How to Find the F Critical Value in Python?

In this article, we are going to learn about how to find the F Critical Value in Python using the SciPy library.

What is F Critical Value?

An F statistic is what you'll obtain after running an F test. Whether the results of the F test are statistically significant can be determined by comparing the F statistic to an F critical value. To put it simply, we compare our F value to the F-critical value as a standard. This article will look at a Python technique for finding the F critical value.

Syntax

To calculate the F critical value, use the Python function scipy.stats.f.ppf(), which has the following syntax ?

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

where:

• q the significance level to use (1 - alpha)
• 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, degrees of freedom for the numerator, and degrees of freedom for the denominator.

Example 1: F Critical Value with Alpha = 0.05

Let's find the F critical value with a significance level of 0.05, numerator degrees of freedom of 6, and denominator degrees of freedom of 8 ?

import scipy.stats

# Find F critical value
f_critical = scipy.stats.f.ppf(q=1-0.05, dfn=6, dfd=8)
print("F critical value:", f_critical)

F critical value: 3.5805803197614603

With a significance level of 0.05, and degrees of freedom in the numerator and denominator of 6 and 8 respectively, the F critical value is 3.5806.

If we're performing an F test, we can compare our F test statistic to 3.5806. The results are considered statistically significant if the F statistic is greater than 3.5806.

Example 2: F Critical Value with Alpha = 0.01

A smaller alpha value will result in a larger F critical value. Let's find the F critical value at a significance level of 0.01 ?

import scipy.stats

# Find F critical value with smaller alpha
f_critical = scipy.stats.f.ppf(q=1-0.01, dfn=6, dfd=8)
print("F critical value (alpha=0.01):", f_critical)

F critical value (alpha=0.01): 6.370680730239201

Notice that with a smaller significance level (0.01), the F critical value increased to 6.3707, making it harder to achieve statistical significance.

Comparison of Different Alpha Levels

Conclusion

Use scipy.stats.f.ppf() to find F critical values in Python. Remember that smaller alpha levels result in larger critical values, making statistical significance harder to achieve. The F critical value serves as a threshold for determining whether your F test results are statistically significant.