Chi-square test
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Overview
A chi-square test is any statistical hypothesis test in which the test statistic has a chi-square distribution when the null hypothesis is true, or any in which the probability distribution of the test statistic (assuming the null hypothesis is true) can be made to approximate a chi-square distribution as closely as desired by making the sample size large enough.
Specifically, a chi-square test for independence evaluates statistically significant differences between proportions for two or more groups in a data set.
- Pearson's chi-square test, also known as the Chi-square goodness-of-fit test, commonly referred to as the chi-square test
- Yates' chi-square test also known as Yates' correction for continuity
- Mantel-Haenszel chi-square test
- Linear-by-linear association chi-square test
Significance and effect size
In the social sciences, the significance of the chi-square statistic is often given in terms of a p value (e.g., p = 0.05). It is an indication of the likelihood of obtaining a result (0.05 = 5%). As such, it is relatively uninformative. A more helpful accompanying statistic is phi (or Cramer's phi, or Cramer's V).[1] Phi is a measure of association that reports a value for the correlation between the two dichotomous variables compared in a chi-square test (2 × 2). This value gives you an indication of the extent of the relationship between the two variables. Cramer's phi can be used for even larger comparisons. It is a more meaningful measure of the practical significance of the chi-square test and is reported as the effect size.
Chi-square test for contingency table
A chi-square test may be applied on a contingency table for testing a null hypothesis of independence of rows and columns.
See also
- General likelihood-ratio tests, which are approximately chi-square tests
- McNemar's test, related to a chi-square test
- The Wald test, which can be evaluated against a chi-square distribution
External links
References
de:Chi-Quadrat-Testfr:Test du χ²
it:Test chi quadrato
lv:Hī kvadrāta kritērijs
nl:Chi-kwadraattoets
ja:カイ二乗検定su:Tes chi-kuadrat
fi:Khii toiseen -testi
vi:Kiểm định chi-bình phương
Acknowledgement and Attribution Regarding Sources of Content
Some of the initial content on this page may be incorporated in part from copyleft sources in the public domain including wikis such as Wikipedia and AskDrWiki. Drug information for patients came from the The National Library of Medicine. Infectious disease information may have come from the Centers for Disease Control (CDC). Differential Diagnoses are drawn from clinicians as well as an amalgamation of 3 sources: 1.The Disease Database; 2. Kahan, Scott, Smith, Ellen G. In A Page: Signs and Symptoms. Malden, Massachusetts: Blackwell Publishing, 2004:3; 3. Sailer, Christian, Wasner, Susanne. Differential Diagnosis Pocket. Hermosa Beach, CA: Borm Bruckmeir Publishing LLC, 2002:7 .
