Degrees of Freedom
Prerequisites
Measures
of Variability, Introduction to Estimation
Learning Objectives
 Define degrees of freedom
 Estimate the variance from a sample of 1 if the population mean is
known
 State why deviations from the sample mean are not independent
 State general formula for degrees of freedom in terms of the number
of values and the number of estimated parameters
 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.
