00282 ü2f085e03aac52a0e08de9cd1e42da1

284

Montgomery & Runger

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

SÄ…uare

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)

FigurÄ™ 1. Yariance Components Estimation ProcedurÄ™.

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

FigurÄ™ 4 provides a plot of the response y against the levels of site for two particular days. FigurÄ™ 4a does not indicate any unusual pattems. However, FigurÄ™ 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. FigurÄ™ 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.

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