After conducting a one-way ANOVA test on a dependent (continuous) variable and an independent (categorical with 3 levels) variable, the positive significant value of .001 suggests that the homogeneity of variance assumption has been violated. subsequently, Welsh and Brown-Forsythe tests were conducted. Welsh came up with a Sig. value of .063 while Brown-Forsythe was .002. What does this mean? I thought the two test were supposed to be in agreement?
I think the different statistic(s) for the test of homogeneity of variance can be different as they use different models. If you used JMP software for the calculation, I remember my professor recommending to look at the Brown-Forsythe value.
The meaning of the value that you obtained is that the p-value is small which means that the groups did not have uniform variance. You may need to either try transforming the data in some way or use a different type of analysis. It is also advisable to check the normality of the distribution of the data or the residuals.
It is believed also that the estimation may of the means may still be okay as ANOVA is a pretty robust model, with some care on the inference side.
Hello Femi Adeniji,
Depending on the magnitude of violation and the magnitude of the differences among treatment means you may experience an increased type I or type II statistical errors. I would use a GLM intead of an ANOVA to overcome problems with homogeneity of variance. The distribution of the error and the link function will depend, of course, on the nature of your response variable and the nature of the violation in homoscedasticity assumption.
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