Why call it contingency table?

The term "contingency table" is used to describe a tabular arrangement of data that displays the frequencies or counts of observations for different categories or levels of two or more categorical variables. It is also known as a cross-tabulation or a crosstab.

The name "contingency table" reflects the idea that the values in the table represent the contingencies or dependencies between the variables being analyzed. It provides a way to examine the relationship between categorical variables and understand how the distribution of one variable may vary across different levels of another variable.

The contingency table typically has rows representing one categorical variable and columns representing another categorical variable. The intersecting cells of the table contain the frequency or count of observations that fall into each combination of categories.

For example, consider a study examining the relationship between gender and voting preference. A contingency table could be constructed with "Gender" as the row variable (with categories "Male" and "Female") and "Voting Preference" as the column variable (with categories "Candidate A," "Candidate B," and "Candidate C"). The table would show the frequencies or counts of individuals falling into each combination of gender and voting preference.

Contingency tables are commonly used in statistical analysis, particularly in the context of chi-square tests, to assess the association or independence between categorical variables. These tables provide a compact and organized way to summarize data and facilitate the exploration of relationships between variables.

The term "contingency" in "contingency table" refers to the fact that the frequencies or counts represented in the table are contingent upon the categories or levels of the variables being examined.