8.2 : Degrees of Freedom

The degree of freedom for a particular statistical calculation is the number of values that are free to vary. Thus, the minimum number of independent numbers can specify a particular statistic. The degrees of freedom differ greatly depending on known and uncalculated statistical components.

For example, suppose there are three unknown numbers whose mean is 10; although we can freely assign values to the first and second numbers, the value of the last number can not be arbitrarily assigned. Since the first two are independent, with the third one dependent, the dataset is said to have two degrees of freedom. In many statistical methods, the number of degrees of freedom is usually calculated as one minus the sample size. The degrees of freedom have broad applications in calculating standard deviation and statistical estimates in methods such as the Student t distribution and the Chi-Square distribution tests.