The Simple Difference Formula: An Approach to Teaching Nonparametric Correlation

Although teaching effect sizes is important, many statistics texts omit the topic for the Mann-Whitney U test and the Wilcoxon signed-rank test. To address this omission, this paper introduces the simple difference formula. The formula states that the correlation equals the simple difference between the proportion of favorable and unfavorable evidence; in symbols this is r = f – u. For the Mann-Whitney U, the evidence consists of pairs. For the signed-rank test, the evidence consists of rank sums. Also, the formula applies to the Binomial Effect Size Display. The formula r = f – u means that a correlation r can yield a prediction so that the proportion correct is f and the proportion incorrect is u.