One-way ANOVA - margins' p-values interpretation

[Jeanne Sinclair]

Hello - this is a basic question. When I run an ANOVA and then margins, how do I interpret the p-values in that table for each category? For example, please see the table at the top of page 17 here: https://www.stata.com/manuals13/ranova.pdf. Is it significance of the difference of each category in relation to the mean?

Thank you!
Jeanne

[Clyde Schechter]

No. Those p-values are pretty meaningless and you should probably just ignore them.

That -margins- output is showing the adjusted mean values of the outcome variable, prob, in various (combinations of) categories of the predictors. For example, in the first row, you are told that when workplace = least and smokes = no, the expected value of prob, adjusted for everything else in the model, is 0.0090672. The p-value in that row tests the null hypothesis that the expected value of prob, adjusted for everything else in the model, is 0 when workplace = least and smokes = no. It is seldom the case that that null hypothesis (or any of the others in this kind of table) is of any interest. If one of your research goals is to test that particular hypothesis, then, of course, this p-value will matter. But it is rare to actually want to test that kind of null hypothesis, so these p-values are just a waste of ink/pixels.

[Jeanne Sinclair]

That is super helpful, Clyde. Thank you very much. I will use contrasts, then I guess, for the post-hoc comparisons! Many thanks!