How to perform an F-test in Python

Statisticians use the F test to check whether two data sets have the same variance. The F-test is named after Sir Ronald Fisher. To use the F-test, we make two hypotheses, a null hypothesis and an alternative hypothesis. We then choose whichever of the two hypotheses is endorsed by the F test.

Variance is a measure of data distribution that describes the deviation of data from the mean. Higher values show greater dispersion than smaller values.

In this article, you will learn how to perform F-Test in the Python programming language and its use cases.

F-Testing Process

The process of performing F-test is as follows:

• First, define the null hypothesis and alternative hypothesis.

• Null hypothesis or H0: σ12 = σ22 (the population variances are equal)

• Alternative hypothesis or H1: σ12 ≠ σ22 (population variances are not equal)

• Select statistics for testing.

• Calculate the overall degrees of freedom. For example, if m and n are population shapes, the degrees of freedom are expressed as(df1) = m–1 and (df2) = n – 1, respectively.

• Now find the F value from the F table.

• Finally, divide the alpha value of the two-tailed test by 2 to calculate the critical value.

Therefore, we define the F value using the overall degrees of freedom. We read df1 in the first row and df2 in the first column.

There are various F-tables for unique degrees of freedom. We compare the F-statistic from step 2 to the critical value calculated in step 4. If the critical value is less than the F-statistic, we can reject the null hypothesis. On the contrary, when the critical value is greater than the F statistic at some significant level, we can accept the null hypothesis.

Assumption

Before conducting the F-test based on the data set, we made some assumptions.

• The data generally obeys a normal distribution, that is, it conforms to a bell-shaped curve.

• There is no correlation between samples, that is, there is no multicollinearity in the population.

In addition to these assumptions, we should also consider the following key points when conducting an F-test:

• The maximum variance value should be in the numerator to perform a right-tailed test.

• In a two-tailed test, divide alpha by 2 to determine the critical value.

• Check if there is variance or standard deviation.

• If there are no degrees of freedom in the F table, the maximum value is used as the critical value.

Application of F-Test in Python

grammar

scipy stats.f()

parameter

x : quantiles q : lower or upper tail probability dfn, dfd shape parameters loc :location parameter scale : scale parameter (default=1) size : random variate shape moments : [‘mvsk’] letters, specifying which moments to compute

Explanation

Explanation

In this method, the user must pass the f_value and the iterable length of each array toscipy.stats.f.cdf()and subtract 1 from it to perform the F test.

algorithm

• First, import the NumPy and Scipy.stats libraries for operation.

• Then create two lists of randomly chosen values with two different variable names, convert them to NumPy arrays, and use Numpy to calculate the variance of each array.

• Define a function to calculate the F-score, where first we divide the variance of the array by the degrees of freedom of 1.

• Then calculate the iterable length of each array and pass the f-value (variance ratio) and length into the CDF function and subtract the length from 1 to calculate the p-value.

• Finally, the function returns p_value and f_value.

Example

import numpy as np import scipy.stats # Create data group1 = [0.28, 0.2, 0.26, 0.28, 0.5] group2 = [0.2, 0.23, 0.26, 0.21, 0.23] # Converting the list to an array x = np.array(group1) y = np.array(group2) # Calculate the variance of each group print(np.var(group1), np.var(group2)) def f_test(group1, group2): f = np.var(group1, ddof=1)/np.var(group2, ddof=1) nun = x.size-1 dun = y.size-1 p_value = 1-scipy.stats.f.cdf(f, nun, dun) return f, p_value # perform F-test f_test(x, y)

Output

Variances: 0.010464 0.00042400000000000017

You can observe that the F-test value is4.38712 andthe corresponding p-value is0.019127.

Since the p-value is less than 0.05, we will abandon the null hypothesis. Therefore, we can say that the variances of the two populations are not equal.

in conclusion

After reading this article, you now know how to use the F-test to check whether two samples belong to a population with the same variance. You've learned about the F-test procedure, assumptions, and Python implementation. Let’s wrap up this article with some key points -

• The F test tells you whether two populations have equal variances.

• Calculate degrees of freedom and calculate critical values.

• Find the F-statistic from the F-table and compare it with the key value calculated in the previous step.

• Accept or reject the null hypothesis based on critical value and F-statistic comparison.

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