ANCOVA post hoc tests and Testing the Homogeneity of Regression Assumption

Post hoc comparison of means in ANCOVA can be done with the following modification of Scheffe. Remember that the X means in the numerator are the adjusted group means as given in the lesson on ANCOVA,

Hays (1994) provides a method for testing the null hypothesis that the regression coefficients for the regression of the covariate and the "dependent" variable for the groups in ANCOVA are all drawn from a single population. In the equations shown below, the covariate is Y and the "dependent" variable is X (if you go to the Hays text, you will find this reversed).

References

Hays, W.L. (1994). Statistics. Fort Worth, TX: Harcourt Brace College Publishers.