Statistics Dictionary

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Degrees of Freedom

The term degrees of freedom (df) refers to the number of independent sample points used to compute a statistic minus the number of parameters estimated from the sample points.

For example, consider the sample estimate of the population variance ( s2 ):

 
nΣi=1
( X i - X ) 2
s2 =
( n - 1 )

where X i is the score for observation i in the sample, X is the sample estimate of the population mean, and n is the number of observations in the sample.

The formula is based on n independent sample points and one estimated population parameter (X). Therefore, the number of degrees of freedom is n minus one. For this example,

df = n - 1

See also:  One-Way Analysis of Variance