Chi-square test

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). 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 &times; 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.