A contingency table provides a way of portraying data that can facilitate calculating probabilities. It is a method of displaying a frequency distribution as a table with rows and columns to show how two variables may be dependent (contingent) upon each other; The table helps determine conditional probabilities quite quickly and can help systematically organize, analyze and quantify data. The table displays sample values concerning two variables that may be dependent or contingent on one another. Here, the outcome of one variable is arranged in rows, while that of the other is arranged in columns. The table displays the observed frequencies of two variables, whose independence is determined by performing a test for independence.

This text is adapted from Openstax, Introductory Statistics, Section 3.4 Contingency Tables.