00293 ¡99c9cd0aba879c895882ead40e05ef

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Experimental Design Models with Random Components

Observation	Observed Value	Predicted Value	Residual
10	30.60000000	30.85000000	-0.25000000
11	30.91000000	30.85000000	0.06000000
12	30.70000000	30.85000000	-0.15000000
13	30.74000000	30.77000000	-0.03000000
14	30.89000000	30.77000000	0.12000000
15	30.69000000	30.77000000	-0.08000000
16	30.76000000	30.77000000	-0.01000000
17	30.84000000	30.78500000	0.05500000
18	30.85000000	30.78500000	0.06500000
19	30.71000000	30.78500000	-0.07500000
20	30.74000000	30.78500000	-0.04500000
21	30.78000000	30.68000000	0.10000000
22	30.53000000	30.68000000	-0.15000000
23	30.71000000	30.68000000	0.03000000
24	30.70000000	30.68000000	0.02000000
25	30.93000000	30.94500000	-0.01500000

FigurÄ™ 6. (continued).

model. The large variability associated with site 1 can also be seen in this residual plot. In FigurÄ™ 7b, the residuals are plotted against day and the large variability at day 6 is evident. FigurÄ™ 7c illustrates the residuals against site with the large variability at site 1 evident.

FigurÄ™ 8 reanalyzes the data after eliminating all responses at site 1. There are 112 remaining measurements. The ANOVA estimates of the components in FigurÄ™ 8 are Ä…uite different from the results for the fuli data. The maximum likelihood estimates for the reduced data are shown in FigurÄ™ 9. NotÄ™ that the negative ANOVA estimate for interaction component is estimated to be 0 by the maximum likelihood method. The restricted maximum likelihood estimates are shown in FigurÄ™ 10. Again, the interaction component is estimated to be 0. The ANOVA estimates are recomputed for the reduced model without the interaction term in FigurÄ™ 11. Notice that the results match the restricted maximum likelihood estimates in FigurÄ™ 10.