Chi-square test

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

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.

A chi-square test may be applied on a contingency table for testing a null hypothesis of independence of rows and columns.

Click here for the chi square calculator.

Editor-In-Chief: C. Michael Gibson, M.S., M.D. [1]; Associate Editor(s)-in-Chief: Alejandro Lemor, M.D. [2]

Chi Square Calculator

The following file contains a 2×2 contingency table for chi square calculation.

Chi Square Calculator

How to use it?

1. Click on the link above to download the spreadsheet.
2. In the white boxes, you should enter the number of individuals for each group.
3. You may also enter the name of the groups (rows) and categories (columns).

• 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

• Chi-Square Calculator from GraphPad

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