RANK stores all values in memory of the variables for which it computes ranks.
Ranks are useful for investigating the
distribution of values
for a variable. The ranks divided by n or n+1 form
values in the range 0 to 1, and these values estimate the cumulative distribution
function. You can apply inverse cumulative distribution functions to these
fractional ranks to obtain probability quantile scores, which you can compare
to the original values to judge the fit to the distribution. For example,
if a set of data has a normal distribution, the normal scores should be a
linear function of the original values, and a plot of scores versus original
values should be a straight line.
Many nonparametric methods are based on analyzing ranks of a variable:
- A two-sample t-test applied to the
equivalent to a Wilcoxon rank sum test using the t approximation
for the significance level. If you apply the t-test to
the normal scores rather than to the ranks, the test is equivalent to the
van der Waerden test. If you apply the t-test to median
scores (GROUPS=2), the test is equivalent to the median test.
- A one-way analysis of variance applied to ranks is equivalent
to the Kruskal-Wallis k-sample test; the F-test generated
by the parametric procedure applied to the ranks is often better than the
approximation used by Kruskal-Wallis. This test can be
extended to other rank scores (Quade 1966).
- You can obtain a Friedman's two-way analysis for block designs
by ranking within BY groups and then performing a main-effects analysis of
variance on these ranks (Conover 1980).
- You can investigate regression relationships by using rank transformations
with a method described by Iman and Conover (1979).
Copyright 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.