Definition: Degrees of freedom

Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Probability distributions ▷ Degrees of freedom

Definition: Degrees of freedom can refer to

• a parameter or parameters of certain probability distributions, such as the chi-squared distribution, the t-distribution or the F-distribution;

• the number of values in the final calculation of a statistic that are free to vary, such as $n-1$ for a sample variance calculated from $n$ data points.

Some statistics have sampling distributions whose parameters (in the former sense) are equal to their degrees of freedom (in the latter sense). For example, a function of the sample variance follows a chi-squared distribution with $n-1$ degrees of freedom.

 

Sources:

• Wikipedia (2024): "Degrees of freedom (statistics)"; in: Wikipedia, the free encyclopedia, retrieved on 2024-10-11; URL: https://en.wikipedia.org/wiki/Degrees_of_freedom_(statistics).
• Animated Software (2024): "Degrees of Freedom"; in: Glossary of Statistical Terms, retrieved on 2024-10-11; URL: https://www.animatedsoftware.com/statglos/sgdegree.htm.

Metadata: ID: D206 | shortcut: dof | author: JoramSoch | date: 2024-10-11, 11:55.