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Chi-square test
Introduction
Overview
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
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
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.
Chi Square Calculator
Click here for the chi square calculator.
Chi Square Calculator
The following file contains a 2×2 contingency table for chi square calculation.
How to use it?
- Click on the link above to download the spreadsheet.
- In the white boxes, you should enter the number of individuals for each group.
- You may also enter the name of the groups (rows) and categories (columns).
Editor-In-Chief: C. Michael Gibson, M.S., M.D. [1]; Associate Editor(s)-in-Chief: Alejandro Lemor, M.D. [2]
See also
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
References
References
- ↑ Aaron, B., Kromrey, J. D., & Ferron, J. M. (1998, November). Equating r-based and d-based effect-size indices: Problems with a commonly recommended formula. Paper presented at the annual meeting of the Florida Educational Research Association, Orlando, FL. (ERIC Document Reproduction Service No. ED433353)
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