A sav file of the dataset is attached.
"Yields" is the dependent variable, and "Soil" is the independent variable.
The ANOVA was used to compare the mean of Yields across Soil groups.
Both post hoc and EM means using Bonferroni tests were equal. Is there any difference between the two methods?
As there is a single factor in the model, there is no difference between the observed and the estimated means, so the results are identical (as Bonferroni is used for both). However, if you include another factor in the model, the results will be different, as post-hoc analysis does not account for the effect of other factors in the model (i.e., it uses the observed means), while the test based on the marginal means does.
Practically speaking, in a two-way ANOVA, if the two factors are not related, the tests based on the marginal means is likely to have more statistical power, as some of the error variance has already excluded (by the other factor), so the F ratio will be larger (as the denominator, MSE, is smaller).
Hello Mehdi,
The difference, as Ali Zia-Tohidi correctly notes, is non-existent in a one-way design. In multi-factor designs that are balanced (equal n per cell), the results will be the same as well; they can and do differ for unbalanced designs.
As well, when you run ancova, do note that the EMM values now represent "adjusted" means, and will therefore differ from the observed means for the data set on the DV.
Good luck with your work.
David Morse Ali Zia-Tohidi Thank you.
You say that the post hoc test is a nu-adjusted multiple comparison test, and the EM means are adjusted tests. Am I right?
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