Table of Contents
What Is the Chi-Square Test?
The chi-square test is a non-parametric statistical test used to compare observed frequencies with expected frequencies. It measures how well observed data fits expected patterns. The two main variants are the goodness-of-fit test (one variable) and the test of independence (two variables in a contingency table).
Developed by Karl Pearson in 1900, it is one of the most widely used statistical tests for categorical data analysis.
Formula
Critical Values (α = 0.05)
| df | Critical Value |
|---|---|
| 1 | 3.841 |
| 2 | 5.991 |
| 3 | 7.815 |
| 5 | 11.070 |
| 10 | 18.307 |
FAQ
When should I use chi-square?
Use it for categorical data when you want to test whether observed frequencies differ from expected frequencies, or whether two categorical variables are independent. Expected frequencies should be at least 5 in each cell.
What if expected frequencies are too small?
If expected frequencies are below 5, use Fisher's exact test or combine categories. The chi-square approximation is unreliable with very small expected counts.