Describe the hypotheses for a two-way ANOVA test.

Question

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Suppose you are conducting a two-way ANOVA with factors E 3 levels, and F 2 levels. Which of the following is not a correct null hypothesis for this test? Awesome. So it appears for this particular problem we're asked to take the information that is provided to us by the prom itself, and we're asked to look at our multiple choice answers and determine which of our multiple choice answers is not a correct null hypothesis for this particular test, noting that we're dealing with a two-way ANOVA, which ANOVA denotes an analysis of variance. So now that we know that we're trying to determine which statement is not the correct null hypothesis for this test, let's take a moment to read off our multiple choice answers to see what our final answer might be. A is H0 to the power of E. The means for all levels of factor E are equal. B is H0 power of F. The means for all levels of factor F are equal. C is H0 to the power of EF. There is an interaction effect between E and F. And finally, D is H0 to the power of EF, there is no interaction effect between E and F. Awesome. So first off, in order to solve this problem, we need to recall and note that the null hypothesis for the factor, so for the factor E will be H0 to the power of E, and this means for all levels of factor E are equal. And for our second step, we need to recall a note that the null hypothesis for factor F will be. H 0 to the power of F. And this means for all levels of factor F are equal. Our third step is we need to recall and note that the null hypothesis for the interaction is H 0 to the power of EF and this is there is no interaction effect between E and F. So that will mean our fourth and final step will make our final conclusions. That will mean that out of all of our multiple choice answers when we look at them, the final answer without a doubt has to be multiple choice answer letter C. Which once again is H0 to the power of EF, there is an interaction effect between E and F because it incorrectly states that the null hypothesis or the interaction as the existence of an interaction effect, which is actually the alternative hypothesis. So, multiple choice answer letter C is not the correct null hypothesis for this particular test. Rather, this statement is technically the alternative hypothesis, but to avoid confusion, out of all of our multiple choice answers, multiple choice answer letter C. This is not a correct null hypothesis for this particular two-way analysis of variance test. And that's it. We've officially solved for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Describe the hypotheses for a two-way ANOVA test.

Key Concepts

Null Hypothesis (H0)

Alternative Hypothesis (H1)

Interaction Effect

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