How to perform a chi-square test

The exact procedure for performing a Pearson’s chi-square test depends on which test you’re using, but it generally follows these steps:

Create a table of the observed and expected frequencies. This can sometimes be the most difficult step because you will need to carefully consider which expected values are most appropriate for your null hypothesis.
Calculate the chi-square value from your observed and expected frequencies using the chi-square formula.
Find the critical chi-square value in a chi-square critical value table or using statistical software.
Compare the chi-square value to the critical value to determine which is larger.
Decide whether to reject the null hypothesis. You should reject the null hypothesis if the chi-square value is greater than the critical value. If you reject the null hypothesis, you can conclude that your data are significantly different from what you expected.

How to report a chi-square test

If you decide to include a Pearson’s chi-square test in your research paper, dissertation or thesis, you should report it in your results section. You can follow these rules if you want to report statistics in APA Style:

You don’t need to provide a reference or formula since the chi-square test is a commonly used statistic.
Refer to chi-square using its Greek symbol, Χ². Although the symbol looks very similar to an “X” from the Latin alphabet, it’s actually a different symbol. Greek symbols should not be italicized.
Include a space on either side of the equal sign.
If your chi-square is less than zero, you should include a leading zero (a zero before the decimal point) since the chi-square can be greater than zero.
Provide two significant digits after the decimal point.
Report the chi-square alongside its degrees of freedom, sample size, and p value, following this format: Χ² (degrees of freedom, N = sample size) = chi-square value, p = p value).

Example: Reporting a chi-square test

There was no significant relationship between handedness and nationality, Χ² (1, N = 428) = 0.44, p = .505.