contingencytable

A contingency table, also known as a cross-tabulation or two-way table, is a type of table in statistics that displays the frequency distribution of variables. It is particularly useful for examining the relationship between two categorical variables. The rows of the table represent the categories of one variable, and the columns represent the categories of the other variable. The cells within the table contain the counts of observations that fall into each combination of categories.

For example, a contingency table could be used to display the relationship between gender (male/female) and opinion on a particular policy (for/against). The table would have two rows for gender and two columns for opinion, resulting in four cells representing the number of males who are for the policy, males against, females for, and females against.

Contingency tables are fundamental in statistical analysis, especially for hypothesis testing. Common statistical tests associated with contingency tables include the chi-squared test of independence, which assesses whether there is a statistically significant association between the two variables. They are also used in calculating measures of association, such as the odds ratio or relative risk, to quantify the strength and direction of the relationship. Visualizations like mosaic plots or stacked bar charts can be derived from contingency tables to illustrate the data.