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Michael Wood

Date:

Tue, 18 May 1999 10:51:10 GMT0BST

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 I've got a random sample of 4 measurements: 10, 10, 10, 12, and I'm interested in a confidence interval for the population mean (a silly, artificial example bu it makes the point). I've generated 10000 resamples in the standard way and found that the middle 95% interval (2.5%ile to 97.5%ile) is 10 - 11.5 with a median of 10.5. The mean (of course) is 10.5 also. I believe that the standard conclusion would be a 95% confidence interval from 10 - 11.5(??) My question is - what is wrong with the following alternative argument? The resample results show that there's a 95% probability of the mean of a sample of 4 being something between 0.5 *below* the population mean and 1.0 *above* the population mean. (Obviously the mean of the pseudopopulation from which the resamples are drawn is 10.5.) Given that the observed sample mean is 10.5, if this is 0.5 below the population mean then the population mean must be 0.5 above the sample mean - ie 11. A similar argument applies to the other limit, so the interval becomes 9.5 - 11: ie the interval is *reversed around the sample statistic*. I can see (intuitively) difficulties with both argument. I'd be grateful for any comments. (The same process with the sample maximum leads to a 95% resample interval of 10 - 12, and a median resample maximum of 12 and a mean of 11.4. The pseudopopulation maximum is 12, so the reversal argument gives a 95% interval of 12-14 with a point estimate of 12 working from the median and 12.6 working from the mean. I know that bootstrapping a maximum is a silly thing to do but this makes more sense than the sample=population argument ...?) Thanks in anticipation of enlightenment Michael ********************************************************** Michael Wood AMS Department, Portsmouth Business School, University of Portsmouth, Locksway Road, Milton, Southsea, Hants, PO4 8JF, England. Tel 01705 844095 Fax 01705 844037 Email [log in to unmask] %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%