Bootstrap or Wilcoxons' test?
Hi Charlotta, to be more constructive toward your goal. If you bootstrap the regression when the regression is ill-specified, the bootstrap may not help you. Further, a test as "difficult" as a regression does not seem to be necessary in your case. A t-test if your dependent variable is (approxiamately) normal for both groups and if variances are equal or a Wilcoxon test if your dependent variable is not normal should do. The bootstrap should be very powerful if you do NOT perform it on the regression (again, bootstrapping the regression may just mean to do the wrong thing over and over again, which is no improvement). Just bootstrap sample means for the two groups and compare them appropriately (see: http://www.stat.berkeley.edu/users/rodwong/Stat131a/boot_diff_twomeans.pdf ). Otherwise, rely on the result of the Wilcoxon test as it is likely more appropriate if your dependent variable is not normal in the two groups. Daniel ------------------------- cuncta stricte discussurus ------------------------- -----Urspr?ngliche Nachricht----- Von: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] Im Auftrag von David Winsemius Gesendet: Friday, February 13, 2009 9:19 PM An: Murray Cooper Cc: r-help at r-project.org Betreff: Re: [R] Bootstrap or Wilcoxons' test? I must disagree with both this general characterization of the Wilcoxon test and with the specific example offered. First, we ought to spell the author's correctly and then clarify that it is the Wilcoxon rank-sum test that is being considered. Next, the WRS test is a test for differences in the location parameter of independent samples conditional on the samples having been drawn from the same distribution. The WRS test would have no discriminatory power for samples drawn from the same distribution having equal location parameters but only different with respect to unequal dispersion. Look at the formula, for Pete's sake. It summarizes differences in ranking, so it is in fact designed NOT to be sensitive to the spread of the values in the sample. It would have no power, for instance, to test the variances of two samples, both with a mean of 0, and one having a variance of 1 with the other having a variance of 3. One can think of the WRS as a test for unequal medians. -- David Winsemius, MD. MPH Heritage Laboratories
On Feb 13, 2009, at 7:48 PM, Murray Cooper wrote:
Charlotta, I'm not sure what you mean when you say simple linear regression. From your description you have two groups of people, for which you recorded contaminant concentration. Thus, I would think you would do something like a t-test to compare the mean concentration level. Where does the regression part come in? What are you regressing? As for the Wilcoxnin test, it is often thought of as a nonparametric t-test equivalent. This is only true if the observations were drawn, from a population with the same probability distribution. The null hypothesis of the Wilcoxin test is actually "the observations were drawn, from the same probability distribution". Thus if your two samples had say different variances, there means could be the same, but since the variances are different, the Wilcoxin could give you a significant result. Don't know if this all makes sense, but if you have more questions, please e-mail your data and a more detailed description of what analysis you used and I'd be happy to try and help out. Murray M Cooper, Ph.D. Richland Statistics 9800 N 24th St Richland, MI, USA 49083 Mail: richstat at earthlink.net ----- Original Message ----- From: "Charlotta Rylander" <zcr at nilu.no> To: <r-help at r-project.org> Sent: Friday, February 13, 2009 3:24 AM Subject: [R] Bootstrap or Wilcoxons' test?
Hi! I'm comparing the differences in contaminant concentration between 2 different groups of people ( N=36, N=37). When using a simple linear regression model I found no differences between groups, but when evaluating the diagnostic plots of the residuals I found my independent variable to have deviations from normality (even after log transformation). Therefore I have used bootstrap on the regression parameters ( R= 1000 & R=10000) and this confirms my results , i.e., no differences between groups ( and the distribution is log-normal). However, when using wilcoxons' rank sum test on the same data set I find differences between groups. Should I trust the results from bootstrapping or from wilcoxons' test? Thanks! Regards Lotta Rylander [[alternative HTML version deleted]]
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______________________________________________ R-help at 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.