<- file stat 97normal.html -> Tests for different purposes: 4 Notes Shapiro-Wilks' for ANOVA warning, Ward K-S tests mid-distribution Dallal X^2 REF, number of categories Lim A "multi-modal" formula Mangeshkar

Testing for normality.

=======================William B Ware, 30 Apr 1997==========spss Message-ID: <Pine.A41.3.95.970430063931.51866A-100000@login1.isis.unc.edu> From: "William B. Ware" <wbware@EMAIL.UNC.EDU> Subject: Re: what kind of testing for normal distribution? On Tue, 22 Apr 1997, Rwziegler wrote: > I'm not sure, which kind of test I have to use to check > for normal distribution (gauss-distribution) in samples > with 50 cases or even less. > In SPSS/PC+ Vs. 5.0 (DOS) there was a examine-procedure > (examine/variables XYZ /plot npplot) presenting a Shapiro- > Wilks-Test (< 50 cases) and Lilifors-Test (> 50 cases). > In SPSS Win Vs. 6.1.2 there's only Kolmogorov-Smirnov-Testing > (K-S-Test) recommended for any kind of sample-size. > In a sample of 39 cases I get different significances in these > testings. K-S tells me a normal distribution (p > 0,05), but > Shapiro-Wilks (p < 0,01) does not. What kind of test is now save? There are many different tests to assess the assumption of normality, and as far as I know, there is no "gold standard." SPSS uses several different ones as you have already noted. SAS is similar in that respect. STATA uses an additional test, K^2. The different tests are designed for different situations and have differential power for detecting different types of departures from normality. The K-S test and the Lillefors modification are sensitive to "deviations" in the midrange, which are not usually the kinds of departures that lead to problems in inference. Given the situation that you describe, I would recommend that you seriously consider the results from the Shapiro-Wilks test. However, I would also recommend that you "look" at your data with a stem-and-leaf plot, histogram, etc. to see if you can tell what type of departure you have. The result might also be the result of an outlier... *--------

Testing normality for t-test

=======================Jerry Dallal, 14 Mar 1997==========ssc From: jerry@mint.hnrc.tufts.edu (Jerry Dallal) Subject: Re: T-tests Message-ID: <1997Mar14.224657@mint.hnrc.tufts.edu> In article <3329C796.45FB@wave.ca>, GaryD <garyd@wave.ca> writes: > this is not normal enough to make a t-test viable? For instance, one > can use the K-S test, but with a large sample this seems to always tell > me that there is not normality. Forget the K-S (actually, Lilliefors; a K-S test is wrong for testing normality when the parameters are unspecified). If you're worried about the t test, you care about the activity in the tails. The Lilliefors test, which looks at the maximum difference between the sample and theoretical df is sensitive to departures in the center of the distribution, which have little effect on the t test. I'm tempted to add that, with only slight exaggeration, if you've got enough data for a viable test for normality, you've probably got enough data to claim that the Central Limit Theorem makes the t test viable. But I'm afraid some might take this too literally, so I decided not to post it. *--------

X^2 test of normality

=======================TS Lim, 23 Feb 1997==========ssm From: tlim@ix.netcom.com (T.S. Lim) Subject: Re: Need help in finding a paper for a research!!! Message-ID: <5eq4sb$2ho@dfw-ixnews10.ix.netcom.com> %AUTHOR = Dahiya, Ram C. %AUTHOR = Gurland, John %TITLE = How many classes in the Pearson chi-square test? %JOURNAL = Journal of the American Statistical Association %VOLUME = 68 %PAGES = 707-712 %YEAR = 1973 %KEYWORDS = Goodness-of-fit In article <33108b9f.858645@news>, dwang@garnet.fsu.edu says... > >Does anyone know where I can find the paper by Dahiya or Gurland which >discusses how many intervals should be used when performing a modified >chi-square test of normality. The paper should be on a journal between >1972-1980. Thank you very much. > >Dagang Wang *--------

Multimodal formula

=======================Milan Mangeshkar, 05 Feb 1997==========ssc From: Milan Mangeshkar <Milan.Mangeshkar@add.ssw.abbott.com> Subject: Re: Multimodal distributions Message-ID: <32F8CECB.458C@add.ssw.abbott.com> mamenzie@aol.com wrote: > > Are we talking discrete or continuous here? If discrete, the problem is > almost trivial. > > I don't know, but there must be a method of moments formula that would > shed some light on the question... > > Mark Menzie We are talking discrete over here. Ya there is a formula based on skewness and kurotosis b=(m3**2+1)/(m4+3*((n-1)**2/((n-1)(n-2)))). If b>.5 then it indicates a multimodal distribution. But it does not seem to work for the data, the reason possibly could be because of low values in the tail. Thanks for your response though. milan * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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