Chi-square distribution, showing X 2 on the x-axis and P-value on the y-axis. A chi-squared test, also referred to as test (or chi-square test), is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-square distribution when the null hypothesis is true.hen T has a chi-square distribution with n − 1 degrees of freedom. For example if the sample size is 21, the acceptance region for T for a significance level of 5% is the interval 9.59 to 34.17.