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Table that displays the frequency of variables
cross tabulation that aggregates by summing, averaging, etc. (rather than only by counting)
In statistics, a contingency table (also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the multivariate frequency distribution of the variables. They are heavily used in survey research, business intelligence, engineering, and scientific research. They provide a basic picture of the interrelation between two variables and can help find interactions between them. The term contingency table was first used by Karl Pearson in "On the Theory of Contingency and Its Relation to Association and Normal Correlation", part of the Drapers' Company Research Memoirs Biometric Series I published in 1904. A crucial problem of multivariate statistics is finding the (direct )dependence structure underlying the variables contained in high dimensional contingency tables. If some of the conditional independences are revealed, then even the storage of the data can be done in a smarter way (see Lauritzen (2002)). In order to do this one can use information theory concepts, which gain the information only from the distribution of probability, which can be expressed easily from the contingency table by the relative frequencies. A pivot table is a way to create contingency tables using spreadsheet software.

Multiple columns (historically, they were designed to use up all the white space of a printed page). Where each row refers to a specific sub group in the population (in this case men or women), the columns are sometimes referred to as banner points or cuts (and the rows are sometimes referred to as stubs). Significance tests. Typically, either column comparisons, which test for differences between columns and display these results using letters, or, cell comparisons, which use color or arrows to identify a cell in a table that stands out in some way. Nets or netts which are sub totals. One or more of: percentages, row percentages, column percentages, indexes or averages. Unweighted sample sizes (counts).

The degree of association between the two variables can be assessed by a number of coefficients. The following subsections describe a few of them. For a more complete discussion of their uses, see the main articles linked under each subsection heading.

Another choice is the tetrachoric correlation coefficient but it is only applicable to 2 × 2 tables. Polychoric correlation is an extension of the tetrachoric correlation to tables involving variables with more than two levels. Tetrachoric correlation assumes that the variable underlying each dichotomous measure is normally distributed. The coefficient provides "a convenient measure of [the Pearson product moment] correlation when graduated measurements have been reduced to two categories." The tetrachoric correlation coefficient should not be confused with the Pearson correlation coefficient computed by assigning, say, values 0.0 and 1.0 to represent the two levels of each variable (which is mathematically equivalent to the φ coefficient).

The lambda coefficient is a measure of the strength of association of the cross tabulations when the variables are measured at the nominal level. Values range from 0.0 (no association) to 1.0 (the maximum possible association). Asymmetric lambda measures the percentage improvement in predicting the dependent variable. Symmetric lambda measures the percentage improvement when prediction is done in both directions.

Gamma test: No adjustment for either table size or ties. Kendall's tau: Adjustment for ties. Tau b: Used for square tables. Tau c: Used for rectangular tables.