant.

Else, we fail to reject Ho and say that there is no sufficient evidence that Factor B is

significant

(c) If the p- value for the Interaction A x B is < alpha, then we reject Ho and accept

Ha, and conclude that there is a significant interaction between A and B

Else, we fail to reject Ho and say that there is no sufficient evidence of an interaction

between A and B.

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