*58*

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

The F critical value can be found by using anÂ F distribution tableÂ or by using statistical software.

To find the F critical value, you need:

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

Using these three values, you can determine the F critical value to be compared with the F statistic.

**How to Find the F Critical Value in Python**

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

**scipy.stats.f.ppf(q, dfn, dfd)**

where:

**q:Â**The significance level to use**dfn**: The numerator degrees of freedom**dfd**: The denominator degrees of freedom

This function returns the critical value from the F distribution based on the significance level, numerator degrees of freedom, and denominator degrees of freedom provided.

For example, suppose we would like to find the F critical value for a significance level of 0.05, numerator degrees of freedom = 6, and denominator degrees of freedom = 8.Â

import scipy.stats #find F critical value scipy.stats.f.ppf(q=1-.05, dfn=6, dfd=8) 3.5806

The F critical value for a significance level of 0.05, numerator degrees of freedom = 6, and denominator degrees of freedom = 8 isÂ **3.5806**.

Thus, if weâ€™re conducting some type of F test then we can compare the F test statistic toÂ **3.5806**.Â If the F statistic is greater than 3.580, then the results of the test are statistically significant.

Note that smaller values of alpha will lead to larger F critical values. For example, consider the F critical value forÂ a significance level of **0.01**, numerator degrees of freedom = 6, and denominator degrees of freedom = 8.Â

scipy.stats.f.ppf(q=1-.01, dfn=6, dfd=8) 6.3707

And consider the F critical value with the exact same degrees of freedom for the numerator and denominator, but with a significance level ofÂ **0.005**:

scipy.stats.f.ppf(q=1-.005, dfn=6, dfd=8) 7.9512

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