Degrees of Freedom

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Degrees of Freedom (dof)


Purpose

To determine the number of measurements that are necessary to make an unbiased estimate of a statistic.


Anatomy

Degrees of Freedom

Reference: Juran’s Quality Control Handbook

Terminology

A. v (nu) = dF : Represents the degrees of freedom

B. n: Represents the number of observations taken.

C. m: Represents the number of parameters to be estimated. A parameter is a constant defining some property of the density function of a variable, such as the mean or standard deviation.

D. This example is using the equation of the sample standard deviation to illustrate the use of degrees of freedom.

E. The denominator (n-1) represents the degrees of freedom. In this equation, it was necessary to establish only one constant (the sample mean) in order to compute the standard deviation. Therefore, the degrees of freedom is equal to n-1. The number of degrees of freedom will vary according to the statistical test and parameters that are used, but it will always be related to the number of observations and constants. Usually, degrees of freedom are represented by n-1 or n-2.

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