Degrees of Freedom
The number of values in a question that are free to vary independently.
Example: Choosing Hats
You have 4 hats (blue, gold, red and green) and want to wear a different one every day.
- On the first day you can choose any hat
- On the 2nd day you have 3 choices left
- On the 3rd day you have 2 choices left
- On the 4th day you have only 1 hat left, so no choice at all really
In fact your "degrees of freedom" turned out to be only 3, by the 4th day you had no freedom to choose.
So, depending on the situation, the degrees of freedom can be less (but never more) than the number of items you are dealing with:
df = n − r
- df = Degrees of Freedom
- n = sample size
- r = number of restrictions
In the hats example, n is the number of hats, and r is the restriction that you have one less choice each day, so df = 4 − 1 = 3
Here are some dfs by topic:
| Formula | ||
|---|---|---|
| Sample Variance | df = n − 1 | the 1 restriction is the mean |
| Independent Student's t-test | df = n1 + n2 − 2 | r=2 because of two separate means |
| Paired Student's t-test | df = n − 1 | We have one (overall) mean |
| Chi Square Test | df = (rows − 1) × (cols − 1) |