Incorporating Contrasts, Unbalanced Designs, and Multiple Means Scenarios

Suppose you want to compute power for the two-way ANOVA described in the section Simple Two-Way ANOVA, but you want to additionally perform the following tasks:

• try an unbalanced sample size allocation with respect to Exposure, using twice as many samples for levels 2 and 3 as for level 1

• consider an additional, less optimistic scenario for the cell means, shown in Table 43.2

• test a contrast of Exposure comparing levels 1 and 3

 Exposure Variety 1 2 3 1 15 16 20 2 11 14 15

To specify the unbalanced design and the additional cell means scenario, you can add two new variables to the exemplary data set (Weight for the sample size weights, and HeightNew for the new cell means scenario). Change the name of the original cell means scenario to HeightOrig. The following statements define the exemplary data set:

```data Exemplary;
input Variety \$ Exposure \$ HeightOrig HeightNew Weight;
datalines;
1   1   14  15  1
1   2   16  16  2
1   3   21  20  2
2   1   10  11  1
2   2   15  14  2
2   3   16  15  2
;
run;
```

In PROC GLMPOWER, specify the name of the weight variable by using the WEIGHT statement, and specify the name of the cell means variables as dependent variables in the MODEL statement. Use the CONTRAST statement to specify the contrast as you would in PROC GLM. The following statements perform the sample size analysis.

```proc glmpower data=Exemplary;
class Variety Exposure;
model HeightOrig HeightNew = Variety | Exposure;
weight Weight;
contrast 'Exposure=1 vs Exposure=3' Exposure 1 0 -1;
power
stddev = 5
ntotal = 60
power  = .;
run;
```

Figure 43.4 shows the output.

Figure 43.4 Sample Size Analysis for More Complex Two-Way ANOVA
The GLMPOWER Procedure

Fixed Scenario Elements
Weight Variable Weight
Error Standard Deviation 5
Total Sample Size 60
Alpha 0.05
Error Degrees of Freedom 54

Computed Power
Index Dependent Type Source Test DF Power
1 HeightOrig Effect Variety 1 0.672
2 HeightOrig Effect Exposure 2 0.911
3 HeightOrig Effect Variety*Exposure 2 0.217
4 HeightOrig Contrast Exposure=1 vs Exposure=3 1 0.951
5 HeightNew Effect Variety 1 0.754
6 HeightNew Effect Exposure 2 0.633
7 HeightNew Effect Variety*Exposure 2 0.137
8 HeightNew Contrast Exposure=1 vs Exposure=3 1 0.705

The power of the contrast of Exposure levels 1 and 3 is about 0.95 for the original cell means scenario (HeightOrig) and only 0.71 for the new one (HeightNew). The power is higher for the test of Variety, but lower for the tests of Exposure and of Variety*Exposure for the new cell means scenario compared to the original one. Note also for the HeightOrig scenario that the power for the unbalanced design (Figure 43.4) compared to the balanced design (Figure 43.1) is slightly lower for the tests of Variety and Exposure, but slightly higher for the test of Variety*Exposure.