*55*

When you conduct a Chi-Square test, you will get a test statistic as a result. To determine if the results of the Chi-Square test are statistically significant, you can compare the test statistic to a **Chi-SquareÂ critical value**. If the test statistic is greater than the Chi-Square critical value, then the results of the test are statistically significant.

The Chi-Square critical value can be found by using aÂ Chi-Square distribution tableÂ or by using statistical software.

To find the Chi-Square critical value, you need:

- A significance level (common choices are 0.01, 0.05, and 0.10)
- Degrees of freedom

Using these two values, you can determine the Chi-Square value to be compared with the test statistic.

**How to Find the Chi-Square Critical Value in Python**

To find the Chi-Square critical value in Python, you can use theÂ scipy.stats.chi2.ppf()Â function, which uses the following syntax:

**scipy.stats.chi2.ppf(q, df)**

where:

**q:Â**The significance level to use**df**: The degrees of freedom

This function returns the critical value from the Chi-Square distribution based on the significance level and degrees of freedom provided.

For example, suppose we would like to find the Chi-Square critical value for a significance level of 0.05 and degrees of freedom = 11.

import scipy.stats #find Chi-Square critical value scipy.stats.chi2.ppf(1-.05, df=11) 19.67514

The Chi-Square critical value for a significance level of 0.05 and degrees of freedom = 11 isÂ **19.67514**.

Thus, if weâ€™re conducting some type of Chi-Square test then we can compare the Chi-Square test statistic toÂ **19.67514**.Â If the test statistic is greater than 19.67514, then the results of the test are statistically significant.

Note that smaller values of alpha will lead to larger Chi-Square critical values. For example, consider the Chi-Square critical value forÂ a significance level of **0.01**, and degrees of freedom = 11.Â

scipy.stats.chi2.ppf(1-.01, df=11) 24.72497

And consider the Chi-Square critical value with the exact same degrees of freedom, but with a significance level ofÂ **0.005**:

scipy.stats.chi2.ppf(1-.005 df=11) 26.75685

*Refer to the SciPy documentation for the exact details of the chi2.ppf() function.*