# SAS/STAT Tools for Power and Sample Size Analysis

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.