## SAS/STAT Tools for Power and Sample Size Analysis

Subsections:

This section demonstrates how you can use the different SAS power analysis tools mentioned in the section Overview to generate graphs, tables, and narratives; implement your own power formulas; and simulate empirical power.

Suppose you want to compute the power of a two-sample t test. You conjecture that the mean difference is between 5 and 6 and that the common group standard deviation is between 12 and 18. You plan to use a significance level between 0.05 and 0.1 and a sample size between 100 and 200. The following SAS statements use the POWER procedure to compute the power for these scenarios:

```proc power;
twosamplemeans test=diff
meandiff = 5 6
stddev = 12 18
alpha = 0.05 0.1
ntotal = 100 200
power = .;
run;
```

Figure 18.1 shows the results. Depending on the plausibility of the various combinations of input parameter values, the power ranges between 0.379 and 0.970.

Figure 18.1: PROC POWER Tabular Output

The POWER Procedure
Two-Sample t Test for Mean Difference

Computed Power
Index Alpha Mean Diff Std Dev N Total Power
1 0.05 5 12 100 0.541
2 0.05 5 12 200 0.834
3 0.05 5 18 100 0.280
4 0.05 5 18 200 0.498
5 0.05 6 12 100 0.697
6 0.05 6 12 200 0.940
7 0.05 6 18 100 0.379
8 0.05 6 18 200 0.650
9 0.10 5 12 100 0.664
10 0.10 5 12 200 0.902
11 0.10 5 18 100 0.397
12 0.10 5 18 200 0.623
13 0.10 6 12 100 0.799
14 0.10 6 12 200 0.970
15 0.10 6 18 100 0.505
16 0.10 6 18 200 0.759

The following seven sections illustrate additional ways of displaying these results using the different SAS tools.