Marginal Means vs Descriptives

ataylor4

I have a 3 x 3 ANOVA with 1 WS and 1 BS factor. I must be overlooking something simple but I cannot understand why the marginal means calculated as part of the ANOVA interaction are somewhat different from the means in the descriptives statement analysis in JASP. It seems that this are the same data, no? The different is not large but concerns me.

JohnnyB

Hi Ataylor4,

The marginal means are calculated in a different way from the descriptives. The descriptive means are simply based on just the observations, whereas the marginal means are an estimation of what the means would be, in case the design would be balanced (i.e., "Estimated marginal means are based on a model – not directly on data"). We use the emmeans package for estimating these marginal means. You can read more about how this works in its documentation: https://cran.r-project.org/web/packages/emmeans/vignettes/basics.html

A relevant quote here: "The point is that the marginal means of cell.means give equal weight to each cell. In many situations (especially with experimental data), that is a much fairer way to compute marginal means, in that they are not biased by imbalances in the data. We are, in a sense, estimating what the marginal means would be, had the experiment been balanced. Estimated marginal means (EMMs) serve that need."

I hope that clarifies it - if not, please let me know and I can elaborate more =)

Kind regards,

Johnny