Introduction to Power and Sample Size Analysis

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.