Contingency Table

Contingency Table, also known as cross-tabulation or crosstab, is a type of table in data analysis used to display the frequency of the joint occurrence of two or more variables. It allows the user to visualize the relationship between two or more variables in an easy-to-read format. This type of table can also be used to pinpoint associations between categorical variables.

Contingency tables use rows and columns to organize information and typically represent categorical variables in a two-way or multi-way configuration. They are used in a wide variety of applications, such as survey analysis, clinical trials, market research, and statistical significance testing.

Contingency tables are created by first identifying the two or more categorical variables of interest. The rows and columns of the table are then populated with counts or percentages of observations that fall into each category. Some contingency tables display only the counts, while others display fractions or percentages instead.

The intersection of the two variables is represented by the cells of the table. The terms “two-way contingency table” and “multi-way contingency table” refer to the number of variables tested. For example, a two-way contingency table tests the relationship between two variables, while a multi-way contingency table tests the relationship between three or more variables.

The main purpose of a contingency table is to test if two variables are associated with one another, either directly or indirectly. To do so, the user must calculate a statistic known as a chi-squared test and compare it to a critical value. If the calculated statistic is greater than the critical value, then an association is said to exist between the two variables.

In conclusion, contingency tables are an important tool for data analysis. They are used to identify relationships between categorical variables, calculate statistical significance, and aid in survey analysis.