Degrees of Freedom

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Degrees of Freedom
Message posted by Shana Ruhnke on September 27, 1999 at 12:00 AM (ET)

Dear Sir or Madam:

We are talking about standard deviation in a psychological statistics course, and the prof. briefly hit on degrees of freedom,as it is included in the formula for finding st. dev. in a sample group. However, I would like to understand degrees of freedom in a more logical way. I understand it to be the closest number to the actual sample size, but since we need to account for the underestimation of the sampling deviation, we use the degrees of freedom, which in turn gives us a larger number. Am I way off? How else does degrees of freedom affect our sample and how do we choose what number would be efficient in different problems?

Thank you for your help, GOD BLESS!!!!

<>< Shana <><

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: Degrees of Freedom
Message posted by Nancy Diehl on September 27, 1999 at 12:00 AM (ET)

Let's see if this helps in the understanding of degrees of freedom.....
If we are talking one sample of data, then the df equals n-1. The
reason for this is that the individual observations minus their mean
sums to zero. So, I can "freely" choose the value for all of my
observations except for the last observation. The
last observation will have to be whatever number it will take to make
that sum of the obs-mean = to zero. Hence, the term, degrees of freedom.
I am free to choose the value of all the observations except the last one.
What I mean by this is, for example, let's say I have five
observations of value 4,4,8,8 and I don't know the fifth one but I know the
mean for the sample is 5. Because the obs.- mean equals 0, then I know the fifth value has
to be 6 in order for the differences to sum to zero. For a sample of 5 the
degrees of freedom are therefore, n-1, or 4df.
You comment is correct that we use n-1 to calculate
std.dev. for a sample so we do not underestimate the true population
std.dev.

Re: Degrees of Freedom
Message posted by JG on September 27, 1999 at 12:00 AM (ET)

Degrees of freedom measures how much data you have. That is, if you have 7 numbers you can only calculated 7 independent quantities from this data and every time you calculate something you loose a degree of freedom.

Another way to look at this is that you need at least 2 numbers to estimate an average and a measure of variability for your data.

Re: Degrees of Freedom
Message posted by Jack Tomsky on September 27, 1999 at 12:00 AM (ET)

Just to add to what Nancy wrote, if the value of the population mean was actually known, then the degrees of freedom would be equal to the sample size. In more complicated models, such as linear regression, the mean is the sample size minus the number of coefficients estimated in the model.

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