A new generalized p-value for ANOVA under heteroscedasticity

For the problem of comparing the means of kk populations with unequal population variances, a new generalized test variable is defined and the generalized pp-value based on this generalized test variable is given. It is shown that the proposed generalized pp-value is invariant under the group of scale transformations. Numerical results show that the proposed generalized pp-value test performs better than a generalized FF-test.