[RsR] minimum sample size for the robust counterpart of the t-test #2
Dear Richard, Since we did not quite cover your specific case, I ran another small simulation. See the attached file. It is basically the simulation study of our paper, but for models having only an intercept. I hope I did not overlook anything when I did this. There was a lot going on today... I apologize for the overloaded plots. I guess Figures 4, 7 and 8 are the most interesting figures. As Rand already stated, the asymmetric error distributions are a problem: all the methods perform quite badly. Otherwise, the levels of the tests are pretty much ok (even for OLS, i.e., t-test). But of course, the power will be pretty bad. In numbers, for n = 5 you will have approximately the correct level (+/- 2%), but a power of about 40% only for an effect size of 1 (10% for an effect size of 0.4). And this does not really depend on which method you are using. To conclude, I would recommend to use lmrob from robustbase with the argument setting="KS2011". I hope this helps, Manuel On Thu, Jun 16, 2011 at 8:19 PM, Richard Friedman
<friedman at cancercenter.columbia.edu> wrote:
Rand, ? ? ? ?Thanks, I know very little about robust methods. I am interested in whether rlm can be used in its default state or if I have to tearn much more to do use the methods correctly. Best wishes, Rich On Jun 16, 2011, at 2:14 PM, Rand Wilcox wrote:
When dealing with M-estimators and the goal is to compute confidence intervals, one thing you have to be careful about is skewed distributions. Have not encountered any non-bootstrap method that performs well in simulations where the confidence interval is based on an estimate of the standard error. Just how symmetric the distribution must be seems unclear. What works better is a percentile bootstrap method, even with fairly small sample sizes. This is why the methods in my book focus on bootstrap techniques when dealing with M-estimators. However, have not yet seen the Koller and Stahel paper. Maybe this problem has been addressed. Rand Rand Wilcox Professor Dept of Psychology USC Los Angeles, CA 90089-1061 FAX: 213-746-9082 For information about statistics books and software, see http://www-rcf.usc.edu/~rwilcox/ as well as http://college.usc.edu/labs/rwilcox/home ----- Original Message ----- From: Richard Friedman <friedman at cancercenter.columbia.edu> Date: Thursday, June 16, 2011 9:02 am Subject: Re: [RsR] minimum sample size for the robust counterpart of the t-test #2 To: Rand Wilcox <rwilcox at usc.edu>, r-sig-robust at r-project.org
Dear Rand (and List), ? ? ? ?I read the relevant sections of your book and while informative it did not answer my question directly as best I can see. I will restate the question more explicitly: A robust analog of the two sample ?t-test is performed with the rlm function with the default parameters of the Huber method with K=1.345. Is there a minimum sample size for which it should be trusted? are 5 samples enough? 10 samples? If this question does not have a simple answer please let me know. Thanks and best wishes, Rich On Jun 15, 2011, at 3:19 PM, Rand Wilcox wrote:
There is general information about sample sizes and p-values, when
using robust analogs of t, in my 2005 book (Introduction to Robust Estimation and Hypothesis Testing, Academic Press) .
(A third edition will be out early in 2012. ) Hope this helps. Rand Rand Wilcox Professor Dept of Psychology USC Los Angeles, CA 90089-1061 FAX: 213-746-9082 For information about statistics books and software, see
as well as http://college.usc.edu/labs/rwilcox/home ----- Original Message ----- From: Richard Friedman <friedman at cancercenter.columbia.edu> Date: Wednesday, June 15, 2011 12:11 pm Subject: [RsR] minimum sample size for the robust counterpart of
the t-test
To: r-sig-robust at r-project.org
Dear List, ? ? ? ?I am a beginner in the use of robust methods. Is there a minimum sample size for which the robust analog of a two sample t-test using rlm with default parameters and categorical explanatory variables may be trusted to yield reliable p-values? Is so, can you please point me at a reference which treats this problem. Thanks and best wishes, Rich ------------------------------------------------------------ Richard A. Friedman, PhD Associate Research Scientist, Biomedical Informatics Shared Resource Herbert Irving Comprehensive Cancer Center (HICCC) Lecturer, Department of Biomedical Informatics (DBMI) Educational Coordinator, Center for Computational Biology and Bioinformatics (C2B2)/ National Center for Multiscale Analysis of Genomic Networks (MAGNet) Room 824 Irving Cancer Research Center Columbia University 1130 St. Nicholas Ave New York, NY 10032 (212)851-4765?(voice) friedman at cancercenter.columbia.edu http://cancercenter.columbia.edu/~friedman/ I am a Bayesian. When I see a multiple-choice question on a test and I don't know the answer I say "eeney-meaney-miney-moe". Rose Friedman, Age 14
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Manuel Koller <koller at stat.math.ethz.ch> Seminar f?r Statistik, HG G 18, R?mistrasse 101 ETH Z?rich ?8092 Z?rich ?SWITZERLAND phone: +41 44 632-4673 fax: ...-1228 http://stat.ethz.ch/people/kollerma/ -------------- next part -------------- A non-text attachment was scrubbed... Name: intercept_only.pdf Type: application/pdf Size: 921710 bytes Desc: not available URL: <https://stat.ethz.ch/pipermail/r-sig-robust/attachments/20110617/8df4fdd9/attachment.pdf>