Introduction to Analysis-of-Variance Procedures

# Nonparametric Analysis of Variance

Analysis of variance is sensitive to the distribution of the error term. If the error term is not normally distributed, the statistics based on normality can be misleading. The traditional test statistics are called parametric tests because they depend on the specification of a certain probability distribution except for a set of free parameters. Parametric tests are said to depend on distributional assumptions. Nonparametric methods perform the tests without making any strict distributional assumptions. Even if the data are distributed normally, nonparametric methods are often almost as powerful as parametric methods.

Most nonparametric methods are based on taking the ranks of a variable and analyzing these ranks (or transformations of them) instead of the original values. The NPAR1WAY procedure performs a nonparametric one-way analysis of variance. Other nonparametric tests can be performed by taking ranks of the data (using the RANK procedure) and using a regular parametric procedure (such as GLM or ANOVA) to perform the analysis. Some of these techniques are outlined in the description of PROC RANK in the SAS Procedures Guide and in Conover and Iman (1981).