The Distribution of the Ratio of Estimates of the Two Variances in a Sample from a Normal Bi-Variate Population

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Abstract
The distribution of this ratio has been investigated by Bose (1935) by a method dependent on term-by-term integration of infinite series. The simplicity of his result suggested the possibility of the more direct approach given below, which is followed by the evaluation of the probability integral for the distribution. It is then shown how, by a simple transformation of existing tables, a test of significance may be applied when the population correlation coefficient is known, and how the test may be adapted when only a sample estimate of this correlation is available.