THE DISTRIBUTION OF THE RATIO OF COVARIANCE ESTIMATES IN TWO SAMPLES DRAWN FROM NORMAL BIVARIATE POPULATIONS

Abstract

This paper is a contribution to statistical tests of significance for 2-variate problems. In particular it deals with testing the difference between 2 correlation-coefficients. To this end the above random-sample distribution is developed and the case where the 2 samples have been drawn from the same normal population is more closely examined. It is shown that under these conditions the probability integral is a finite weighted sum of incomplete [beta]-functions, the weights being complete [beta]-functions and simple polynomials in [rho]2 ([rho] denoting the correlation coefficient of the underlying normal population). As [rho] approaches the value +1 or the value[long dash]1 the test is shown to approach the 2-test as a limiting form. The performance of the test is demonstrated with data from a Cambridge nutrition exp. on pigs.