Degrees of Freedom

Definition: The Degrees of Freedom refers to the number of values involved in the calculations that have the freedom to vary. In other words, the degrees of freedom, in general, can be defined as the total number of observations minus the number of independent constraints imposed on the observations.

The degrees of freedom are calculated for the following statistical tests to check their validity:

  1. t-Distribution
  2. F- Distribution
  3. Chi-Square Distribution

These tests are usually done to compare the observed data with the data that is expected to be obtained with a specific hypothesis.

Degrees of Freedom is usually denoted by a Greek symbol ν (mu) and is commonly abbreviated as, df. The statistical formula to compute the value of degrees of freedom is quite simple and is equal to the number of values in the data set minus one. Symbolically:

df= n-1

Where n is the number of values in the data set or the sample size. The concept of df can be further understood through an illustration given below:

Suppose there is a data set X that includes the values: 10,20,30,40. First of all, we will calculate the mean of these values, which is equal to:

(10+20+30+40) /4 = 25.

Once the mean is calculated, apply the formula of degrees of freedom. As the number of values in the data set or sample size is 4, so,

df = 4-1=3.

Thus, this shows that there are three values in the data set that have the freedom to vary as long as the mean is 25.

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