Thanks for your response. The background is that I am trying to test whether a small sample and a much larger sample actually came from the same distribution. I could just perform a KS test on the 2 samples, but as I said, ideally I'd like a test that is more powerful than that. So I look at the percentile ranks of the small sample within the large sample, which should be uniformly distributed if the 2 samples are from the same population, and then transform using "qnorm". The result should be standard normal. Perhaps the next best alternative is to do chi-square test on the percentiles, checking for equal numbers in each decile bin. This would certainly work, and the only disadvantage that I can see is that the selection of the bin boundaries is somewhat arbitrary.
Alan Herschtal Senior Biostatistician Peter MacCallum Cancer Centre Phone +61 3 9656 3639 Fax +61 3 9656 1420 Email alan.hersch...@petermac.org -----Original Message----- From: Rolf Turner [mailto:rolf.tur...@xtra.co.nz] Sent: Friday, 9 November 2012 2:17 PM To: Herschtal Alan Cc: r-help@r-project.org Subject: Re: [R] Looking for a test of standard normality Others may correct me, but I cannot imagine any test of standard normality giving appreciably more power than is given by the Kolmogorov-Smirnov test. I also wonder about the point of testing for (standard) normality in the first place. There is a quote --- I think it refers to testing for heteroscedasticity, but I believe it applies equally to testing for normality --- about such testing being analogous to going out of the harbour in a rowing dinghy to see if it's safe for an ocean liner to put to sea. cheers, Rolf Turner On 09/11/12 13:23, Herschtal Alan wrote: > Dear list members, > > I am looking for a goodness of test that will tell me if a sample is > likely to have come from a standard normal distribution. I can find > plenty of omnibus tests for normality in the nor.test package, but none > of them appear to allow me to test against the specific alternative that > the data are not standard normal. My back up option is to use a > Kolmogorov-Smirnov test, but my impression is that that is not a very > powerful test. Any suggestions? This email (including any attachments or links) may contain confidential and/or legally privileged information and is intended only to be read or used by the addressee. If you are not the intended addressee, any use, distribution, disclosure or copying of this email is strictly prohibited. Confidentiality and legal privilege attached to this email (including any attachments) are not waived or lost by reason of its mistaken delivery to you. If you have received this email in error, please delete it and notify us immediately by telephone or email. Peter MacCallum Cancer Centre provides no guarantee that this transmission is free of virus or that it has not been intercepted or altered and will not be liable for any delay in its receipt. ______________________________________________ R-help@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.
