Split-plot setup using SAS

[Russ Lenth]

I received the following question by e-mail and am copying it here.

> Hi :

>       I am trying to use your app to design a split plot design.
> But I am not quite sure what is the SD of whole or split. Where I can find that value in SAS.

Briefly, what you need to do is run PROC MIXED on your pilot data, making sure that your
whole-plots, at least, are specified in a RANDOM statement. The output will include estimates
of the random effects, and you use those in your power dialog. As an example (derived from a
class handout), consider a semiconductor experiment that includes several runs -- these are blocks.
In each run, we have 4 wafers, and those wafers are randomly assigned to whole-wafer
treatments (factor FP, 4 levels) -- note that RUN*FP identifies an individual wafer. We measure oxide
thickness at several sites on each wafer; and SITE is treated as the split-plot factor.

The SAS code is

proc mixed data = oxide;
class Run FP site;
model thick = FP | site / ddfm = satterthwaite outp = diags;
random Run Run*FP / solution;

And the output includes...

The Mixed Procedure
Covariance Parameter Estimates

Cov Parm Estimate
RUN      0.06351
RUN*FP   0.06752
Residual 2.4411

Type 3 Tests of Fixed Effects
       Num   Den
Effect  DF    DF  F Value  Pr > F
FP       3  19.6     7.79  0.0013
site     8   208    23.45  <.0001
FP*site 24   208     1.24  0.2099

In the power applet, we would specify:

• Model: RUN + FP + RUN*FP + SITE + FP*SITE    (note this includes both fixed and random effects)
• Random: RUN     (this will make both RUN and RUN*FP random)

Then click on Contrasts.comparisons. In the power dialog, enter:

• 0.252 (sqrt(.06351)) for the SD of RUN,
• 0.260 (sqrt(.06752)) for SD of RUN*FP, and
• 1.56 (sqrt(2.4411)) for SD of residual