I have a question about resampleing that one of my students came up with and I hope someone on the list can help me understand and be able to answer his question. Perhaps Prof. Buce is "listening" out there. Using data from the death age of males (data shown below,I think I got this data from the DASL data base but don't remember for sure) The actual output from the program is below. In brief, his approach was to use the program RESAMPLEING STATS to draw samples of 18 from the data values without replacement and find the mean of the sample. This was done 1000 times and then the 2.5 and 97.5 percentile values were found for these results. His observation was that in most situations the confidence interval found by resampleing was a little narrower than the 95% CI given by mini-tab. I had him nest the test in a larger loop and repeat it 50 times and find the mean of the lower and upper Limits of the CI and that is what he did. The CI created by the average of Lows to Avg of highs from resampleing was (68.44 ... 80.167) as compared to the minitab results of (67.66...80.78). Taking the half interval width of the resampleing averages CI and dividing by the SE of the mean given by mini-tab we estimated that the resampleing averages would be about a 92% CI for the t-test, but with a slightly different mean... NOW the question is WHY?? I know this is a small difference, but it was consistently true (we ran this several times) that the resampleing means interval fell Inside the 95% CI by mini-tab. Is this a difference in the accuracy of the tests? .. Something related to the use of pseudo-random generation of numbers?... or have we misunderstood the resampleing approach to the t-test question?
The results are below, and include the program file for those who Know the software. I am inspired by the understanding their questions show, but frustrated by my inability to answer. I feel undereducated for the task I have assumed. Thanks in advance to anyone who can help.
'simulated t-test for one sample 95% conf interval ' minitab gives limits of 67.66 to 80.78 'norm plot p-value is .478 'data from minitab sample age dagem copy (55 60 62 71 74 79 84 90 98 61 70 58 70 93 77 62 82 90) a repeat 50 clear z repeat 1000 sample 18 a b mean b c score c z end percentile z (2.5 97.5) conint95 min conint95 lv max conint95 hv score lv zl score hv zh end mean lv meanlv mean hv meanhv print meanlv print meanhv