Dan Nordlund wrote: "It would be necessary to see the code for your 'brief test' before anyone could meaningfully comment on your results. But your results for a single test could have been a valid "random" result."
I've re-created what I did below. The problem appears to be with the weighting process: the unweighted sample came out much closer to the actual than the weighted sample (>1% error) did. Comments? Jim > x [1] 1 2 3 4 5 6 7 8 9 10 11 12 > weights [1] 1 1 1 1 1 1 2 2 2 2 2 2 > a = mean(replicate(1000000,(sample(x, 3, prob = weights))));a # (1 million samples from x, of size 3, weighted by "weights"; the mean should be 7.50) [1] 7.406977 > 7.406977/7.5 [1] 0.987597 > b = mean(replicate(1000000,(sample(x, 3))));b # (1 million samples from x, of size 3, not weighted this time; the mean should be 6.50) [1] 6.501477 > 6.501477/6.5 [1] 1.000227 Jim Bouldin, PhD Research Ecologist Department of Plant Sciences, UC Davis Davis CA, 95616 530-554-1740 ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.