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Introduction to Nonparametric Analysis |

SAS/STAT software provides several nonparametric tests for location and scale differences.

When you perform these tests, your data should consist of a random sample of observations from two different populations. Your goal is either to compare the location parameters (medians) or the scale parameters of the two populations. For example, suppose your data consist of the number of days in the hospital for two groups of patients: those who received a standard surgical procedure and those who received a new, experimental surgical procedure. These patients are a random sample from the population of patients who have received the two types of surgery. Your goal is to decide whether the median hospital stays differ for the two populations.

When data are sparse, skewed, or heavily tied, the usual
asymptotic tests may not be appropriate. In these situations,
exact tests may be suitable for analyzing your data.
The NPAR1WAY procedure can produce exact *p*-values for
all of the two-sample tests for location and scale
differences.

Chapter 47, "The NPAR1WAY Procedure," provides detailed statistical formulas for these statistics, as well as examples of their use.

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. - 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 use the CHISQ option in the TABLES statement.
For a 2 ×*c* table, use the EXACT option
in the TABLES statement to obtain the test.

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