Degrees Of Freedom

Published May 15, 2023

Definition of Degrees of Freedom

Degrees of freedom (df) refers to the number of independent values in a statistical analysis that can vary without affecting the number of dependent values that are being analyzed. In other words, it tells us how many values in a statistical calculation are free to vary.

Example

Imagine a sample size of 10 people, and we are calculating the mean of their ages. The formula for calculating the mean is as follows: sum of all ages / total number of people. Now, if we know the ages of 9 out of the 10 people, we can calculate the age of the 10th person since we know that the total sum of their ages should add up to a certain amount. That means, in this case, we have only one degree of freedom.

However, if we are analyzing a regression model that has three coefficients (e.g., y = b₀ + b₁x₁ + b ₂x₂), and we have a sample size of 100, then the degrees of freedom for this analysis are 97. That is because we have 100 observations and three coefficients that we are estimating. Hence, we have 97 degrees of freedom.

Why Degrees of Freedom Matters

Degrees of freedom help researchers to perform statistical tests and draw appropriate conclusions based on the data they have collected. As we have seen in the previous example, degrees of freedom can vary based on the size of the sample and the number of parameters being estimated.

Understanding the degrees of freedom, in turn, helps the analysts to determine appropriate levels of significance and confidence intervals. It also helps them to choose appropriate statistical tests that account for the variability in the data set. Thus, degrees of freedom play a crucial role in ensuring the accuracy and validity of statistical analyses.