Use of transformations of correlation coefficients in tests of significance

This paper is written with two objectives in mind. The first is to present the common tests of significance in a logical and straightforward manner, with emphasis on tests of the significance of a relationship between variables. These tests are shown to be basically alike and are discussed in terms of the sampling characteristics of the test criteria rather than in terms of specific applications. In line with this first objective, some well-known, but misleading, expositions in the literature of tests of significance are examined and criticized. The second objective is to examine a new criterion for testing the significance of r, a measure of the correlation between two variables. The new criterion is called g and its sampling distributions are compared on probability paper with those of r and of Fisher's z transformation of r.