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Peter Frank science forum beginner
Joined: 12 Apr 2006
Posts: 2

Posted: Wed Apr 12, 2006 4:09 pm Post subject:
Population SD or sample SD with many replicates?



Hi,
The standard deviation is supposed to be calculated with N1 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 N1.
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 

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Dr. Dickie science forum beginner
Joined: 14 Jul 2005
Posts: 23

Posted: Wed Apr 12, 2006 4:21 pm Post subject:
Re: Population SD or sample SD with many replicates?



"Peter Frank" <peter_frankde@yahoo.de> wrote in message
news:1144858178.299230.264760@v46g2000cwv.googlegroups.com...
Quote:  Hi,
The standard deviation is supposed to be calculated with N1 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 N1.
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 SDsince this is what you measured. If it is not
different, what difference does it make?

Dr. Dickie
Skepticult member in good standing #39400596438
Poking kooks with a pointy stick
Repeal the 17th amendment; let's reinstate the proper checks and balances
and end mob rule in my lifetime! 

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Peter Frank science forum beginner
Joined: 12 Apr 2006
Posts: 2

Posted: Wed Apr 12, 2006 4:36 pm Post subject:
Re: Population SD or sample SD with many replicates?



Dr. Dickie wrote:
Quote:  "Peter Frank" <peter_frankde@yahoo.de> wrote in message
news:1144858178.299230.264760@v46g2000cwv.googlegroups.com...
Hi,
The standard deviation is supposed to be calculated with N1 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 N1.
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 SDsince 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 N1 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 N1 anyway, and
for larger numbers of replicates it doesn't really matter.
Regards,
Peter 

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David Stone science forum beginner
Joined: 27 Mar 2006
Posts: 14

Posted: Wed Apr 12, 2006 7:29 pm Post subject:
Re: Population SD or sample SD with many replicates?



In article <1144859782.869766.157900@e56g2000cwe.googlegroups.com>,
"Peter Frank" <peter_frankde@yahoo.de> wrote:
Quote:  Dr. Dickie wrote:
"Peter Frank" <peter_frankde@yahoo.de> wrote in message
news:1144858178.299230.264760@v46g2000cwv.googlegroups.com...
Hi,
The standard deviation is supposed to be calculated with N1 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 N1.

s/indefinite/infinite/
[snip]
Quote: 
I would say, if the sample SD is different from the population SD, then you
should use the sample SDsince 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 N1 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 N1 anyway, and
for larger numbers of replicates it doesn't really matter.

If you use the (N1) formula, you will never be wrong within the
limits of your calculation since, as already noted, (N1) > N for
large N. That way, you also eliminate the risk of accidentally using
the (N) instead of (N1) formula for small numbers of replicates.
N >= 20 is the usual rule of thumb for biased vs. unbiased standard
deviations as estimates for sigma 

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Dr. Dickie science forum beginner
Joined: 14 Jul 2005
Posts: 23

Posted: Thu Apr 13, 2006 10:43 am Post subject:
Re: Population SD or sample SD with many replicates?



"Peter Frank" <peter_frankde@yahoo.de> wrote in message
news:1144859782.869766.157900@e56g2000cwe.googlegroups.com...
Quote:  Dr. Dickie wrote:
"Peter Frank" <peter_frankde@yahoo.de> wrote in message
news:1144858178.299230.264760@v46g2000cwv.googlegroups.com...
Hi,
The standard deviation is supposed to be calculated with N1 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 N1.
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 SDsince 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 N1 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 N1 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 casethat 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 icecream."
 Wallace Stevens 

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Marvin science forum Guru Wannabe
Joined: 24 Mar 2005
Posts: 224

Posted: Thu Apr 13, 2006 5:38 pm Post subject:
Re: Population SD or sample SD with many replicates?



Peter Frank wrote:
Quote:  Hi,
The standard deviation is supposed to be calculated with N1 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 N1.
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
In either case, the data give an estimate of SD, with an 
uncertainty. 

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