Re: Population SD or sample SD with many replicates?


"Peter Frank" <peter_frankde@xxxxxxxx> wrote in message
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Dr. Dickie wrote:

"Peter Frank" <peter_frankde@xxxxxxxx> wrote in message
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Hi,

The standard deviation is supposed to be calculated with N-1 for
samples and N for the population.

However, in analytical chemistry the population is practically always
indefinite because there is an indefinite number of possible
measurements. So, to be exact the standard deviation would always have
to be calculated with N-1.

Nonetheless, on http://science.widener.edu/svb/stats/descript.html I
read that the population standard deviation can be calculated for large
sample sets (usually more than 20 measurements). Is it an alright
practice to use the population SD formula for measurements with many
replicates or do you always use the sample SD formula?

Regards,
Peter


I would say, if the sample SD is different from the population SD, then
you
should use the sample SD--since this is what you measured. If it is not
different, what difference does it make?

Well, I guess, this is what the above rule of thumb is based on. With
larger numbers of replicates, the differences between sample SD and
population SD become smaller and smaller since N-1 and N get closer and
closer to each other (relatively speaking).

So, I conclude from your statement that for smaller numbers of
replicates, the standard deviation is calculated using N-1 anyway, and
for larger numbers of replicates it doesn't really matter.

Regards,
Peter

That about sums it up (except that since it "doesn't matter," you use the
sample SD in every case--that way, you do not have to worry whether or not
it is different from the population SD).

--
------
Dr. Dickie
"Let be be finale of seem.
The only emperor is the emperor of ice-cream."
-- Wallace Stevens


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