# Degrees of freedom

#### ron

##### New Member
Hi everyone,

Can somebody please explain the concept of degrees of freedom in depth but made simple
Thanks

#### JohnM

##### TS Contributor
It's the number of independent data points or observations, or the number that are free to vary.

If you have a sample of 4 numbers, and you tell me three of them along with the sample mean, I can "determine" what the 4th number is - in other words, it's determined by the other 3 items and the sample mean - it's not free to vary. That's why degrees of freedom is often n-1.

#### PeterVincent

##### New Member
JohnM said:
It's the number of independent data points or observations, or the number that are free to vary.

If you have a sample of 4 numbers, and you tell me three of them along with the sample mean, I can "determine" what the 4th number is - in other words, it's determined by the other 3 items and the sample mean - it's not free to vary. That's why degrees of freedom is often n-1.
John,
I take it that the degrees of freedom in your example is zero can you give examples where the degrees of freedom is not zero?

Thanks
PeterVincent

#### JohnM

##### TS Contributor
In my example the sample size is 4, so degrees of freedom would be n-1 or 4-1 = 3.

E

#### elnaz

##### Guest
hello
Degrees of Freedom
Used in slightly different senses throughout the study of statistics, Degrees of Freedom were first introduced by Fisher based on the idea of degrees of freedom in a dynamical system (e.g., the number of independent co-ordinate values which are necessary to determine it). The degrees of freedom of a set of observations are the number of values which could be assigned arbitrarily within the specification of the system. For example, in a sample of size n grouped into k intervals, there are k-1 degrees of freedom, because k-1 frequencies are specified while the other one is specified by the total size n. Thus in a p by q contingency table with fixed marginal totals, there are (p-1)(q-1) degrees of freedom. In some circumstances the term degrees of freedom is used to denote the number of independent comparisons which can be made between the members of a sample.