6. Latin square and nested analysis of variance
It is possible to generalize analysis of variance to 3, 4, 5... controlled factors. However, it is not certain that the use of such generalizations is to be recommended. Firstly, because it leads to experiments that are costly in relation to what they generally teach. Secondly, because it is often very difficult to transform the two-by-two or three-by-three interactions uncovered into usable physical conclusions – due to the very complexity of these multiple interactions.
An analysis of variance with four controlled factors A, B, C, D involves the following interactions:
That's eleven possible interactions for which you...
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Latin square and nested analysis of variance
Regression analysis
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