The Probability Integral Transformation for Testing Goodness of Fit and Combining Independent Tests of Significance

Publisher Website
Google Scholar
Abstract
This paper draws attention to the somewhat novel character of the problem to be faced in dealing with statistical tests based on the probability integral transformation (see work of R. A. Fisher, Karl Pearson and J. Neyman). The intuitional notions that have often served to determine the most appropriate test when dealing with normal variation are hardly applicable when, as in this case, we are concerned with a transformed variable following the rectangular distribution. The tests proposed by the 3 authors referred to are discussed, and emphasis is laid on the need for consideration of the possible alternatives to the hypothesis tested. Some illustration of the ideas involved is given in the case where the hypothesis regarding the form of a probability law p(x) is incorrect, (a) in the position of the mean, (b) in the magnitude of the standard deviation, (c) in the shape of the probability curve.