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Calculating a 4-way ANOVA by hand

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I really need to be able to follow this through every step by hand. This is the only reference I am allowed and I cannot use a computer during exams.

I was told this was called a 4 way ANOVA. It was only taught in lecture and we were given this example to work on. Here is a list of what I need:
1) All possible combinations of [A] [B] [C] [D] [S](subjects)

2) Determine the degrees of freedom

3) Develop the sum of squares computational formulas

4) Determine error terms

5) Calculate the sum of squares

I believe I once heard of it refered to as a MANOVA, Multiple Analysis of Variance,

Also The Omnibus F test

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Solution Summary

The data from a 4-way ANOVA was run on a computer package that generated an Analysis of Variance table. That table and the means for each level of the 4 factors are displayed below. Following that is a step-by-step method for creating that same table by hand.