Degrees Of Freedom

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DEFINITION of 'Degrees Of Freedom'

In statistics, the number of values in a study that are free to vary. For example, if you have to take ten different courses to graduate, and only ten different courses are offered, then you have nine degrees of freedom. Nine semesters you will be able to choose which class to take; the tenth semester, there will only be one class left to take - there is no choice, if you want to graduate.


Degrees of freedom are commonly discussed in relation to chi-square and other forms of hypothesis testing statistics. It is important to calculate the degree(s) of freedom when determining the significance of a chi square statistic and the validity of the null hypothesis.

INVESTOPEDIA EXPLAINS 'Degrees Of Freedom'

There are two types of chi square tests: the goodness-of-fit test (does a coin tossed 100 times turn up heads 50 times and tails 50 times?) and the test of independence (is there a relationship between gender and a perfect SAT score?).


Degrees of freedom are used to then determine whether a particular null hypothesis can be rejected based on the number of variables and samples of in the experiment. For example, while a sample size of 50 students might not be large enough to obtain significant information, obtaining the same results from a study of 500 samples can be judged as being valid.




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