Degrees of freedom describe the number of scores in a sample that are independent and free to vary. Why do formulas for degrees of freedom vary?

Degrees of freedom describe the number of scores in a sample that are independent and free to vary. Why do formulas for degrees of freedom vary?

• A. Because the degrees of freedom depend on the total sample size.
• B. Different formulas for different tests.
• C. They are always equal to the sample size minus one.
• D. They depend on the number of groups.

Answer: (B)

Degrees of freedom measure how many independent pieces of information remain after accounting for the constraints in a calculation. Those constraints differ by the statistical procedure, so the df formula changes with the test. For a simple one-sample mean, you fix the sample mean from the data, which uses up one piece of information, leaving n minus one independent pieces. In more complex designs, such as ANOVA, you estimate multiple group means and an overall mean, creating different pools of independent information: between-group degrees of freedom equals the number of groups minus one, within-group degrees of freedom equals the total observations minus the number of groups. In contingency-table chi-square tests, the margins impose constraints that yield (rows minus one) times (columns minus one) degrees of freedom. Because each test uses information and imposes constraints in its own way, the degrees-of-freedom formulas vary across procedures.

Degrees of freedom measure how many independent pieces of information remain after accounting for the constraints in a calculation. Those constraints differ by the statistical procedure, so the df formula changes with the test. For a simple one-sample mean, you fix the sample mean from the data, which uses up one piece of information, leaving n minus one independent pieces. In more complex designs, such as ANOVA, you estimate multiple group means and an overall mean, creating different pools of independent information: between-group degrees of freedom equals the number of groups minus one, within-group degrees of freedom equals the total observations minus the number of groups. In contingency-table chi-square tests, the margins impose constraints that yield (rows minus one) times (columns minus one) degrees of freedom. Because each test uses information and imposes constraints in its own way, the degrees-of-freedom formulas vary across procedures.