Statistics are just tools. Using the best tool for the job is what's being discussed here.
If a statistical technique is more powerful than another, models the data on it's natural scale, and can do all of the things ANOVA can do why not use it. That would, at least to me, seem a much more efficient approach since with greater power you'll increase the amount of bang you get per replicate. Since you can use the same principles in design of the experiment, just a different analysis (that essentially works the same way) I think that it isn't a great idea to try and 'make' data fit ANOVA. As Alain has pointed out, anything you can do with ANOVA you can do with generalized linear models. There are ways to deal with random effects, mixed models, and repeated measures using these models. You can also easily do contrasts in these models since contrasts are just comparisons of parameters of the model. In short, why do you want to use a hammer to build a house when a nail gun is available? On Mar 14, 2007, at 6:10 AM, John Gerlach wrote: > You seem a trifle sensitive about models and modeling - statistics are > just= > tools. Nearly every modern text book clearly points out that ANOVA, > regres= > sion, etc are specific applications of a general mathematical approach > but = > that each is a tool designed for a particular purpose. So, yes they > are dif= > ferent in practice.=0A =0AIt makes no sense to say that something is > wrong = > with the data. Either the program works for its intened purpose or it > doesn= > 't. If one of the statisticians who helped debug the program for SAS > and an= > other professional statistician/programmer cannot get the program to > work w= > ith a data set I'd say that the functionality of of the algorithm > depends o= > n the data set - it is a tool that sometimes can't handle the data.=0A > =0A = > I agree with you completely about the importance of real world > variation. I= > think that too often the review process cleans up really messy data > sets f= > or publication and we as scientists lose out on seeing good approaches > to a= > range of difficult statistical issues as well as catching a glimpse > of jus= > t darn good data. I did have one good experience in this area where I > was a= > llowed to publish a figure that just included means and ranges of the > data = > - sort of a retro analysis.=0A=0ABy efficient I mean the totality of > the ex= > permient from using space at a field site or on a lab bench > efficiently, th= > e cost in time and money of putting the experiment in the ground, the > amoun= > t of useful data that the experiment produces, your ability to say > somethin= > g interesting about the data. the time involved in analyzing the data, > the = > time involved in writing it up, etc.=0A=0AWith regard to planned > contrasts.= > If you designed the experiment right and you have some experience > with the= > study system significant main effects and interactions are a given. > What y= > ou really want to know is are your specific hypotheses correct. Things > such= > as in environment 1 A>B>C and in environment 2 C>B>A are the critical > thin= > gs that you want to know. Perhaps I have not been schooled properly > but the= > se sorts of questions seem easier to answer using the ANOVA tool > followed b= > y planned contrasts.=0A =0A=0A =0A----- Original Message ----=0AFrom: > Highl= > and Statistics Ltd. <[EMAIL PROTECTED]>=0ATo: > [EMAIL PROTECTED] > =0ASent: Tuesday, March 13, 2007 4:39:29 PM=0ASubject: Re: [ECOLOG-L] > Deali= > ng with non-normal, ordinal data for 2-way ANOVA with > interactions=0A=0A=0A= >> Date: Mon, 12 Mar 2007 15:35:18 -0700=0A>From: John Gerlach >> <gerlach= > [EMAIL PROTECTED]>=0A>Subject: Re: Dealing with non-normal, ordinal data > for 2-= > way ANOVA =0Awith interactions=0A=0A>My short answer is that for > controlled= > blocked factorial experiments where =3D=0A>interactions are important > and = > where you have planned contrasts - since you=3D=0A>designed it you > should k= > now what the important questions are - I'm not awa=3D=0A>re of any > tool exc= > ept ANOVA that will suffice.=0A=0A=0AAm I missing something here?? > ANOVA is= > linear regression...linear =0Aregression is GLM (generalised linear > modell= > ing)....if you can set up =0Ayour explanatory variables in an ANOVA > context= > (for interactions with =0Aplanned contrasts), you can do the same in > a log= > istic regression =0Acontext, and for ordinal data. The only thing that > is c= > hanging is the =0Aexact interpretation of the parameters if you swap > famili= > es, but that =0Ashouldn't be a problem? We all seem to agree that the > logis= > tic =0Aregression (or better: its extension to ordinal data) is a > better = > =0Aapproach for your ordinal data. If your GLM software crashed for > your = > =0Adata, then there is something wrong with your data or model, not > with = > =0Athe software (provided it is decent software like SAS or > R).=0A=0A=0A>up= > a design and a response variable. That said, you should use the > correct = > =3D=0A>statistical tool but, where you have choices, ANOVA seems to be > the = > most ef=3D=0A>ficient.=0A=0AWhat is your definition of "efficient"? I > have= > n't seen many examples =0Afor which all the assumptions of linear > regressio= > n/ANOVA were met. My =0Abelief is that everything in ecology is > heterogeneo= > us....hence the =0Aonly thing I do is mixed modelling (or GLS). > Heterogenei= > ty is part of =0Athe nature of the data, and should be taken into > account..= > ..not =0Ahidden behind a transformation. Chapter 5 in Pinheiro and > Bates gi= > ves =0Aa good intro.=0A=0AAs to one of the other respondents to this > postin= > g.....6-8 weeks ago =0Athere was a posting on the statistical > newsgroup all= > stat that =0Asummarised 10-20 replies on the significance of main > terms if = > the =0Ainteraction is also significant. It is not that trivial. I > don't hav= > e =0Agood email access this week, hence can't provide the URL for the > =0Asu= > mmary posting on allstat ; just google on "allstat significance main > terms"= > =0A=0AAlain=0A=0A=0A=0ADr. Alain F. Zuur=0AFirst author > of:=0A=0AAnalysing = > Ecological Data (2007). Zuur, AF, Ieno, EN and Smith, GM. > =0ASpringer. 680= > p.=0AURL: www.springer.com/0-387-45967-7=0A=0AAnalysing Ecological > data us= > ing GLMM and GAMM in R. (2008). Zuur, AF, =0AIeno, EN, Walker, N and > Smith,= > GM=0ASpringer.=0A=0AOther books: > http://www.brodgar.com/books.htm=0A=0ASta= > tistical consultancy, courses, data analysis and software=0AHighland > Statis= > tics Ltd.=0A6 Laverock road=0AUK - AB41 6FN Newburgh=0ATel: 0044 1358 > 78817= > 7=0AEmail: [EMAIL PROTECTED]: www.highstat.com=0AURL: > www.brodgar= > .com
