A Comparative Study of Analyses of 2 n Factorial Experiments with a Poisson Distributed Response Variable

Many industrial experiments involve a Poisson response where a square root (SQRT) or log transformation (LOG) is employed to obtain properties needed to use analysis of variance (ANOVA). These approaches have many drawbacks. Generalized linear models (GLM) are an attractive alternative. This article attempts a comparative study among the above-mentioned approaches, for 2 n full factorial experiments with a Poisson response. Each of these methods gave very poor performances when the expected response was small. A modification is suggested to improve this behavior. The modified GLM method turns out to be uniformly best amongst all approaches.