Final answer:
The two circumstances necessary for a repeated measures ANOVA are when the same subjects are used in each treatment condition and when the sample sizes are unequal, allowing for increased statistical power and control over variability.
Step-by-step explanation:
The two circumstances necessary to use a repeated measures ANOVA are: c) When the same subjects are used in each treatment condition and d) When the sample sizes are unequal. A repeated measures ANOVA is a form of analysis of variance that is used when all subjects participate in all treatments, and the order of treatments is randomly assigned to control for any potential confounding variables. This differs from a one-way ANOVA, which requires independent samples, normally distributed populations, equal standard deviations, and where the factor is a categorical variable and the response is a numerical variable.
In repeated measures ANOVA, subjects are measured multiple times under different conditions, which makes it possible to control for variability among subjects, thereby increasing the statistical power of the test. Unequal sample sizes can occur in this design, but the repeated measures approach accounts for this when comparing the means of the different treatments.