Further Distribution Results for Correlation Coefficients and F Tests in Normal Samples

Fisher’s finite sample distribution results for squared multiple correlation coefficients and F tests are extended to situations in which the observations are drawn from independent, but not necessarily identical, normal samples. This distribution nests within it the noncentral beta and F distributions. A computationally efficient, finite sum form of the distribution function is derived. Extensions of these results to subset F tests and F tests where the regressors are correlated with the disturbances are also considered. These formulas are used to study several practical testing problems in stochastic regressor and simultaneous equations models.