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An ANOVA for this data using an additive model is shown in Table 21.16. Notice that the differences in the workloads explains only 1.4% of the variation. Thus, the conclusions regarding processors using this data would be statistically more valid than one using data in which the workloads are responsible for a large part of the variation. Only 6.7% of the variation is unexplained.
TABLE 21.15 Measured Elasped Times for the Processor Comparison Study

Processors
Workload A B C D

ASM 54 101 111 83
TECO 60 92 110 90
SIEVE 42 121 127 86
DHRYSTONE 49 97 122 81
SORT 52 100 107 82

TABLE 21.16 ANOVA Table for the Processors Comparison Study

Sum of Percentage of Degrees of Mean F- F-
Component Squares Variation Freedom Square Computed Table

y 168,653.00
156,114.45
12,538.55 100.0 19
Processors 11,522.15 91.9 3 3840.72 54.9 2.6
Workloads 176.30 1.4 4 44.07 0.6 2.5
Errors 840.10 6.7 12 70.01

TABLE 21.17 ANOVA Table for the Processor Comparison Study

Sum of Percentage of Degrees of Mean F- F-
Component Squares Variation Freedom Square Computed Table

y 74.56
74.17
0.39 100.00 19
Processors 0.36 93.15 3 0.121 57.55 2.61
Workloads 0.00 0.37 4 0.000 0.17 2.48
Errors 0.03 6.47 12 0.002

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.


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