The analysis of designed experiments with non-normal responses

In recent years, attention has focused on designed experiments for situations with a non-Normal response variable of interest such as a count of defects, the proportion defective, or the time to failure. Classical linear least squares is the most widely used technique for modeling the relationship between this response variable of interest and one or more independent variables. The optimality properties of least squares, however, depend on the assumptions of normality and constancy of variance. Clearly, when dealing with this type of data, there is not constancy of variance. Traditionally, to correct for nonconstant variance, a variance-stabilizing transformation is applied to the response variable to bend the data into shape. This allows the application of classical least squares to the transformed data. However, there remain significant problems with data transformations and the resulting inverse transformation to return the, variables to their original units. An alternative to the data transformation approach is the generalized linear model (GLM). The GLM is a regression-type model fitted by maximum likelihood, rather than least squares. GLM extends the traditional linear model to allow for responses that are not normally distributed. Comparisons of models built with the traditional data transformations and those built with GLM often indicate that better models are possible with GLM. Therefore, the purpose of this article is to illustrate the application of the GLM and highlight the analogous model-building process of the GLM and Normal theory linear models.