# What is the meaning of 'Marginal mean'?

My problem with understanding this expression might come from the fact that English is not my first language, but I don't understand why it's used in this way.

The marginal mean is typically the mean of a group or subgroup's measures of a variable in an experiment, but why not just use the word mean? What's the marginal here for?

• A marginal mean is the mean of a marginal distribution. This can be applied to empirical (sample) distributions to also apply to things like tables of discrete (categorized/binned) observations, for example. – Glen_b -Reinstate Monica Aug 31 '16 at 5:38

Perhaps, the term originates from how the data is represented in a contingency table. See this example from the wiki.

In the above example, we would speak of marginal totals for gender and handedness when referring to the last column and the bottom row respectively. If you see the wiktionary the first definition of marginal is:

1. of, relating to, or located at a margin or an edge

Since the totals (and means if means are reported) are at the edge of the table they are referred to as marginal totals (and marginal means if the edges have means).

• Wow, that would be really useless then :D Can't people see that the means are at the edges already? – levesque Nov 5 '10 at 15:03
• @JCL Perhaps, they can if they see the table. But, what if there is no table? Then a table can be re-constructed to some extent using the text which refers to such things as 'grand means', 'marginal means' etc. I am guessing the phrase 'marginal mean' is a literary convention to signal what we are talking about. In a similar vein you could argue that why use the term 'sample average' when 'average' is sufficient. Qualifying words such as 'sample', 'marginal' add some context. – user28 Nov 5 '10 at 15:07
• @Skrikant (+1) I think the term now extends beyond contingency table since we also speak of a marginal (vs. conditional or subject-specific) approach, e.g. in mixed-effects model. So I think, the distinction has to be made between computing a marginal statistic or working with conditional values (this applies for an ANOVA table as for a contingency table). – chl Nov 5 '10 at 15:18

I'd assume it means the sample analogue of the marginal expectation $\operatorname{E}(X)$, as opposed to the sample analogue of a conditional expectation $\operatorname{E}(X \mid Y)$, where $Y$ could be anything.

• Funny, tex doesn't render on my browser... Chrome on ubuntu. – levesque Nov 5 '10 at 20:17
• A good quote from a UMich document: "The marginal probability (of A) is obtained by summing all the joint probabilities. Marginal probability can be used whether the events are dependent or independent. If the events are independent then the marginal probability is simplified to simply the probability. The following example will clarify this computation." – Wayne Nov 6 '10 at 1:43
• @JCL i admit i was experimenting with some more slightly advanced (but mathematically correct) TeX. it renders fine for me in Firefox on Windows XP, and in Internet Explorer on Windows XP after a refresh. It doesn't render in IE on Windows Mobile 6, but then no TeX on this site does. I have Ubuntu on a USB drive so i'll be back after a quick reboot... – onestop Nov 6 '10 at 8:55
• @JCL Renders fine for me in Chrome (v 5.0.375.125) on Ubuntu 10.04 running from a USB drive on my laptop. – onestop Nov 6 '10 at 9:06

Can't add it as a comment, so here it comes as an answer: As user28 already said, the marginal mean refers to the mean of a factor level, which - in a cross-table - is at the table's margins, hence the name marginal mean.

Why this term is not entirely redundant? "Mean" could mean just any mean, e.g. the mean of all right handed men in the example of user28. By saying "mean of factor A" you should mean the mean of all levels of factor A, but you could mean (or be misunderstood as meaning) the mean of one level of factor A. Using the term "marginal mean of factor A" makes it unambiguously clear what you mean.