Confidence interval coverage for designed experiments analyzed with GLMs

There are many industrial experiments where the response variable is nonnor mal. Traditionally, variance-stabilizing transformations are made on such a response in order to obtain properties needed to use ordinary least square s and analysis of variance. Generalized linear models (GLMs) offer a powerf ul alternative to data transformation. Specifically, the performance in res ponse estimation and prediction for a GLM is often superior to the model bu ilt using data transformations. The confidence interval constructed around the estimate of the mean for each experimental run provides the experimente r with critical information about model quality. In generalized linear mode ls, confidence intervals are based on asymptotic theory. As such, they are regarded as statistically valid only for large samples. Therefore, in order to use confidence intervals to compare models. it is essential to evaluate these asymptotic intervals in terms of coverage for sample sizes typically encountered in designed industrial experiments. This paper uses Monte Cart e methods to investigate the coverage of confidence intervals for the GLM f or factorial experiments with 8, 16, and 32 runs.