In statistics, the degrees of freedom is a measure of the level of precision required to estimate a parameter (i.e., a quantity representing some aspect of the population). It expresses the number of independent factors on which the parameter estimation is based and is often a function of sample size. In general, the number of degrees of freedom increases with increasing sample size and with decreasing number of estimated parameters. The quantity is commonly abbreviated df or denoted by the lowercase Greek letter nu, v.

For a set of observations, the degrees of freedom is the minimum number of independent values required to resolve the entire data set. It is equal to the number of independent observations being used to determine the estimate (n) minus the ...