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Introduction to Nonparametric Analysis |

One goal in comparing *k* independent
samples is
to determine whether the location parameters (medians) of
the populations are different. Another goal
is to determine whether the scale parameters for the
populations are different.
For example, suppose new employees are randomly
assigned to one of three training programs.
At the end of the program, the employees receive a standard
test that gives a rating score of their job ability.
The goal of analysis is to compare the
median scores for the three groups and decide whether
the differences are real or due to chance alone.

To compare *k* independent samples, either the NPAR1WAY
or the FREQ procedure provides a Kruskal-Wallis test.
PROC NPAR1WAY also provides the Savage,
median, and Van der Waerden tests.
In addition, PROC NPAR1WAY produces
the following tests for scale differences: Siegel-Tukey test,
Ansari-Bradley test, Klotz test, and Mood test.
Note that you can obtain exact *p*-values for all of
these tests.

In addition, you can specify the SCORES=DATA option to use the input data observations as scores. This enables you to produce a very wide variety of tests. You can construct any scores using the DATA step, and then PROC NPAR1WAY computes the corresponding linear rank and one-way ANOVA tests. You can also analyze the raw data with the SCORES=DATA option; for two-sample data, this permutation test is known as Pitman's test.

See Chapter 47, "The NPAR1WAY Procedure," for details, formulas, and examples.

To produce a Kruskal-Wallis test in the FREQ procedure,
use SCORES=RANK and the CMH2 option in the TABLES statement.
Then, look at the second Cochran-Mantel-Haenszel
statistic (labeled "Row Mean Scores
Differ") to obtain the Kruskal-Wallis test.
The FREQ procedure also provides the Jonckheere-Terpstra
test, which is more powerful than the Kruskal-Wallis
test for comparing *k* samples against ordered
alternatives. The exact test is also available.
In addition, you can obtain a ridit analysis, developed by
Bross (1958), by specifying SCORES=RIDIT or SCORES=MODRIDIT
in the TABLES statement in the FREQ procedure.

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