Question

1. What are two things in the repeated measure anova test that we can do in our study that would increase our power?

Answer 1

The 2 things in the repeated measure ANOVA test that we can do in our study to increase our power are listed below:

1)  we partition the variability attributable to the differences between groups (SSconditions) and variability within groups (SSw) exactly as we do in a between-subjects (independent) ANOVA. However, with a repeated measures ANOVA, as we are using the same subjects in each group, we can remove the variability due to the individual differences between subjects, referred to as SSsubjects, from the within-groups variability (SSw). WE treat each subject as a block. That is, each subject becomes a level of a factor called subjects. We then calculate this variability as we do with any between-subjects factor. The ability to subtract SSsubjects will leave us with a smaller SSerror term, as highlighted below:

Independent ANOVA : Serror =SSw

repeated measured ANOVA: Serror= SSw - Ssubjects

2) Now that we have removed the between-subjects variability, our new SSerror only reflects individual variability to each condition. You might recognise this as the interaction effect of subject by conditions; that is, how subjects react to the different conditions. Whether this leads to a more powerful test will depend on whether the reduction in SSerror more than compensates for the reduction in degrees of freedom for the error term (as degrees of freedom go from (n - k) to (n - 1)(k - 1) (remembering that there are more subjects in the independent ANOVA design).