Degrees of freedom, often represented by v or df, is the number of independent pieces of information used to calculate a statistic. It’s calculated as the sample size minus the number of restrictions.
Degrees of freedom are normally reported in brackets beside the test statistic, alongside the results of the statistical test.
Example: Degrees of freedomSuppose you randomly sample 10 American adults and measure their daily calcium intake. You use a one-sample t test to determine whether the mean daily intake of American adults is equal to the recommended amount of 1000 mg.
The test statistic, t, has 9 degrees of freedom:
df = n − 1
df = 10 − 1
df = 9
You calculate a t value of 1.41 for the sample, which corresponds to a p value of .19. You report your results:
“The participants’ mean daily calcium intake did not differ from the recommended amount of 1000 mg, t(9) = 1.41, p = 0.19.”
What are degrees of freedom?
In inferential statistics, you estimate a parameter of a population by calculating a statistic of a sample. The number of independent pieces of information used to calculate the statistic is called the degrees of freedom. The degrees of freedom of a statistic depend on the sample size:
- When the sample size is small, there are only a few independent pieces of information, and therefore only a few degrees of freedom.
- When the sample size is large, there are many independent pieces of information, and therefore many degrees of freedom.
When you estimate a parameter, you need to introduce restrictions in how values are related to each other. As a result, the pieces of information are not all independent. To put it another way, the values in the sample are not all free to vary.
The following analogy and example show you what it means for a value to be free to vary and how it’s affected by restrictions.
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