Previous Table of Contents Next



FIGURE 21.11   Confidence intervals for effects in the RISC code size study.

Box 21.1 Analysis of Two-Factor Designs without Replications

1.  Model: yij = µ + αj + βi + eij; the effects are computed so that
  
2.  Effects:
3.  Allocation of variation: SSE can be calculated after computing other terms below:

SSY = SS0 + SSA + SSB + SSE

4.  Degrees of freedom:

SSY = SS0 + SSA + SSB + SSE

ab = 1 + (a - 1) + (b - 1) + (a - 1)(b - 1)

5.  Mean squares:

6.  Analysis of variance:
MSA/MSE should be greater than F[1-α;a-1,(a-1)(b-1)].
MSB/MSE should be greater than F[1-α;b-1,(a-1)(b-1)].
7.  Standard deviation of effects: s2µ = s2e/ab;
s2αj = s2e(a -1)/ab;s2βi = s2e(b - 1)/ab
8.  Contrasts:

9.  All confidence intervals are calculated using t[1-α/2;(a-1)(b-1)].
10.  Model assumptions:
(a)  Errors are IID normal variates with zero mean.
(b)  Errors have the same variance for all factor levels.
(c)  The effects of various factors and errors are additive.
11.  Visual tests:
(a)  The scatter plot of errors versus predicted responses should not have any trend.
(b)  The normal quantile-quantile plot of errors should be linear.
If any test fails or if the ratio ymax/ymin is large, multiplicative models or transformations should be investigated.

EXERCISES

21.1  Analyze the data of Case Study 21.2 using an additive model. Plot residuals as a function of predicted response. Also, plot a normal quantile-quantile plot for the residuals. Determine 90% confidence intervals for the paired differences. Are the processors significantly different? Discuss what indicators in the data, analysis, or plot would suggest that this is not a good model.
21.2  Analyze the data of Table 21.18 using a multiplicative model and verify your analysis with the results presented in Table 21.19.
21.3  Analyze the code size data of Table 21.23. Ignore the second column corresponding to the 68000 for this exercise. Answer the following:
a.  What percentage of variation is explained by the processor?
b.  What percentage of variation can be attributed to the workload?
c.  Is there a significant (at 90% confidence) difference between any two processors?
21.4  Repeat Exercise 21.3 with the 68000 column included.


Previous Table of Contents Next

Copyright © John Wiley & Sons, Inc.