Why use estimated marginal means

The question then arises: how do these analyses differ from each other? Statistically speaking — not that much. Yet, scientifically speaking they do. This means we have two within subjects factors Attractiveness and Charisma , and one between subjects factor gender. The main analysis gives us quite overwhelming evidence that the average preference scores differ for the three levels of Charisma see the descriptives plot below for an illustration.

To follow up on this main effect there are either the post hoc tests or the contrast analyses. In JASP, even though these are under separate menus, in both instances the underlying analysis code uses the emmeans package. For starters, what are marginal means? Often, marginal means are equal to the descriptive means. However, in some cases, for instance in the case of unbalanced designs or inclusion of other variables in the model, the two differ. This is because the descriptive means are based solely on the observed data , whereas the marginal means are estimated based on the statistical model.

So, in case gender is included in the model, the marginal means estimate tries to estimate what the mean would have been, had there been a balanced design i.. Here it does not make a huge difference, but it is definitely something to think about and take into account. As can be seen from the standard errors and range of the confidence intervals of the estimates, including gender in the model also makes for a more specific estimate i. If your focus is on planned comparisons, then you can bypass the test of significance of the interaction term in your model and proceed directly to perform these comparisons.

If the em means plot helps you towards that goal, then you are fine to use it. If you are uncertain what comparisons to test, look at the p-value for the interaction term. If that p-value is statistically insignificant, you have no evidence of an interaction and would stop there, since there would be no need for performing post-hoc comparisons. It is possible that your study has inadequate power for testing the significance of the interaction term.

You can look at the point estimate and confidence interval for the interaction term to get an idea of the magnitude of the interaction effect. The study could be inconclusive. If year and treatment are declared as factors in R, whose reference levels are set to for year and Control for treatment, then your model could be stated as:.

Also, year is a dummy variable equal to 1 for the year and 0 for the year Furthermore, treatmentTreatment is a dummy variable which is equal to 1 for your active treatment and 0 for your control treatment.

But if the values of either of these dummy variables would be the same across all offspring from the same mother, the index j would be dropped. Anyway, in the model as formulated above, you would be interested in the relative effect of Treatment vs Control with respect to body mass on average in each of the two years. Let's make this effect more obvious by re-writing the model:. In other words, beta2 represents the difference in the mean body mass between Treatment and Control in year The key is to realize that these two effects are linear combinations of the fixed effects coefficients beta0, beta1, beta2 and beta3.

If you have a covariate in your model which does not contribute to the interaction between year and treatment , you need to write down your model again:. When you proceed to test them or estimated as suggested above, you need to set up K1 and K2 like this:. Of course, the model with covariate would look like this:. People seem to have an assortment of pretty rigid practices. They can be useful for deciding what model is suitable for a dataset; but they do not help much, in my opinion, for doing any meaningful inference.

In particular, if you have fitted a two-way factorial model including interaction, and the residual diagnostics look good, I don't see anything wrong with proceeding to do post hoc means and comparisons without even looking at the ANOVA table. Appropriate multiplicity adjustments should be used, and I think it's important to look at the means themselves, not just the pairwise differences -- both from a subject-matter perspectives -- and probably plot them as well.

I am a lot more comfortable with what is described in the preceding paragraph than I am with some analysis where rigid rules and "significance" criteria are applied, but no diagnostic plots or descriptive plots are examined. I see this kind of routinized method way, way too often. This would suggest something potentially important that could be investigated in further experimentation. A devoted user of ANOVA tables may summarily throw the interaction out of the model, hence never having the opportunity to notice this potentially important result.

Remember, just because something isn't "statistically significant," that doesn't prove it isn't there; it just means you don't have enough data to be sure it isn't part of the noise. Sign up to join this community. The best answers are voted up and rise to the top.

Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Estimated Marginal Means or means from descriptives? Ask Question. Asked 9 years, 7 months ago. Active 5 years, 8 months ago. Viewed 27k times. However - I'm am struggling to find information regarding the reporting of means.

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