Statistics Definitions > Marginal Mean, Cell Mean

## What is a Marginal Mean?

A marginal mean is (as the name suggests) a mean found in the *margins * (i.e. the edges) of a contingency table. In other words, it’s the average scores from a group or subgroup in an experiment. The more technical definition is that one factor’s marginal means are the means for the factors averaged for all levels of the other factors.

## Example

**Question**: What are the marginal means for the following two-way table showing the percentage of males/females who own pets?

**Solution**: The contingency table shows **two factors**: **sex **(male or female) and **pet ownership status **(has pets or does not have pets). Each of these factors has two “levels” (i.e. male/female or yes/no). Therefore you’ll need to find *four *marginal means:

- Male.
- Female.
- Pets.
- No pets.

As you can probably, tell, when it’s written out this way: each level in each factor will have a marginal mean. Another way to look at is is that **each column and each row in a contingency table has an associated marginal mean.**

## 1. Male

Take the average across the row:

(0.41 + 0.08) / 2 = 0.245.

## 2. Female

Take the average across the row:

(0.45 + 0.06) / 2 = 0.255.

## 3. Pets

Take the average down the column:

(0.41 + 0.45) / 2 = 0.43.

## 4. No Pets

Take the average down the column:

(0.08 + 0.06) / 2 = 0.07.

The bottom left column is left blank (taking the averages of all the averages is not necessary).

## Cell Mean and Other Items in Contingency Tables

A **cell mean** is a count in a cell that represents a mean, instead of a total. “Cell mean” is an informal term, and there aren’t any hard and fast rules for differentiating it from anything else in a cell. If you’re reading a contingency table, you can probably figure out if you’ve got a cell mean from the context. If you’re making a table, you may want to make it clear if the counts are totals or means.

For example, the following image shows several numbers (..45, .41. .08 & .06).

It’s not clear from the image if these are counts or cell means (as they aren’t labeled). The implication is that 41% of men have pets, so you could interpret it as “on average, 41% of men have pets”. That would make it a cell mean.

**Marginal totals** also appear in the same place in a contingency table as marginal means (i.e. in the margins). To avoid confusing the two, **make sure the margins are clearly labeled as means or totals.**

Another item you might find in the margin is a marginal distribution.

Marginal distributions relate to probabilities and bivariate data (for the full definition, see: What is a Marginal Distribution?). Again, the column should be clearly labeled as a probability distribution (e.g. p(x) ) to avoid confusions with totals and means.

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