ABSTRACT
All of the models discussed to this point have been such that the treatments can have an effect on the mean (or model) of the response, but not on the variance of the response. A more general model allows for the variances to also be affected by the application of the treatments as well as by the factors defining the design structure. The heterogeneous variance model could involve unequal variances for each treatment group or unequal variances for groups of treatments. An appropriate analysis includes the estimation of the different variances and then uses the estimated variances to estimate the parameters of the regression models and to compare the regression models. Some discussions of the unequal variance problem involve transforming the response variable in an attempt to stabilize the variances. Such transformations could change the relationship between the mean of the transformed response and the covariates. The process used in this chapter is to identify the source of the unequal variances and then to use software that allows for unequal variance models to be fit to the data set, i.e., no transformations are to be used. This chapter begins with a description of the model with unequal variances, followed by procedures to test the equal variance hypothesis. The analysis of covariance strategy is described for the case involving unequal variances, including the estimation of the parameters of the model, testing the equal slopes and slopes equal to zero hypotheses, and making comparisons between models. Three examples are presented to demonstrate the required analysis of covariance process. The process consists of (1) selecting an adequate form of the regression models, (2) selecting the simplest form of the variance structure, (3) simplifying the form of the regression model, and (4) comparing the resulting regression models.
