crosstabulation

Crosstabulation, also known as cross-tabulation, is a statistical method used to examine the relationship between two or more categorical variables by creating a contingency table. In such a table, each row represents a category or level of one variable, each column represents a category of another variable, and each cell contains the frequency or count of observations with that combination. The table can also display marginal totals and can be converted into row percentages, column percentages, or overall percentages to aid interpretation.

Crosstabs are used to explore whether distributions differ across groups, to identify patterns, and to prepare data for statistical tests such as the chi-square test of independence or homogeneity. They are common in survey research, market research, epidemiology, and the social sciences, where categorical data are frequent. Multi-way crosstabs extend to three or more variables, though they can become difficult to interpret.

Interpretation requires caution: a relationship visible in a crosstab does not establish causation, and small expected counts can affect the validity of statistical tests. It is common to report effect size measures such as Phi or Cramér’s V and to examine alternative normalizations like row-wise or column-wise percentages to understand the association structure.