Le quotient de deux variances corr\'el\'ees, sa distribution et son test

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Laurencelle, Louis
131-137
Keywords: Correlated variances , t-test on correlated variances
(no sample data)   (no appendix)

The joint sampling distribution of two correlated variances, i.e. variances stemming from a bivariate normal distribution or from two normal $\rho$-correlated distributions, is hardly known and used, by contrast with the distribution of $F$, the quotient of two independent, zero-correlated variances. The distribution of $F_\rho$, the quotient of two correlated variances, established by Bose (1935) and Finney (1938), is given along with its main characteristics, to which is added a handy $F_\rho$ to $F$ transformation. Finally, data based on Monte Carlo simulations document and compare the accuracy and power of two approximate tests of the difference between two correlated sample variances.