degrees of freedom

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degrees of freedom
Message posted by Miner,John on May 25, 2000 at 12:00 AM (ET)

Hi!
I don't get it...How do you really know that a small sample N<30 will not contain an outlier (ie) an item with a high degree of variance. All 30 could be outliers! Is this concept based on real mathmatical probabilities or is it just highly probable and therefore the convention to use N-1? Iwould also appreciate an extremely simple explanation of degrees of freedom. Thanx!

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Re: degrees of freedom
Message posted by nancy diehl on June 2, 2000 at 12:00 AM (ET)

...explanation of degrees of freedom.....
First of all, you need to understand that if you were to sum the difference
between each observation and that sample's mean, this sum would be zero.
Given that, then you can understand that all you need to know is the
value of n-1 of your observations because the last observation can be
determined due to the fact that the sum of the differences have to be zero.
Hence, you can "freely" choose the values of your observations for all
but 1, hence degrees of freedom are n-1.

Think of this in small terms. I have 3 observations, I tell you two of
them are 4 and 7 and the average is 5. Given this, I know the third
observation has to be 4 in order for the sum of these (observations-mean)
to equal 0.

(4-5)=-1
(7-5)= 2
________
=-1, hence the third observation has to be 4 to get a difference of -1.

Three observations, two degrees of freedom.

Re: degrees of freedom
Message posted by John F. Miner on June 4, 2000 at 12:00 AM (ET)

For:Nancy Diehl/June4,2000

That was the best explanation of degrees of freedom I have seen.Thanx a lot! John

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