Exploring Degrees of Freedom T Test: Gaining Statistical Power

Degrees of freedom are the maximum numbers of logically independent values that have a freedom of varying in a sample dataset. Degrees of freedom are taken into consideration while studying various hypotheses testing methods in statistics like a t-test method. 

It is important to calculate degrees of freedom to justify your results if it either rejects or accepts a null hypothesis. Let us understand degrees of freedom concept through an example:

Say we have 5 integers determining the scores of students in maths out of 10. 4 of the numbers are as follows – 3,8,5,4. The average of these numbers is 6. This leaves us with the 5th number being 10 since it does not have freedom to vary. But why is it that there are five numbers in the sample but only one of them has no freedom to vary?

We can say it is because of the degrees of freedom formula:

Df​=N−1

Where, 

Df is degrees of freedom

N is sample size 

Now, the definition of degrees of freedom is the number of values that are free to vary. So when you are asked to choose three numbers whose average mean is 10 like: {9,10,11} {8,10,12} {7,10,13}

When you choose first two numbers, you are left with no choice but to choose the third number as 10. So once you choose 9+10 or 8+12, you have no choice but to select a number that will help you get an average of 10. 

Here the degrees of freedom for three numbers is 2.