 # Degrees of Freedom

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Definition

This term is used to account for the number of independent data points available for calculations of parameter estimates from the sample. It can also be defined as the number of data points that are free to vary after the Parameters are estimated. The degrees of freedom for a statistical test give a measure of the power of that test. It is generally denoted by the abbreviation “df”.

An analogy would be to consider the degrees of freedom as a bank account. We start the account with the “df” equal to the total number of data points. As we compute statistics in the analysis, withdrawals are made from the bank account, one d.f. for each additional statistic. Note that at this bank the balance cannot be zero! We must always have at least 1 “df” for the unexplained, or error term.

Examples

The three observations 2, 9, and 4 yield a mean value of (2+9+4)/3 = 5. Now suppose the record for the last observation is misplaced. We could still reconstruct the original sample as follows: 2 and 9 add up to 11. Because the original sum is 15 (the only way to divide a number by 3 and get a mean of 5), the missing observation must be 15-11 = 4. Thus, we only need the values of two out of the three values in order to completely describe this dataset. The degrees of freedom in this case are (n-1) = 3-1 = 2.