Subject:Re: [AUDITORY] stats (mis)use in psychology and hearing scienceFrom:"Oberfeld-Twistel, Daniel" <oberfeld@xxxxxxxx>Date:Thu, 26 Sep 2013 12:13:52 +0000List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>Dear list, > From: Pierre Divenyi <pdivenyi@xxxxxxxx> > Subject: Re: stats (mis)use in psychology and hearing science >=20 > That may be correct under certain circumstances but the real problem is > ascertaining that ANOVA is, indeed, appropriate. And it is truly a "REAL" > problem! >=20 > On 9/22/13 11:15 PM, "Kyle Nakamoto" <knakamoto@xxxxxxxx> wrote: >=20 > >Nonparametrics are not automatically better. If you use a nonparametric > >statistic when an ANOVA is appropriate the chance of missing a real effe= ct > >increases (False Negative). It is of course true that we should all pay attention to the assumptions of= statistical tests. For example, one should not use tests assuming independ= ent observations when analyzing data from a repeated-measures design. Anoth= er example, as I mentioned in a previous posting, is that repeated-measures= ANOVAs are sensitive to departures from normality, and many additional pro= blems arise when the design is unbalanced (i.e., unequal group sizes, see (= Keselman, Algina, & Kowalchuk, 2001)). However, it is a sort of "magical" thinking that nonparametric methods are = *free* of assumptions - this is of course not the case. Just to give you two simple examples: 1) The nonparametric Friedman rank test that can be used for analyzing data= from a one-factorial repeated-measures design assumes equal variances and = covariances of the measures. In real data sets, this assumption is almost a= lways violated, known as a deviation from sphericity. That's why we (hopefu= lly) use for example the Huynh-Feldt correction for the degrees-of-freedom = when computing a repeated-measures ANOVA with the univariate approach. Simu= lation studies showed that when the (co-)variances are heterogeneous, Fried= man's test does *not* control the Type I error rate (i.e., probability to p= roduce a significant p-value (e.g., p < .05) when the population means are = *identical*), especially when the distribution of the response measure is s= kewed (Harwell & Serlin, 1994; St. Laurent & Turk, 2013). 2) The (nonparametric) Mann-Whitney U-test that can be used to compare the = means of two independent samples does not control the Type I error rate in = the case of variance heterogeneity (i.e., the two groups have different var= iances), especially when the distribution of the response measure is asymme= tric (skewed). In fact, the U-test was shown to be *more* sensitive to viol= ations of these assumption than the classical t-test in several conditions = (Stonehouse & Forrester, 1998). Thus, it is not a given that "nonparametric" methods are more "robust" (or = even "free of assumptions") than parametric methods like the GLM. Instead, = if you have reason to believe that the assumptions for a parametric test ar= e violated, then it will be a good idea to consult the (sometimes very exte= nsive, sometimes very sparse) literature on simulation studies concerning t= he effects of such violations - sometimes it might turn out that using the = "bad" good old t-test or another parametric method is in fact superior to a= pplying a nonparametric procedure. But sometimes the answer will likely nei= ther be "parametric better" or "nonparametric better", but "it's complicate= d" (or: "we don't know yet")... I would be interested to learn which data analysis problems you are facing = in your research -- maybe we could use this list to identify the best solut= ions to these problems? Best, Daniel Harwell, M. R., & Serlin, R. C. (1994). A Monte-Carlo study of the Friedman= test and some competitors in the single factor, repeated-measures design w= ith unequal covariances. Computational Statistics & Data Analysis, 17(1), 3= 5-49. Keselman, H. J., Algina, J., & Kowalchuk, R. K. (2001). The analysis of rep= eated measures designs: A review. British Journal of Mathematical and Stati= stical Psychology, 54, 1-20. St. Laurent, R., & Turk, P. (2013). The effects of misconceptions on the pr= operties of Friedman's test. Communications in Statistics-Simulation and Co= mputation, 42(7), 1596-1615. Stonehouse, J. M., & Forrester, G. J. (1998). Robustness of the t and U tes= ts under combined assumption violations. Journal of Applied Statistics, 25(= 1), 63-74. PD Dr. Daniel Oberfeld-Twistel Johannes Gutenberg - Universitaet Mainz Department of Psychology Experimental Psychology Wallstrasse 3 55122 Mainz Germany Phone ++49 (0) 6131 39 39274=20 Fax ++49 (0) 6131 39 39268 http://www.staff.uni-mainz.de/oberfeld/ http://www.facebook.com/daniel.oberfeldtwistel

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