Degrees of Freedom (df)

Degrees of Freedom denotes the number of samples that a statistician has the freedom to choose. Degrees of Freedom is based on a concept that one could not have exercised his /her freedom to select all the samples.

The concept can be explained by an analogy:

X+Y = 10 (1)

In the above equation you have freedom to choose a value for X or Y but not both because when you choose one, the other is fixed. If you choose 8 for X, then Y has to be 2. So the degree of freedom here is 1.

X+Y+Z = 15 (2)

In the formula (2), one can choose values for two variables but not all. You have freedom to choose 8 for X and 2 for Y, If so, then Z is fixed, So the degree of freedom is 2. df is calculated by subtracting 1 from the size of each group. The methods of df calculation may vary with the test used.

Reference

http://statisticalconcepts.blogspot.in/2010/03/degrees-of-freedom-df.html