Degrees og freedom (statistik)

Jeg synes, denne forklaring er god:

In many statistical problems we are required to determine the degrees of freedom. This refers to a positive whole number that indicates the lack of restrictions in our calculations. The degree of freedom is the number of values in a calculation that we can vary.

A Few Examples

For a moment suppose that we know the mean of data is 25 and that the values are 20,10, 50, and one unknown value. To find the mean of a list of data, we add all of the data and divide by the total number of values. This gives us the formula (20 + 10 + 50 + x)/4 = 25, where x denotes the unknown . Despite calling this unknown, we can use some algebra to determine that x = 20.

Let's alter this scenario slightly. Instead we suppose that we know the mean of a data set is 25, with values 20, 10, and two unknown values. These unknowns could be different, so we use two different variables, x and y to denote this. The resulting formula is (20 + 10 + x + y)/4 = 25. With some algebra we obtain y = 70 - x. The formula is written in this form to show that once we choose a value for x, the value for y is determined. This shows that there is one degree of freedom.

Now we'll look at a sample size of one hundred. If we know that the mean of this sample data is 20, but do not know the values of any of the data, then there are 99 degrees of freedom. All values must add up to a total of 20 x 100 = 2000. Once we have the values of 99 elements in the data set, then the last one has been determined.