On 27-Nov-03 [EMAIL PROTECTED] wrote: > I've 2 samples A (111 items) and B (10 items) drawn from the same > unknown population. Witihn A I find 9 "positives" and in B 0 > positives. I'd like to know if the 2 samples A and B are different, > ie is there a way to find out whether the number of "positives" is > significantly different in A and B?
Pretty obviously not, just from looking at the numbers: 9 out of 111 -> p = P(positive) approx = 1/10 P(0 out of 10 when p = 1/10) is not unlikely (in fact = 0.35). However, a Fisher exact test will give you a respectable P-value: > library(ctest) > ?fisher.test > fisher.test(matrix(c(102,9,10,0),nrow=2)) [...] p-value = 1 alternative hypothesis: true odds ratio is not equal to 1 95 percent confidence interval: 0.000000 6.088391 > fisher.test(matrix(c(102,9,9,1),nrow=2)) p-value = 0.5926 > fisher.test(matrix(c(102,9,8,2),nrow=2)) p-value = 0.2257 > fisher.test(matrix(c(102,9,7,3),nrow=2)) p-value = 0.0605 > fisher.test(matrix(c(102,9,6,4),nrow=2)) p-value = 0.01202 So there's a 95% CI (0,6.1) for the odds ratio which, for identical probabilities of "+", is 1.0 hence well within the CI. And, keeping the numbers for the larger sample fixed for simplicity, you have to go quite a way with the smaller one to get a result significant at 5%: (102,9):(7,3) -> P = 0.06 (102,9):(6,4) -> P = 0.01 and, to have 80% power (0.8 probability of this event), the probability of "+" in the second sample would have to be as high as 0.41. Conclusion: your second sample size is quite inadequate except to detect rather large differences between the true proportions in the two cases! Best wishes, Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 167 1972 Date: 27-Nov-03 Time: 17:43:00 ------------------------------ XFMail ------------------------------ ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
