00282 �2f085e03aac52a0e08de9cd1e42da1

284

Montgomery & Runger

Source	Expected Mean
DAY	Var (Error) + 4
SITE	Var (Error) + 4
DAY* SITE	Var (Error) + 4
Error	Var (Error)

Sąuare

Var (DAY*SITE) + 20 Var (DAY) Var (DAY*SITE) + 28 Var (SITE) Var (DAY*SITE)

Dependent Variable: Y

Source	DF	TypeISS	Type I MS
DAY	6	0.29954857	0.04992476
SITE	4	0.04769571	0.01192393
DAY* SITE	24	0.11934429	0.00497268
Error	105	0.39560000	0.00376762
Corrected Total	139	0.86218857

Estimate

0.00224760

0.00024826

0.00030126

0.00376762

Variance Component Var (DAY)

Var (SITE)

Var (DAY*SITE) Var (Error)

Figurę 1. Yariance Components Estimation Procedurę.

the ANOVA estimates. Figurę 3 also provides the ANOVA estirnates for the model with only day and site as random efifects.

Figurę 4 provides a plot of the response y against the levels of site for two particular days. Figurę 4a does not indicate any unusual pattems. However, Figurę 4b illustrates dramatically larger variability at site 1, than at the other sites at day 6. This plot demonstrates the importance of graphical inspections of data and residuals. Figurę 5a further explores this variability by plotting the response at site 1 for each day in the experiment. The unusual results at day 6 are obvious. Figures 5b-e plot the response at each of the other sites against day. No unusual pattems are discemed.

Figurę 6 provides the output from SAS procedurę GLM for the same data and model. Figurę 7a displays a plot of residuals against predicted values from the