What is a Marginal Distribution?
A marginal distribution is a distribution of values for one variable that ignores a more extensive set of related variables in a dataset.
That definition sounds a bit convoluted, but the concept is simple. The idea is that when you have a larger set of related variables that you collected for a study, you might want to focus on one of them to answer a specific question.
Imagine you’re studying computer sales and record both the type of computer and gender. Now suppose that while you measured both variables, you want to know the distribution of computer types without factoring in gender—that’s a marginal distribution. Let’s build on this example to bring it to life!
How to Find a Marginal Distribution
It’s easiest to understand and find marginal distributions using a two-way contingency table. In fact, the origin of the term originates from these tables. The table below organizes the data we collected for our computer type by gender study.
Related posts: Contingency Tables: Definition, Examples & Interpreting and Two-Way Tables Explained.
To find them, look in the margins of a contingency table, hence the name. I’ve circled the values in the margin that represent the dispersal of one variable without considering the other variable. There’s a marginal distribution for computer type and another for gender.
Let’s go back to understanding the dispersal of computer types while disregarding gender. By looking at the margins in the table, we see that there have the following sales:
- PC: 96
- Mac: 127
Statisticians say you need to “marginalize out” the other variables to find a marginal distribution. In the example above, we marginalized out gender to reveal the dispersal of computer type.
When you have marginal distributions, you can calculate marginal probabilities. For more information, read Using Contingency Tables to Calculate Probabilities.
This type of distribution contrasts with a conditional distribution, which is the dispersal of one variable while specifying particular values of other variables.