Analysis of 2 Factorial Experiments with Exponentially Distributed Response Variable

This paper assesses and compares the performance of generalized linear models (GLM) with respect to log transformation and ANOVA approaches on the basis of coverage results and expected length of confidence intervals (CI) for the expected responses for exponentially distributed response variable. We also focus on the power functions of tests of hypothesis for testing significance of underlying factorial effects. Although, the comparison is mainly simulation based, whenever possible, theoretical investigation is carried out for saturated 2-level factorial experiments. The coverage results of log transformation approach are uniformly superior to GLM for two replications (very small sample) which is most frequently encountered situation in the industrial experiments. We also suggested a modification to GLM based confidence intervals that shows decisive improvement over the GLM. t-test under GLM approach exhibits best power function for testing significance of factorial effects but t-test under log transformation approach is also equally good. Mathematics Subject Classification: 62K15