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I have a problem where I need to measure the standard deviation of a population that is difficult to sample, and so I would like to use as few samples as I can practically get away with.
In the limit of large numbers, and with the assumption that the underlying distribution is normally distributed, I know that the appropriate estimates are:
Where the standard error in the standard deviation is
Which implies that if I had 200 samples, I would expect to know the standard deviation to about 5%.
But this is devised in the limit of large N. I would like to know how the uncertainty might change in the limit of small N (e.g. N = 5 or 10). Applied as is, the formulas suggest at N = 5, the estimate of the population standard deviation will have an error of about 30% in the typical case. But is that really true, or in considering such small numbers would my error be significantly worse than that (and how much worse)?
Also, in the limit of small numbers, are there any procedures that can improve the estimate the population standard deviation. For example, would the interquartile range be less subject to fluctuations. I doubt it, but it is probably worth asking. Dragons flight ( talk) 18:03, 23 July 2011 (UTC)
Mathematics desk | ||
---|---|---|
< July 22 | << Jun | July | Aug >> | July 24 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
I have a problem where I need to measure the standard deviation of a population that is difficult to sample, and so I would like to use as few samples as I can practically get away with.
In the limit of large numbers, and with the assumption that the underlying distribution is normally distributed, I know that the appropriate estimates are:
Where the standard error in the standard deviation is
Which implies that if I had 200 samples, I would expect to know the standard deviation to about 5%.
But this is devised in the limit of large N. I would like to know how the uncertainty might change in the limit of small N (e.g. N = 5 or 10). Applied as is, the formulas suggest at N = 5, the estimate of the population standard deviation will have an error of about 30% in the typical case. But is that really true, or in considering such small numbers would my error be significantly worse than that (and how much worse)?
Also, in the limit of small numbers, are there any procedures that can improve the estimate the population standard deviation. For example, would the interquartile range be less subject to fluctuations. I doubt it, but it is probably worth asking. Dragons flight ( talk) 18:03, 23 July 2011 (UTC)