Understanding Statistics:  Difference between STDEV.P and =STDEV.S in Excel, maybe lotus too?

brothertruffle880
brothertruffle880 used Ask the Experts™
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I'm trying to understand statistics here:
I read that the difference between the Population Standard Deviation and Sample is
The StDevP function evaluates a population, and the StDev function evaluates a population sample.

If your sample size is N.

StDev will divide by N
and StDevP will divide by N-1


1.  This does not make sense.  How does subtracting one item turn a data set from a whole population into a sample?
2.  Which do I use when I'm evaluating my company's sales numbers.  the "P" or "S"?
I guess population because I'm including the entire group of sales people in my firm?
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Top Expert 2010

Commented:
To be most correct, if your data cover a sample and not the entire population, use the STDEV.S

For large samples, there is very little difference.
SteveCost Accountant
Top Expert 2012

Commented:
As Patric says, for large samples there is little difference.
But if applying Hypothesis Testing it is the Sample Sandard Deviation which is used.
www.sjsu.edu/faculty/gerstman/StatPrimer/hyp-test.pdf

Author

Commented:
My misunderstanding is this:  It seems kind of arbitrary to merely subtract "1" and suddenly it's  a sample formula versus a population formula.. If that's all it takes then why not subtract "2" or "3"  wouldn't that make it better?

I'm trying to grasp the thinking behind the construction of the formula.
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Cost Accountant
Top Expert 2012
Commented:
Indeed it is rather arbritrary, especially as it doesn't vary based upon 'N'.

It is more about gaining a sigma value which can be applied for sample sizes around 10 to 100, which tend to be a "little off" if the one isn't subtracted. Above 100 it tends to be far less material as to which method is used.

So it comes down to population size and the reason for using Standard Deviation.
Drawing conclusions about longe term data from short term data is always S (n-1).
There is probably a long lost paper somewhere about the need to reduce the divisor when dealing with samples. maybee it would explain why the 1 and not som other value.
byundtMechanical Engineer
Most Valuable Expert 2013
Top Expert 2013

Commented:
The difference between dividing by n-1 or n was developed by Friedrich Bessel to counteract the systematic underestimation of sample variance. By dividing by a smaller number, the calculated value of standard deviation for a sample was increased.
http://en.wikipedia.org/wiki/Bessel%27s_correction

If you take many samples from a given population, ideally the standard deviation of the samples would have a mean value equal to that of the standard deviation of the population. But because the mean of each sample inevitably drifts to one side or the other of the mean of the population, calculating the standard deviation of that sample (and dividing by n) will tend to result in a smaller standard deviation than that for the overall population. Bessel identified this problem, and proposed dividing by n-1 to introduce a correction opposing this trend.
SteveCost Accountant
Top Expert 2012

Commented:
The correction factor is probably more properly attributed to Gauss, who used it in this connection as early as 1823 (Gauss 1823).
Gauss, C. F. "Theoria combinationis obsevationum erroribus minimis obnoxiae." Werke, Vol. 4. Göttingen, Germany: p. 1, 1823.

1823 ... so it has been arround a while.

Author

Commented:
The_Barman:

Thank you!

Yes!  I think it should vary based on "n"
Anyway, your answer was precisely the insight I needed on this point.

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