Contingency Table: Statistics, Probability & Examples

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  • 0:01 What Is a Contingency Table?
  • 0:44 Using a Contingency Table
  • 2:09 Examples
  • 3:12 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

In statistics, dealing with situations where there are more than one variable can be difficult. Contingency tables can provide a way to make sense of the data given. This lesson will describe contingency tables and give some examples of them.

What Is a Contingency Table?

Contingency tables are tools used by statisticians when they need to make sense of data that has more than one variable. Contingency tables are also called cross tabulation tables or cross tab. Contingency tables are displayed in matrix, or grid, form. The numbers displayed give the frequency of each data point.

The term contingency table was first used in 1904 by Karl Pearson, an English mathematician who is credited with launching the study of mathematical statistics.

One of the difficulties in attempting to decipher data that has more than one variable is finding the structure of the data. Using a contingency table allows the statistician to better understand the data using probability and relative frequencies.

Using a Contingency Table

A random set of 100 people who have pets were polled to see if there was a correlation between gender and whether they had a dog or a cat. This is a contingency table outlining the data.


The number of males, females, dog owners and cat owners are called marginal totals. The total number of people involved in the study is called the grand total.

By placing the data in a table, some conclusions can be drawn that might not be evident if the data was just in a list. The user can see that there seems to be a correlation between gender and pet ownership. It seems that more men own dogs while more women own cats. Statistical tests such as Pearson's chi-squared test, the G-test, Fisher's exact test, and Barnard's test can give the significance of the data in the contingency table.

If there is a correlation between the sets of data (in this example, the strong correlation between gender and pet ownership) the data is said to be contingent, or dependent. If there is not a relationship between the data, then the data is not contingent, or independent.

The 2 x 2 contingency table, like the above example, is a simple contingency table, however contingency tables can have any number of rows and columns depending on the amount of data that is being studied. Tables with large numbers of variables are rarely used because they can become confusing.

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