chapter  5
Tests Based on Regression and Correlation
WithMichael A. Stephens
Pages 40

This chapter examines another graphical method, related to probability plots, in which the order statistics X(i) are plotted on the vertical axis of the graph, against T(i), a suitable function of i, on the horizontal axis. The statistic is easier to calculate than W or W' but must be used with both tails; d'Agostino has shown by Monte Carlo studies that alternative distributions may produce large or small values of the statistic. The various techniques regression tests of normality and exponentiality have not been so extensively developed for other distributions, and the tests to follow, for the extreme-value, logistic, and Cauchy distributions, are all based on the simple correlation coefficients. In general, consistency of a test based on the ratio of two estimates of scale must depend critically on how these are chosen, and this question deserves closer examination.