## Degrees of Freedom

When a statistic is used to estimate a population parameter, it is sometimesnecessary to specify the degrees of freedom of the data. The number of degreesof freedom represent the number of ways the data may vary. For everyrestriction imposed on the data, one degree of freedom is lost. Degrees offreedom are expressed as:

N (sample size) - number of restrictions The concept of degrees of freedom arises from the **calculations** thatare performed on the data. For example, say we are comparing the standarddeviations of a set of scores. According to the formula for standard deviation,the sum of all the standard deviations in the data set must equal zero. If wehave 5 scores, then 4 of the standard deviations can be anything (they are freeto vary). But the fifth standard deviation must make the whole set equalzero--it is not free to vary. (Garrett, 1966)

Our sample size is 5, and we imposed 1 restriction, that standard deviationsmust equal zero. So degrees of freedom is 4.