Our »Streuspanne Lexicon« is not a regular series, but a section to refer to small explanations without having to go on and on in a separate series. Today we continue with »F wie Freiheitsgrade« (English: D for Degrees of Freedom)
In statistics, degrees of freedom describe the number of independent pieces of information that are included in an estimate. So if a mean value is calculated from n data, then n independent pieces of information are included - i.e. the mean value has n degrees of freedom. In contrast, the standard deviation or variance only has n-1.
A well-known example of the use of degrees of freedom is the analysis of variance. This involves analysing whether there are significant differences in a certain characteristic between different groups, for example in life expectancy between the sexes or between smokers and non-smokers. The variance of the group mean values is compared with the variance within the groups. In order to determine the dispersion within the groups, as many group mean values must be calculated as there are groups. Therefore, when calculating the degrees of freedom, not only 1 but also the number of groups is subtracted from the sample size.
Incorrectly calculated degrees of freedom lead to inaccurate estimates and biased results. With large samples, small errors can be less significant, but an exact calculation of the degrees of freedom is crucial, especially for variance analyses, as it forms the basis for the interpretation of the critical values. By the way, we explain what critical values are in the encyclopaedia entry »C for critical values«.
We would like to thank our follower Anne, who requested exactly this entry. Have you discovered statistics or mathematical observations from everyday life that you would like us to discuss or explain? Or are there terms that you would like us to shed light on in the »Streuspanne Lexicon«? Then get in touch with us at presse(at)itwm.fraunhofer.de with new ideas.
If you have just found your way here from a regular episode of the »Streuspanne« podcast, jump back quickly!
[Our Podcast is only available in German.]
Find the podcast on all major portals including Spotify, Podcasters, Amazon Music, Apple Podcasts, Deezer, Google , RadioPublic , Pocket Casts or directly here on our website.
Fraunhofer Institute for Industrial Mathematics ITWM