## What are Contingency Tables?

Contingency tables list multiple variables and their frequencies simultaneously, in order to simplify interactions between them in multivariate statistics. Also called crosstabs or two-way tables, these special types of frequency distribution tables are used to summarize the relationship between several categorical variables at the same time.

The rows, or “stubs” in these tables are labelled with specific sub-groups of the population (the variables). The columns, or “cuts” are filled with relevant analysis points, such as:

- Frequency of occurrence
- Significance tests. These test for differences between columns.
- Unweighted counts or sample sizes.
Various statistical features, such as: means, medians, standard deviation, etc…

- Net sub-totals

### How are Contingency Tables Used?

For example, a researcher might be investigating the relationship between lung cancer rates among different states. The two variables would be Lung Cancer Rates per 100,000 population and US State. The question is “Is there a significant relationship between lung cancer rates and state residence?” A chi-square test would then be run on the table to determine if there is a correlation between the two variables.