## RMAOV32

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

Updated 17 Jan 2006

This is a three-factor analysis of variance design in which there are repeated measures on two of the factors. 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).

With only one RM factor there is only one error term that involves an interaction with the subject factor, and that error term is found easily by subtraction. However, with two RM factors the subject factor interacts with each RM factor separately, and with the interaction of the two of them, yielding three different error terms. The extraction of these extra error terms requires the collapsing of more intermediate tables, and the calculation of more intermediate SS terms.

For each RM factor the appropriate error term is based on the interaction of the subject factor with that RM factor. The more that subjects move in parallel from one level of the RM factor to another, the smaller the error term. The error term for each RM factor is based on averaging over the other factor. However, the third RM error term, the error term for the interaction of the two RM factors, is based on the three-way interaction of the subject factor and the two RM factors, with no averaging of scores. To the extent that each subject exhibits the same twoway interaction for the RM factors, this error term will be small.

Inputs:
X - data matrix (Size of matrix must be n-by-5;dependent variable=column 1; independent variable 1=column 2;independent variable 2 (within- subjects)=column 3; independent variable 3 (within-subjects)=column 4; subject=column 5 [Be careful how the code for the subjects are entered.])
alpha - significance level (default = 0.05).

Outputs:
- Complete Analysis of Variance Table.

### Cite As

Antonio Trujillo-Ortiz (2023). RMAOV32 (https://www.mathworks.com/matlabcentral/fileexchange/9632-rmaov32), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R14
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