# Contingency table

**cross tabulationcontingency tablescrosstabCross-tabulationcontingencyContingency coefficientCross tabcross tabulatedcross tabulatescross-check**

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.wikipedia

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### Frequency distribution

**distributionfrequency tabledistributions**

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.

Bivariate joint frequency distributions are often presented as (two-way) contingency tables:

### Fisher's exact test

**Fisher exact testexact testFisher test**

The significance of the difference between the two proportions can be assessed with a variety of statistical tests including Pearson's chi-squared test, the G-test, Fisher's exact test, and Barnard's test, provided the entries in the table represent individuals randomly sampled from the population about which conclusions are to be drawn.

Fisher's exact test is a statistical significance test used in the analysis of contingency tables.

### Odds ratio

**ORoddsodds ratios**

The strength of the association can be measured by the odds ratio, and the population odds ratio estimated by the sample odds ratio.

Since N_E=D_E+H_E and similarly for the N_{N} numbers, we only have four independent numbers, which we can organize in a table:

### Barnard's test

The significance of the difference between the two proportions can be assessed with a variety of statistical tests including Pearson's chi-squared test, the G-test, Fisher's exact test, and Barnard's test, provided the entries in the table represent individuals randomly sampled from the population about which conclusions are to be drawn.

In statistics, Barnard's test is an exact test used in the analysis of contingency tables.

### Pearson's chi-squared test

**chi-square statisticPearson chi-squared testchi-square**

The significance of the difference between the two proportions can be assessed with a variety of statistical tests including Pearson's chi-squared test, the G-test, Fisher's exact test, and Barnard's test, provided the entries in the table represent individuals randomly sampled from the population about which conclusions are to be drawn.

Each observation is allocated to one cell of a two-dimensional array of cells (called a contingency table) according to the values of the two outcomes.

### G-test

**G''-testFisher's G testG''-tests**

The commonly used chi-squared tests for goodness of fit to a distribution and for independence in contingency tables are in fact approximations of the log-likelihood ratio on which the G-tests are based.

### Phi coefficient

**mean square contingency**

A simple measure, applicable only to the case of 2 × 2 contingency tables, is the phi coefficient defined by

The square of the phi coefficient is related to the chi-squared statistic for a 2×2 contingency table (see Pearson's chi-squared test)

### Cramér's V

**Cramer's VV**

Two alternatives are the contingency coefficient C, and Cramér's V.

In the case of a 2 × 2 contingency table Cramér's V is equal to the Phi coefficient.

### Goodman and Kruskal's lambda

**Lambda coefficientGoodman and Kruskal's lambda ''r''**

The lambda coefficient is a measure of the strength of association of the cross tabulations when the variables are measured at the nominal level.

In probability theory and statistics, Goodman & Kruskal's lambda (\lambda) is a measure of proportional reduction in error in cross tabulation analysis.

### Ordinal data

**ordinalordinal variableordered categorical data**

The relation between ordinal variables, or between ordinal and categorical variables, may also be represented in contingency tables, although such a practice is rare.

Linear trends are also used to find associations between ordinal data and other categorical variables, normally in a contingency tables.

### Goodman and Kruskal's gamma

**Gamma test (statistics)Yule's ''Qgamma**

For more on the use of a contingency table for the relation between two ordinal variables, see Goodman and Kruskal's gamma.

It measures the strength of association of the cross tabulated data when both variables are measured at the ordinal level.

### Iterative proportional fitting

**RAS algorithm**

The iterative proportional fitting procedure (IPFP, also known as biproportional fitting in statistics, RAS algorithm in economics, raking in survey statistics, and matrix ranking or matrix scaling in computer science) is an iterative algorithm for estimating cell values of a contingency table such that the marginal totals remain fixed and the estimated table decomposes into an outer product.

### TPL Tables

TPL Tables is a cross tabulation system used to generate statistical tables for analysis or publication.

### Confusion matrix

**confusion matrices**

It is a special kind of contingency table, with two dimensions ("actual" and "predicted"), and identical sets of "classes" in both dimensions (each combination of dimension and class is a variable in the contingency table).

### Kendall rank correlation coefficient

**Kendall tau rank correlation coefficientKendall's tauKendall's τ**

The Tau-a statistic tests the strength of association of the cross tabulations.

### OLAP cube

**cubescube datadata Cubes**

The motivation behind OLAP displays harks back to the cross-tabbed report paradigm of 1980s DBMS, and to earlier contingency tables from 1904.

### Statistics

**statisticalstatistical analysisstatistician**

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.

### Table (information)

**tabletabulartables**

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.

### Matrix (mathematics)

**matrixmatricesmatrix theory**

### Karl Pearson

**PearsonPearson, KarlCarl Pearson**

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.

### Multivariate statistics

**multivariatemultivariate dataMultivariate testing**

A crucial problem of multivariate statistics is finding the (direct-)dependence structure underlying the variables contained in high-dimensional contingency tables.

### Conditional independence

**conditionally independentconditional dependenciesconditional independencies**

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)).

### Information theory

**information-theoreticinformation theoristinformation**

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.

### Pivot table

**pivot tablespivotingPivot**

A pivot table is a way to create contingency tables using spreadsheet software.

### Handedness

**right-handedleft-handedsouthpaw**

Suppose there are two variables, sex (male or female) and handedness (right or left handed).