Degrees of Freedom


David M. Lane


Measures of Variability, Introduction to Estimation

Learning Objectives
  1. Define degrees of freedom
  2. Estimate the variance from a sample of 1 if the population mean is known
  3. State why deviations from the sample mean are not independent
  4. State general formula for degrees of freedom in terms of the number of values and the number of estimated parameters
  5. Calculate s2

Some estimates are based on more information than others. For example, an estimate of the variance based on a sample size of 100 is based on more information than an estimate of the variance based on a sample size of 5. The degrees of freedom (df) of an estimate is the number of independent pieces of information on which the estimate is based.

In general, the degrees of freedom for an estimate is equal to the number of values minus the number of parameters estimated en route to the estimate in question.

Recall from the section on variability that the formula for estimating the variance in a sample is:

The denominator of this formula is the degrees of freedom.

Please answer the questions:
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