Chapter 12: Introduction to Nonparametric Analysis

Overview

In statistical inference, or hypothesis testing, the traditional tests are called parametric tests because they depend on the specification of a probability distribution (such as the normal) except for a set of free parameters. Parametric tests are said to depend on distributional assumptions. Nonparametric tests , on the other hand, do not require any strict distributional assumptions. Even if the data are distributed normally, nonparametric methods are often almost as powerful as parametric methods .

Many nonparametric methods analyze the ranks of a variable rather than the original values. Procedures such as PROC NPAR1WAY calculate the ranks for you and then perform appropriate nonparametric tests. However, there are some situations in which you use a procedure such as PROC RANK to calculate ranks and then use another procedure to perform the appropriate test. See the section 'Obtaining Ranks' on page 198 for details.

Although the NPAR1WAY procedure is specifically targeted for nonparametric analysis, many other procedures also perform nonparametric analyses. Some general references on nonparametrics include Hollander and Wolfe (1999), Conover (1999), Gibbons and Chakraborti (1992), Hettmansperger (1984), Randles and Wolfe (1979), and Lehmann (1975).

Testing for Normality

Many parametric tests assume an underlying normal distribution for the population. If your data do not meet this assumption, you may prefer to use a nonparametric analysis.

Base SAS software provides several tests for normality in the UNIVARIATE procedure. Depending on your sample size , PROC UNIVARIATE performs the Kolmogorov-Smirnov, Shapiro-Wilk, Anderson-Darling, and Cram r-von Mises tests. For more on PROC UNIVARIATE, refer to the Base SAS 9.1 Procedures Guide .

Comparing Distributions

To test the hypothesis that two or more groups of observations have identical distributions, use the NPAR1WAY procedure, which provides empirical distribution function (EDF) statistics. The procedure calculates the Kolmogorov-Smirnov test, the the Cram r-von Mises test, and, when the data are classified into only two samples, the Kuiper test. Exact p -values are available for the two-sample Kolmogorov-Smirnov test. To obtain these tests, use the EDF option in the PROC NPAR1WAY statement. For details, see Chapter 52, 'The NPAR1WAY Procedure.'