Some tests for the constancy of regressions under heteroscedasticity

For testing the equality of coefficients of a linear regression model under heteroscedasticity, we suggest an F criterion conditioned on the posterior mean of the ratio of standard deviations of error terms in two subsamples. For pairable subsamples, and exact F test is derived. Sampling experiments show that the Chow test differs substantially from the nominal significance level when the two subsample sizes are unequal, and that the F test conditioned on the posterior mean is superior to other tests when sample sizes are small.