**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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