Degrees of freedom

 In statistical inference, degrees of freedom is a measure of the available amount of independent information. For example, when estimating a mean value of a population, the degrees of freedom, df, are the same as the number of observations, n. When estimating the variance of the same population, one degree of freedom is first lost when estimating the mean value because variance is defined relative to the mean value. The population variance is thus estimated with n - 1 degrees of freedom.

More generally, with independent observations the degrees of freedom can be calculated as the number of observations minus the number of estimated parameters, df = n - p, where p is the number of estimated parameters.

However, with repeated measurements, things become more complicated because observations from the same person are correlated and do not provide as much independent information as the same number of measurements from different people. Ignoring this problem is a common mistake, which typically produces too optimistic results because it leads to an overestimation of the degrees of freedom and an underestimation of the variance. The latter is usually the consequence of contaminating between-subject variance with within-subject variance.

However, the degrees of freedom can be adjusted for the correlation between repeated measurements. One method that is commonly used in the analysis of linear mixed models, is Satterthwaite's method (1). Note that the adjusted degrees of freedom is a decimal number, not an integer.

References

1. Luke SG. Evaluating significance in linear mixed-effects models in R. Behav Res Methods. 2017 Aug;49(4):1494-1502. doi: 10.3758/s13428-016-0809-y. PMID: 27620283.

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