In one of our previous articles, we discussed how to calculate the test statistic in a chi-square test of independence or goodness-of-fit test. We also discussed that the test statistic in a chi-square test follows the chi-square distribution. So, how can we calculate the critical value for a chi-square test? In this article, we will discuss that.

Let’s say our test statistic is 6.4, and the degrees of freedom is 5. Let’s also assume that the significance level alpha = 0.05. We can use the following Python code to calculate the critical value in that case:

from scipy.stats import chi2
 
# Calculate critical value for test statistic 6.4 and alpha = 0.05
test_statistic = 6.4
 
critical_value = chi2.ppf(0.95, df=5)
print("Critical value: ", critical_value)

Here, we are using the chi2.ppf() function from the scipy.stats module to calculate the critical value. The chi2.ppf() function is the percent point function.

The output of the above program will be like the following:

Critical value:  11.070497693516351

Please note that the chi-square distribution graph is skewed to the right. And the hypothesis test is a right-tailed test. So, if the test statistic is less than the critical value, we fail to reject the null hypothesis. Alternatively, if the test statistic is more than the critical value, we reject the null hypothesis.