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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 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
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 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?

--

Dr. Dickie
Skepticult member in good standing #394-00596-438
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!
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" wrote in message news:1144858178.299230.264760@v46g2000cwv.googlegroups.com... 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
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" wrote in message news:1144858178.299230.264760@v46g2000cwv.googlegroups.com... 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.

s/indefinite/infinite/

[snip]
 Quote: 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.

If you use the (N-1) formula, you will never be wrong within the
limits of your calculation since, as already noted, (N-1) -> N for
large N. That way, you also eliminate the risk of accidentally using
the (N) instead of (N-1) formula for small numbers of replicates.

N >= 20 is the usual rule of thumb for biased vs. unbiased standard
deviations as estimates for sigma
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" wrote in message news:1144858178.299230.264760@v46g2000cwv.googlegroups.com... 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
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 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 In either case, the data give an estimate of SD, with an

uncertainty.
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