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Contingency Table

Contingency Table:

A contingency table is a tabular representation of categorical data . A contingency table usually shows frequencies for particular combinations of values of two discrete random variable s X and Y. Each cell in the table represents a mutually exclusive combination of X-Y values.

For example, consider a sample of N=200 beer-drinkers. For each drinker we have information on sex (variable X, taking on 2 possible values: "Male" and "Female") and preferred category of beer (variable Y, taking on 3 possible values: "Light", "Regular", "Dark"). A contingency table for these data might look like the following

Light Regular Dark Total
Male 20 40 50 110
Female 50 20 20 90
Total: 70 60 70 200

This is a two-way 2x3 contingency table (i.e. two rows and three columns).

Sometimes three-way (and more) contingency tables are used. Suppose the beer-drinkers data, besides sex and preference, are also stratified by age group. The third discrete variable Z ("Age") in this case might, for example, take on 4 values: "65".

In this case we would have a three-way 2x3x4 contingency table, equivalent to 4 two-way 2x3 contingency tables (one 2x3 table for each of the 4 age-groups).

See also: Contingency tables analysis

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Courses Using This Term

Biostatistics 1 – For Medical Science and Public Health
This course will teach you the principal statistical concepts used in medical and health sciences. Basic concepts common to all statistical analysis are reviewed, and those concepts with specific importance in medicine and health are covered in detail.
Categorical Data Analysis
This course will teach you the analysis of contingency table data. Topics include tests for independence, comparing proportions as well as chi-square, exact methods, and treatment of ordered data. Both 2-way and 3-way tables are covered.
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