RMAOV33

Three-way Analysis of Variance With Repeated Measures on Three Factors Test.

This is a three-factor analysis of variance design in which all factors are within-subjects variables. In repeated measures designs, the same participants are used in all conditions. This is like an extreme matching. This allows for reduction of error variance due to subject factors. Fewer participants can be used in an repeated measures design. Repeated measures designs make it easier to see an effect of the independent variable on the dependent variable (if there is such an effect).

Due that there is no way to obtain an independent estimate of error component, for we have only one score per cell, and therefore no within-cell variance. However, each of the interactions with subjects can be shown to serve as a denominator for an F ratio. So, each effect to be tested has its own error term. Thus every effect is tested by the interaction of that effect with the Subject effect.

Inputs:
X - data matrix (Size of matrix must be n-by-5;dependent variable=column 1; independent variable 1 (within subjects)=column 2;independent variable 2 (within subjects)=column 3; independent variable 3 (within subjects)=column 4; subject=column 5).
alpha - significance level (default = 0.05).
Outputs:
- Complete Analysis of Variance Table.