The ANOVA using a multiplicative model is shown in Table 21.17. Processors explain about 93.2% variation, workloads explain only 0.4%, and the residuals account for the remaining 6.5%. Although not shown here, both models pass the visual tests equally well.
Thus, for a statistician looking at the two models, there is not much difference between the two. It is only the physical considerations that demand that a multiplicative model should be used. This is because it is more appropriate to say that processor B takes twice (10α2 - α1) as much time as processor A than to say that processor B takes 50.7 milliseconds more than processor A. The second statement is valid only for the set of workloads used in the study. The first statement may apply more generally. Thus, simply because a model passes all statistical tests does not mean that it is a good model. It should be valid from the physical considerations as well. In fact, physical validity of the model is required before its statistical validity.
Case Study 21.4 In an attempt to quantify the performance of the Intel iAPX 432 architecture, 12 different processor-operating system-language-word size combinations were measured on four different workloads. Measured execution times in milliseconds for the 12 systems are listed in Table 21.18. Physical considerations as well as the range of data dictate the necessity for a log transformation. The ANOVA is presented in Table 21.19. Notice that this is a good model since only 0.6% variation is unexplained. However, since the workloads explain a much larger percentage of variation than the systems, the workload selection is poor. The confidence intervals for the log system effects are shown in Figure 21.5.