Two-Sample Tests

Tests in the FREQ Procedure

This procedure provides a test for comparing the location of two groups and for testing for independence between two variables .

The situation in which you want to compare the location of two groups of observations corresponds to a table with two rows. In this case, the asymptotic Wilcoxon rank sum test can be obtained by using SCORES=RANK in the TABLES statement and by looking at either of the following:

• the Mantel-Haenszel statistic in the list of tests for no association. This is labeled as 'Mantel Haenszel Chi-Square' and PROC FREQ displays the statistic, the degrees of freedom, and the p -value. To obtain this statistic, specify the CHISQ option in the TABLES statement.

• the CMH statistic 2 in the section on Cochran-Mantel-Haenszel statistics. PROC FREQ displays the statistic, the degrees of freedom, and the p -value. To obtain this statistic, specify the CMH2 option in the TABLES statement.

When you test for independence, the question being answered is whether the two variables of interest are related in some way. For example, you might want to know if student scores on a standard test are related to whether students attended a public or private school. One way to think of this situation is to consider the data as a two-way table; the hypothesis of interest is whether the rows and columns are independent. In the preceding example, the groups of students would form the two rows, and the scores would form the columns . The special case of a two-category response (Pass/Fail) leads to a 2 — 2 table; the case of more than two categories for the response (A/B/C/D/F) leads to a 2 — c table, where c is the number of response categories.

For testing whether two variables are independent, PROC FREQ provides Fisher's exact test. For a 2 — 2 table, PROC FREQ automatically provides Fisher's exact test when you specify the CHISQ option in the TABLES statement. For a 2 — c table, use the FISHER option in the EXACT statement to obtain the test.

See Chapter 29, 'The FREQ Procedure,' for details, formulas, and examples of these tests.

Comparing Two Related Samples

SAS/STAT software provides the following nonparametric tests for comparing the locations of two related samples:

• Wilcoxon signed rank test

• sign test

• McNemar's test

The first two tests are available in the UNIVARIATE procedure, and the last test is available in the FREQ procedure. When you perform these tests, your data should consist of pairs of measurements for a random sample from a single population. For example, suppose your data consist of SAT scores for students before and after attending a course on how to prepare for the SAT. The pairs of measurements are the scores before and after the course, and the students should be a random sample of students who attended the course. Your goal in analysis is to decide if the median change in scores is significantly different from zero.

Tests in the UNIVARIATE Procedure

By default, PROC UNIVARIATE performs a Wilcoxon signed rank test and a sign test. To use these tests on two related samples, perform the following steps:

1. In the DATA step, create a new variable that contains the differences between the two related variables.

2. Run PROC UNIVARIATE, using the new variable in the VAR statement.

For discussion of the tests, formulas, and examples, refer to the chapter on the UNIVARIATE procedure in the Base SAS 9.1 Procedures Guide .