Question

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, describe the mean differences and interactions between factors that are evaluated by each of the three hypothesis tests that make up a two-factor ANOVA.

Answer 1

Following are the solution to this question:

Explanation:

It provides three different hypotheses in such a two-factor ANOVA:

In point A:

H o: With all factor A levels, the ways are equivalent

Ha: A least another element A level does have a transfer to another

In point B:

Ha: The least one Factor A the level does have a transfer to another

H o: With all Factor B levels the results are about the same.

In point C:

Ha: At most one Variable B level does have a transfer than any other level.

H o: There are no interactions among the factors

Ha: The interactions of factors are important

When ANOVA is executed, they get three p-sets (one for all 3 hypotheses)

(a) If Variable A's p-value is much less alpha, we will reject the null and embrace Ha and infer that Factor A is important. Anything else, H o also isn't rejected and that there is no evidence which Factor A is important

(b) If p- is < alpha, otherwise we reject The null, accept Ha, and infer which Factor B is relevant. Factor B is significant. Conversely, we may not condemn H o but claim there isn't enough proof which Factor B is important

(c)

If they reject H o and agree to the point p- for the A x B interaction is a < alpha Ha, and conclude that the interaction from A to B is important. So, perhaps we can deny H o and claim, that neither proof of interactions is sufficient From A to B.