"Padmanabhan, Sudharsha" <[EMAIL PROTECTED]> We know trhat as the sample size increases, the variance should decrease,
Should it? I can paraphrase his test case thus: v100 <- sapply(1:100, function(i) var(rnorm(100, 0, 3))) # We expect the elements of v100 to cluster around 3^2 v1000 <- sapply(1:1000, function(i) var(rnorm(1000, 0, 3))) # We expect the elements of v1000 to cluster around 3^2 too. fivenum(v100) => [1] 6.469134 7.884637 8.916314 10.189463 13.897817 # ^^^^^^^^ fivenum(v1000) => [1] 7.874345 8.692326 8.967684 9.268955 10.503038 # ^^^^^^^^ The population parameter sigma-squared is 3^2 = 9. The estimates are 8.92 in one case and 8.97 in the other; sounds about right to me. Looking at density(v100) and density(v1000) is enlightening. Means and standard deviations: mean(v100) var(v100) => 9.080676 2.376193 mean(v1000) var(v1000) => 8.98147 0.1721246 Are these not pretty much as expected? Not that a t-test is the ideal test for the distributions involved, but it's familiar and since the distribution is pretty bell-shaped, it may be usable as a rough guide to whether to be worried or not. > t.test(v100, v1000) Welch Two Sample t-test data: v100 and v1000 t = 0.6413, df = 100.439, p-value = 0.5228 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -0.2077100 0.4061231 sample estimates: mean of x mean of y 9.080676 8.981469 ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help