Hi Christopher and Uwe. thanks for your time and guidance. I deeply appreciate it.
-dev Quoting Christoph Buser <[EMAIL PROTECTED]>: > Hi > > As Uwe mentioned be careful about the difference the > significance level alpha and the power of a test. > > To do power calculations you should specify and alternative > hypothesis H_A, e.g. if you have two populations you want to > compare and we assume that they are normal distributed (equal > unknown variance for simplicity). We are interested if there is > a difference in the mean and want to use the t.test. > Our Null hypothesis H_0: there is no difference in the means > > To do a power calculation for our test, we first have to specify > and alternative H_A: the mean difference is 1 (unit) > Now for a fix number of observations we can calculate the power > of our test, which is in that case the probability that (if the > true unknown difference is 1, meaning that H_A is true) our test > is significant, meaning if I repeat the test many times (always > taking samples with mean difference of 1), the number of > significant test divided by the total number of tests is an > estimate for the power. > > > In you case the situation is a little bit more complicated. You > need to specify an alternative hypothesis. > In one of your first examples you draw samples from two gamma > distributions with different shape parameter and the same > scale. But by varying the shape parameter the two distributions > not only differ in their mean but also in their form. > > I got an email from Prof. Ripley in which he explained in > details and very precise some examples of tests and what they > are testing. It was in addition to the first posts about t tests > and wilcoxon test. > I attached the email below and recommend to read it carefully. It > might be helpful for you, too. > > Regards, > > Christoph Buser > > -------------------------------------------------------------- > Christoph Buser <[EMAIL PROTECTED]> > Seminar fuer Statistik, LEO C13 > ETH (Federal Inst. Technology) 8092 Zurich SWITZERLAND > phone: x-41-44-632-4673 fax: 632-1228 > http://stat.ethz.ch/~buser/ > -------------------------------------------------------------- > > ________________________________________________________________________ > > From: Prof Brian Ripley <[EMAIL PROTECTED]> > To: Christoph Buser <[EMAIL PROTECTED]> > cc: "Liaw, Andy" <[EMAIL PROTECTED]> > Subject: Re: [R] Alternatives to t-tests (was Code Verification) > Date: Thu, 21 Jul 2005 10:33:28 +0100 (BST) > > I believe there is a rather more to this than Christoph's account. The > Wilcoxon test is not testing the same null hypothesis as the t-test, and > that may very well matter in practice and it does in the example given. > > The (default in R) Welch t-test tests a difference in means between two > samples, not necessarily of the same variance or shape. A difference in > means is simple to understand, and is unambiguously defined at least if > the distributions have means, even for real-life long-tailed > distributions. Inference from the t-test is quite accurate even a long > way from normality and from equality of the shapes of the two > distributions, except in very small sample sizes. (I point my beginning > students at the simulation study in `The Statistical Sleuth' by Ramsey and > Schafer, stressing that the unequal-variance t-test ought to be the > default choice as it is in R. So I get them to redo the simulations.) > > The Wilcoxon test tests a shift in location between two samples from > distributions of the same shape differing only by location. Having the > same shape is part of the null hypothesis, and so is an assumption that > needs to be verified if you want to conclude there is a difference in > location (e.g. in means). Even if you assume symmetric distributions (so > the location is unambiguously defined) the level of the test depends on > the shapes, tending to reject equality of location in the presence of > difference of shape. So you really are testing equality of distribution, > both location and shape, with power concentrated on location-shift > alternatives. > > Given samples from a gamma(shape=2) and gamma(shape=20) distributions, we > know what the t-test is testing (equality of means). What is the Wilcoxon > test testing? Something hard to describe and less interesting, I believe. > > BTW, I don't see the value of the gamma simulation as this > simultaneously changes mean and shape between the samples. How about > checking holding the mean the same: > > n <- 1000 > z1 <- z2 <- numeric(n) > for (i in 1:n) { > x <- rgamma(40, 2.5, 0.1) > y <- rgamma(40, 10, 0.1*10/2.5) > z1[i] <- t.test(x, y)$p.value > z2[i] <- wilcox.test(x, y)$p.value > } > ## Level > 1 - sum(z1>0.05)/1000 ## 0.049 > 1 - sum(z2>0.05)/1000 ## 0.15 > > ? -- the Wilcoxon test is shown to be a poor test of equality of means. > Christoph's simulation shows that it is able to use difference in shape as > well as location in the test of these two distributions, whereas the > t-test is designed only to use the difference in means. Why compare the > power of two tests testing different null hypotheses? > > I would say a very good reason to use a t-test is if you are actually > interested in the hypothesis it tests .... > > > > > > [EMAIL PROTECTED] writes: > > thanks for your response. btw i am calculating the power of the wilcoxon > test. i > > divide the total no. of rejections by the no. of simulations. so for 1000 > > simulations, at 0.05 level of significance if the no. of rejections are 50 > then > > the power will be 50/1000 = 0.05. thats y im importing in excel the p > values. > > > > is my approach correct?? > > > > thanks n regards > > -dev > > > > > ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html