Conditional Distribution: Definition & Finding

What is a Conditional Distribution?

A conditional distribution is a distribution of values for one variable that exists when you specify the values of other variables. This type of distribution allows you to assess the dispersal of your variable of interest under specific conditions, hence the name.

That might sound a bit complex, but the idea is straightforward.

Suppose you’re selling computers, and you record the type of computer and gender for each sale. Now imagine that you want to assess the dispersal of computer types for only female customers. That’s an example of a conditional distribution. We’re conditioning computer types on the gender variable value of female.

How to Find a Conditional Distribution

The process of conditioning one variable on the value of another variable might sound complicated. However, it’s simple to find a conditional distribution using a contingency table. Just look down a column or across a row.

The table below organizes our data for the computer type by gender study.

I highlight two examples in the table. Let’s stick with our original example of computer types for females. By looking at horizontal highlight in the table, we see that females have purchased the following:

PC: 30
Mac: 87

Statisticians say that you condition one variable on the value of another. In our example, we are conditioning computer type on the gender value of female. This process allows us to understand our data in a more specific context.

We could also assess a different conditional distribution to understand a different context, such as gender conditioned on Mac sales. That’s the vertical example I highlight in the contingency table above.

When you have conditional distributions, you can calculate conditional probabilities. For more information, read Using Contingency Tables to Calculate Probabilities.

A conditional distribution differs from a marginal distribution, which is the dispersal of one variable while disregarding all other variables.