A First Course in Statistics, 12th Edition

9.8 A Nonparametric Test for Correlation (Optional)

When the simple linear regression assumptions (Section 9.3) are violated (e.g., the random error has a highly skewed distribution), an alternative method of analysis may be required. One approach is to apply a nonparametric test for correlation based on ranks.

To illustrate, suppose 10 new paintings are shown to two art critics and each critic ranks the paintings from 1 (best) to 10 (worst). We want to determine whether the critics’ ranks are related. Does a correspondence exist between their ratings? If a painting is ranked high by critic 1, is it likely to be ranked high by critic 2? Or do high rankings by one critic correspond to low rankings by the other? That is, are the rankings of the ...