Abstract
This chapter assumes that multi-factor experiments are complete and balanced. In addition to the improved efficiency obtained from the use of multi-factor designs, one is also afforded the opportunity to study possible interaction between the factors. Factorial designs can estimate interactions, and if none are present they allow the effect of every factor to be evaluated as if the entire experiment were devoted entirely to that factor. An interaction plot can only indicate the possible presence of an interaction. Whether the differences in the slopes of the line segments in an interaction plot are statistically significant depends on the experimental error. In order to indicate the magnitude of the experimental error, confidence intervals are sometimes drawn around the end points of the line segments in an interaction plot.
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