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# Degrees of Freedom

Estimates of parameters can be based upon different amounts of information. The number of independent pieces of information that go into the estimate of a parameter is called the degrees of freedom (df). In general, the degrees of freedom of an estimate is equal to the number of independent values that go into the estimate minus the number of parameters estimated as intermediate steps in the estimation of the parameter itself.

For example, for a random sample of independent data points, if the sample mean, is estimated using the standard formula , then the degrees of freedom for is . This is because uses all of the independent values from the sample and does not rely on any other parameter estimates in its calculation. However, if the variance, , is estimated using the standard formula , then the degrees of freedom is equal to the number of independent values ( ) minus the number of parameters estimated as intermediate steps (one, ) and is therefore equal to N-1.    Next: Chi-Square Goodness of Fit Up: How to ask questions Previous: P-Values   Index

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Frank Starmer 2004-05-19
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