The alternative hypothesis for the interaction of factors A and B in a 3 × 4 between-subjects analysis of variance is H1:.
A) All $\mu _ { A B } \neq 0$
B) $\operatorname { All } \left( \mu _ { A B } - \mu _ { A } - \mu _ { B } + \mu _ { G } \right) = 0$
C) Not all $\left( \mu _ { A B } - \mu _ { A } - \mu _ { B } + \mu _ { G } \right) = 0$
D) Not all $\left( \mu _ { A B } + \mu _ { A } + \mu _ { B } - \mu _ { G } \right) = 0$

Question

The alternative hypothesis for the interaction of factors A and B in a 3 × 4 between-subjects analysis of variance is H1:. 
A) All $\mu _ { A B } \neq 0$
B) $\operatorname { All } \left( \mu _ { A B } - \mu _ { A } - \mu _ { B } + \mu _ { G } \right) = 0$
C) Not all $\left( \mu _ { A B } - \mu _ { A } - \mu _ { B } + \mu _ { G } \right) = 0$
D) Not all $\left( \mu _ { A B } + \mu _ { A } + \mu _ { B } - \mu _ { G } \right) = 0$

Quizplus · Accepted Answer

The alternative hypothesis for the interaction of factors A and B in a 3 × 4 between-subjects analysis of variance is that not all means of the combination of A and B are equal to their respective main effects plus the grand mean. This can be expressed as $\left( \mu _ { A B } - \mu _ { A } - \mu _ { B } + \mu _ { G } \right) \neq 0$ for at least one combination of A and B levels. Thus, the correct choice is C. Options A and B are incorrect because they do not fully capture the specifics of the alternative hypothesis for interaction in a between-subjects ANOVA. Option D expresses a hypothesis of parallelism rather than interaction.

The Alternative Hypothesis for the Interaction of Factors a and B