Use of the Correlation Coefficient with Normal Probability Plots

Abstract

The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodness-of-fit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position p_i = (i - .375)/(n + .25) yields a competitive regression test of fit for normality.

Key Words:

• Shapiro—Wilk test
• Shapiro—Francia test
• Filliben test
• Plotting position
• Empirical power comparison
• Regression tests of fit