This is an interesting discussion. Why do we want to put a square peg into a round hole? So despite the fact that ANOVA is robust to all of these problems with normality and variance heterogeneity, why use it in this case? There are lots of techniques for modeling ordinal or categorical data (e.g. log-linear models, logistic regression etc.). These won't pretend the response variable is continuous (like ANOVA or Regression would) and, I'm certain with binomially distributed data, logistic regression is much more powerful than the arc-sine sqrt transformed ANOVA. Also, with the availability of generalized linear models in many different statistical packages (e.g. R, SAS, etc..) there's no need to try and force things to fit into an ANOVA framework when the data clearly don't.
Cheers, Sean On Mar 11, 2007, at 4:29 PM, Highland Statistics Ltd. wrote: > At 16:19 11/03/2007, John Gerlach wrote: > >> After lengthly reviews of the literature drilling down through the >> numerous citations that all cite secondary sources, I found that all >> of the statements that ANOVA is robust to normality or homogeneity >> were based on a couple of early simulations using one-way models. >> All bets are off once you leave the simplistic realm of one-way ANOVA. > > Similar statements are made within linear regression (and anova is > linear regression)..... Montgomery and Peck (2002?). > >> In my analysis the distributions of normality or homogeneity >> patterns across the data structure were critically important for >> interpreting effects. After a lot of pain, including failing to get >> proc GLM to run without crashing, > > If a GLM fails (in whichever package) I would rather try to > understand why it fails. To me, that is more a warning that something > "funny" goes on with your data. Perhaps a certain combination of > factors with not enough observations? > > Alain > >> I went with a weighted ANOVA approach for Case 2 and for Case 1 I'll >> probably use a detection limit approach that is used to analyze >> water quality data - failure time approaches don't lend themselves >> to factorial ANOVA. >> >> John Gerlach >> >> >> >> ----- Original Message ---- >> From: Highland Statistics Ltd. <[EMAIL PROTECTED]> >> To: ECOLOG-L@LISTSERV.UMD.EDU >> Sent: Sunday, March 11, 2007 4:38:10 AM >> Subject: Re: [ECOLOG-L] Dealing with non-normal, ordinal data for >> 2-way ANOVA with interactions >> >> On Wed, 7 Mar 2007 16:19:31 -0500, Ryan Earley <[EMAIL PROTECTED]> >> wrote: >> >>> Help with stubbornly non-normal data.... >>> >>> We have a data set with 2 independent variables and 1 dependent >>> (Gosner >>> stage for amphibian larvae). >> >> Hello, >> Normality is less important. What about homogeneity? >> >> We have tried every creative way to transform >>> the data >> >> a waste of your time I am afraid >> >>> and end up with significant deviation from normality each time. >> >> Just make a histogram or QQ plot, and judge by eye. Normality is not >> soo >> important....compared to independence and homogeneity. But it also >> depends >> on sample size, whether the data are balanced and how significant your >> results are. And perhaps your non-normality is caused by an improper >> model? >> See also: >> <http://www.springer.com/0-387-45967-7>www.springer.com/0-387-45967-7 >> for possible solutions. >> >>> What we'd like to ultimately do is test both main effects and their >> >> testing the main efffects while the interaction is significant??? >> There is >> a whole discussion on this topic. See Underwood (200-something). >> >>> interaction (which effectively eliminates the use of two >>> Kruskal-Wallis >>> tests or Friedman's two-way ANOVA). We would be indebted to anyone >>> who >> might >> >> Is your response (dependent) ordinal??? Then I guess it has only a few >> unqiue values....? No wonder it is not normal. In thas case, have a >> look >> at multinomial logistic regression (MLR). There is also an >> "extension" of >> MLR that takes into account the fact that the data are ordinal. See: >> >> Kleinbaum DG Klein M (2002) Logistic Regression A Self-Learning Text. >> New >> York: Springer-Verlag >> >> >> Alain >> >> Dr. Alain F. Zuur >> First author of: >> >> Analysing Ecological Data (2007). Zuur, AF, Ieno, EN and Smith, GM. >> Springer. 680 p. >> URL: >> <http://www.springer.com/0-387-45967-7>www.springer.com/0-387-45967-7 >> >> Analysing Ecological data using GLMM and GAMM in R. (2008). Zuur, AF, >> Ieno, EN, Walker, N and Smith, GM >> Springer. >> >> Other books: >> <http://www.brodgar.com/books.htm>http://www.brodgar.com/books.htm >> >> Statistical consultancy, courses, data analysis and software >> Highland Statistics Ltd. >> 6 Laverock road >> UK - AB41 6FN Newburgh >> Tel: 0044 1358 788177 >> Email: [EMAIL PROTECTED] >> URL: <http://www.highstat.com>www.highstat.com >> URL: <http://www.brodgar.com>www.brodgar.com >> >> >> >> >> >> >> >> >>> have a suggestion on how to proceed statistically. Thanks for your >>> help >> in >>> advance. >> >> >> >> >>> >>> Best, >>> Ryan L. Earley & Foung Vang >>> Cal State Fresno >>> ===================================================================== >>> ==== >> >> No virus found in this incoming message. >> Checked by AVG Free Edition. >> Version: 7.5.446 / Virus Database: 268.18.8/718 - Release Date: >> 11/03/2007 09:27 > > Dr. Alain F. Zuur > First author of: > > Analysing Ecological Data (2007). Zuur, AF, Ieno, EN and Smith, GM. > Springer. 680 p. > URL: www.springer.com/0-387-45967-7 > > Analysing Ecological data using GLMM and GAMM in R. (2008). Zuur, AF, > Ieno, EN, Walker, N and Smith, GM > Springer. > > Other books: http://www.brodgar.com/books.htm > > Statistical consultancy, courses, data analysis and software > Highland Statistics Ltd. > 6 Laverock road > UK - AB41 6FN Newburgh > Tel: 0044 1358 788177 > Email: [EMAIL PROTECTED] > URL: www.highstat.com > URL: www.brodgar.com
