Definition - A measure of how many runs are available to form an estimate. Each preceding estimate in a sequence absorbs one degree of freedom from the number available. Before any estimates are made, the number of degrees of freedom equals the number of independent data.

Another definition of the degrees of freedom is that it is the number of values in a sample that you could vary given that you know the value for the descriptive statistic in the sample. Thus, if you had a sample with 10 values, and you knew the mean of the sample, you could change 9 of the values, but when those 9 values were changed, you couldn't change the tenth, because it would be fixed to produce the known mean. Thus, there would be nine degrees of freedom in this case.

If the treatment groups are considered separately, the sample means can also be considered as estimates of the population mean, and thus SSb/(g - 1) can be used as an estimate. The remaining ("within-group", "error") variance can be estimated from SSw/(n - g). This example demonstrates the partitioning of df: df total = n - 1 = df(between) + df(within) = (g - 1) + (n - g).

Ways of determining df