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Main effects and interaction in a 2 x 2 factorial experiment

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What is the relationship between main effects and interaction?

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Solution Summary

This solution discusses the relationship between main effects and interactions in a 2 x 2 factorial experiment.

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Suppose you have done an experiment to study the effects of two explanatory variables, A and B, on a response variable Y. Both A and B were measured at two levels (low and high), resulting in 4 combinations of settings for the two explanatory variables:

1. A low, B low
2. A low, B high
3. A high B low
4. A high B high

The main effect of A is found by finding the average value of Y for settings 1 and 2 (the two combinations where A is low) and subtracting it from the average value ...

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