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Forum index » Science and Technology » Math » num-analysis
Sample standard deviation accuracy
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Rob McDonald
science forum beginner


Joined: 01 Dec 2005
Posts: 36

PostPosted: Wed Jun 14, 2006 6:47 pm    Post subject: Sample standard deviation accuracy Reply with quote
I think this should be a straightforward question, but my searches must
be using the wrong keywords. I apologize for not asking in a
statistics newsgroup, but I frequent this group, and it should be close
enough to on topic.

Is there an equation to estimate the accuracy of a sample standard
deviation based on the sample size?

I'm doing a Monte Carlo sample around a computer program. A few of the
inputs have probability distributions specified in terms of deviation
from the baseline. The distributions are all Gaussian with zero mean,
and a specified standard deviation.

I run the MC w/ 10,000 samples and calculate the sample standard
deviation of the program outputs relative to the baseline outputs. The
results match what I expect.

Is there a standard equation to estimate how close we expect the sampel
standard deviation to be to the true standard deviation?

Thanks in advance,

Rob
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Ray Koopman
science forum Guru Wannabe


Joined: 25 Mar 2005
Posts: 216

PostPosted: Wed Jun 14, 2006 7:26 pm    Post subject: Re: Sample standard deviation accuracy Reply with quote
Rob McDonald wrote:
Quote:
I think this should be a straightforward question, but my searches must
be using the wrong keywords. I apologize for not asking in a
statistics newsgroup, but I frequent this group, and it should be close
enough to on topic.

Is there an equation to estimate the accuracy of a sample standard
deviation based on the sample size?

I'm doing a Monte Carlo sample around a computer program. A few of the
inputs have probability distributions specified in terms of deviation
from the baseline. The distributions are all Gaussian with zero mean,
and a specified standard deviation.

I run the MC w/ 10,000 samples and calculate the sample standard
deviation of the program outputs relative to the baseline outputs. The
results match what I expect.

Is there a standard equation to estimate how close we expect the sampel
standard deviation to be to the true standard deviation?

Thanks in advance,

Rob

Kendall & Stuart, _Advanced Theory of Statistics_ (vol 1, 2nd ed,
1963; sec 10.15, p 243) give the s.d. of the large-sample s.d. as
sqrt((mu_4 - mu_2^2)/(4*n*mu_2)), where mu_k is the kth central
moment. For sampling from a normal distribution, this reduces to
sigma/sqrt(2n).
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Rob McDonald
science forum beginner


Joined: 01 Dec 2005
Posts: 36

PostPosted: Wed Jun 14, 2006 8:28 pm    Post subject: Re: Sample standard deviation accuracy Reply with quote
Ray Koopman wrote:
Quote:
Kendall & Stuart, _Advanced Theory of Statistics_ (vol 1, 2nd ed,
1963; sec 10.15, p 243) give the s.d. of the large-sample s.d. as
sqrt((mu_4 - mu_2^2)/(4*n*mu_2)), where mu_k is the kth central
moment. For sampling from a normal distribution, this reduces to
sigma/sqrt(2n).

Thanks a bunch.

Of course, for rule of thumb use, in terms of fraction of the standard
deviation, we are left with 1/sqrt(2n). Which means a doubling of N
for a halving of the error. Furthermore, it means that 10,000 points
gets you a little better than 1%.

Rob
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Ray Koopman
science forum Guru Wannabe


Joined: 25 Mar 2005
Posts: 216

PostPosted: Wed Jun 14, 2006 9:11 pm    Post subject: Re: Sample standard deviation accuracy Reply with quote
Rob McDonald wrote:
Quote:
... [I]n terms of fraction of the standard
deviation, we are left with 1/sqrt(2n). Which means a doubling of N
for a halving of the error.

doubling --> quadrupling ?
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Rob McDonald
science forum beginner


Joined: 01 Dec 2005
Posts: 36

PostPosted: Wed Jun 14, 2006 11:15 pm    Post subject: Re: Sample standard deviation accuracy Reply with quote
Ray Koopman wrote:
Quote:
Rob McDonald wrote:
... [I]n terms of fraction of the standard
deviation, we are left with 1/sqrt(2n). Which means a doubling of N
for a halving of the error.

doubling --> quadrupling ?

Yes, absolutely. Sorry about that.

Rob
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