Dear R-Aficionados: I realize that no random number generator is perfect, so what I report below may be a result of that simple fact. However, if I have made an error in my thinking I would greatly appreciate being corrected.
I wish to illustrate the behavior of small samples (n=10) and so generate 100,000 of them. n.samples <- 1000000 sample.size = 10 p <- 0.0001 z.normal <- qnorm(p) # generate n.samples of sample.size each from a normal(mean=0, sd=1) density # small.sample <- matrix(rnorm(n=sample.size*n.samples, mean=0, sd=1), nrow=n.samples, ncol=sample.size) # Verify that from the entire small.sample matrix, p sampled values are below, p above. # observed.fraction.below <- sum(small.sample < z.normal)/length(small.sample) observed.fraction.above <- sum(small.sample > -z.normal)/length(small.sample) > observed.fraction.below [1] 6.3e-05 > observed.fraction.above [1] 0.000142 > I've checked the behavior of the entire sample's mean and median and they seem fine. The total fraction in both tails is 0.0002, as it should be. However in every instance about 1/3 are in the lower tail, 2/3 in the upper. I also observe the same 1/3:2/3 ratio for one million samples of ten. Is this simply because random number generators aren't perfect? Or have I stepped in something? Thank you for your kind counsel. Charles Annis, P.E. [EMAIL PROTECTED] phone: 561-352-9699 eFAX: 503-217-5849 http://www.StatisticalEngineering.com ______________________________________________ [EMAIL PROTECTED] mailing list http://www.stat.math.ethz.ch/mailman/listinfo/r-help
