International Encyclopedia of Statistical Science
pp 363365
Degrees of Freedom
 Chong Ho YuAffiliated withArizona State University
Many elementary statistics textbooks introduce the concept of degrees of freedom (df) in terms of the number scores that are “free to vary.” However, this explanation cannot clearly show the purpose of df. There are many other approaches to present the concept of degrees of freedom. Two of the most meaningful ways are to illustrate df in terms of sample size and dimensionality. Both represent the number of pieces of useful information.
DF in Terms of Sample Size
Toothaker (1986) explained df as the number of independent components minus the number of parameters estimated. This approach is based upon the definition provided by Walker (1940): the number of observations minus the number of necessary relations, which is obtainable from the observations (df = n − r). Although Good (1973) criticized that Walker’s approach is not obvious in the meaning of necessary relations, the number of necessary relationships is indeed intuitive when there are just a few variables. ...
 Title
 Degrees of Freedom
 Reference Work Title
 International Encyclopedia of Statistical Science
 Pages
 pp 363365
 Copyright
 2011
 DOI
 10.1007/9783642048982_204
 Print ISBN
 9783642048975
 Online ISBN
 9783642048982
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 Industry Sectors
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 Editors

 Miodrag Lovric ^{(620)}
 Editor Affiliations

 620. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac
 Authors

 Chong Ho Yu ^{(413)}
 Author Affiliations

 413. Arizona State University, Tempe, AZ, USA
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