Degree of freedom

Suppose you are asked to choose 10 numbers. You then have the freedom to choose 10 numbers as you please, and we say you have 10 degrees of freedom.

But suppose a condition is imposed on the numbers. The condition is that the sum of all the numbers you choose must be 100. In this case, you cannot choose all 10 numbers as you please. After you have chosen the ninth number, let’s say the sum of the nine numbers is 94. Your tenth number then has to be 6, and you have no choice. Thus you have only 9 degrees of freedom.

In general, if you have to choose n numbers, and a condition on their total is imposed, you will have only (n — 1) degrees of freedom

In general, Calculating the degrees of freedom is often the sample size minus the number of parameters you’re estimating or the number of constraints c

Therefore, degree of freedom= (n-c)

Example:

suppose that I wrote five checks last month, and the total amount of these checks is $80.

Now if I know that the first four checks were for $30, $20, $15, and $5, then I don’t need to be told that the fifth check was for $10.

I can simply deduce this information by subtraction of the other four checks from $80.

My degrees of freedom are thus four, and not five.

Sample variance df:

where SSD is the sum of squared deviations from the sample mean.

If we take a sample of size n and take the deviations from the (known) population mean, then the deviations, and therefore the SSD, will have df n.

But if we take the deviations from the sample mean, then the deviations, and therefore the SSD, will have df n 1

Degree of freedom is calculated as the sample size minus the number of restrictions.

Degrees of Freedom Formula:

Calculating the degrees of freedom is often the sample size minus the number of parameters you’re estimating:

DF = N — P

Where:

N = sample size

P = the number of parameters or relationships or constraints or conditions