GENERALIZATION FOR THE DISTRIBUTION OF HARTLEY'S FMAX STATISTIC UNDER HETEROGENEITY OF VARIANCES WITH UNEQUAL SAMPLE SIZES

The exact distribution of Hartley's Fmax statistic under heterogeneity of variances with or without unequal sample sizes is given. This exact distribution can now provide a statistical test for several variances under unbalanced design of the Analysis of Variance (ANOVA). This distribution under heterogeneity of variances can provide the power of the test with or without unequal sample sizes. The relaxation of the conditions for the equal sample sizes and for homogeneity of variances will require an astronomical number of statistical tables which cannot practically be shown. We therefore provide a Fortran program which calculates, to a high accuracy, the upper tail probabilities, probability points and probability densities for Fmax statistic under heterogeneity or homogeneity of variances and with or without unequal sample sizes. Usually the accuracy of the calculation is 13 to 14 digits for double precision arithmetic. The probability density functions under heterogeneity or homogeneity of variances and with or without unequal sample sizes are shown.