What Is Chi-Square?

Chi-square is a statistical test that detects whether an observed set of sample results are obtained by mere chance, or whether something other than chance is causing the data to vary. If the observed results sufficiently deviate from what is statistically expected, the calculated chi-square is statistically significant.

Chi-square is calculated by subtracting each expected result from each observed result, squaring the difference and dividing each squared difference by its corresponding expected result. The numbers at the end of this process are all summed to obtain the chi-square statistic, which is then compared to critical values on a chi-square table. A significant chi-square means that the observed results were not obtained due to chance variation in the data.