I agree completely with the tool analogy and with using the correct tool fo=
r the data. As I mentioned before, the scale of the data is not always obvi=
ous after you have run the experiment. Do you analyze population size data =
inflated with zeros as a continuous or a bivariate response data?=0A =0AI'l=
l also point out the obvious about other tools having problems. I use ANOVA=
primarily to compare mean responses of treatments that I've more or less a=
rbitrarily set at fixed levels that my educated guess suggests are near the=
mean, min, and max of what I would expect in the "real" world - sure I inc=
lude random blocking effects where needed but since I'm not doing quantitat=
ive genetics I'm mostly doing fixed effects analyses. I'm not so concerned =
about what happens throughout the whole range of possible values for the ef=
fect - I'd use a regression approach if that were the case or when I'd like=
to predict the value of one variable from another. One application of the =
latter might be using aerial photos with ground truthing to predict the den=
sity of oak tress present in similar areas at other sites. Now despite the =
fact that everyone does this sort of thing, just look at the vast remote se=
nsing industry, unless I set the levels of the area analyzed in the aerial =
view in
some way to qualify my data set for the Berkson exception, which I can't w=
ith oaks growing on canyon sides because of distortion and the inability to=
establishing large qudrats accurately in the canyons, I cannot legitimatel=
y use regression as a tool. There are a number of work-arounds such as majo=
r or minor axis regression techniques but nothing that does not have an inh=
erent bias due to the asymmetrical way regression minimizes the variances f=
or only one or the other of the variables. Sometimes I wonder if this bias =
creeps into analyses that use regression approaches in lieu of ANOVA - I sl=
eep better knowing that I at least set the levels of one variable so I can =
always rely on Dr. Berkson's exception if the subject was ever broached by =
a reviewer. I'd appreciate any clarification of these issues.=0A=0A=0A-----=
Original Message ----=0AFrom: Swalker <[EMAIL PROTECTED]>=0ATo: [EMAIL
PROTECTED]
STSERV.UMD.EDU=0ASent: Wednesday, March 14, 2007 8:33:55 AM=0ASubject: Re: =
[ECOLOG-L] Dealing with non-normal, ordinal data for 2-way ANOVA with inter=
actions=0A=0A=0AStatistics are just tools. Using the best tool for the job=
is what's =0Abeing discussed here.=0A=0AIf a statistical technique is more=
powerful than another, models the =0Adata on it's natural scale, and can d=
o all of the things ANOVA can do =0Awhy not use it. That would, at least t=
o me, seem a much more efficient =0Aapproach since with greater power you'l=
l increase the amount of bang =0Ayou get per replicate. Since you can use =
the same principles in design =0Aof the experiment, just a different analys=
is (that essentially works =0Athe same way) I think that it isn't a great i=
dea to try and 'make' data =0Afit ANOVA. As Alain has pointed out, anythin=
g you can do with ANOVA =0Ayou can do with generalized linear models. Ther=
e are ways to deal with =0Arandom effects, mixed models, and repeated measu=
res using these models. =0A You can also easily do contrasts in these mod=
els since contrasts are =0Ajust comparisons of parameters of the model.=0A=
=0AIn short, why do you want to use a hammer to build a house when a nail =
=0Agun is available?=0A=0A=0AOn Mar 14, 2007, at 6:10 AM, John Gerlach wrot=
e:=0A=0A> You seem a trifle sensitive about models and modeling - statistic=
s are =0A> just=3D=0A> tools. Nearly every modern text book clearly points=
out that ANOVA, =0A> regres=3D=0A> sion, etc are specific applications of =
a general mathematical approach =0A> but =3D=0A> that each is a tool design=
ed for a particular purpose. So, yes they =0A> are dif=3D=0A> ferent in pra=
ctice.=3D0A =3D0AIt makes no sense to say that something is =0A> wrong =3D=
=0A> with the data. Either the program works for its intened purpose or it =
=0A> doesn=3D=0A> 't. If one of the statisticians who helped debug the prog=
ram for SAS =0A> and an=3D=0A> other professional statistician/programmer c=
annot get the program to =0A> work w=3D=0A> ith a data set I'd say that the=
functionality of of the algorithm =0A> depends o=3D=0A> n the data set - i=
t is a tool that sometimes can't handle the data.=3D0A =0A> =3D0A =3D=0A> I=
agree with you completely about the importance of real world =0A> variatio=
n. I=3D=0A> think that too often the review process cleans up really messy=
data =0A> sets f=3D=0A> or publication and we as scientists lose out on se=
eing good approaches =0A> to a=3D=0A> range of difficult statistical issue=
s as well as catching a glimpse =0A> of jus=3D=0A> t darn good data. I did =
have one good experience in this area where I =0A> was a=3D=0A> llowed to p=
ublish a figure that just included means and ranges of the =0A> data =3D=0A=
> - sort of a retro analysis.=3D0A=3D0ABy efficient I mean the totality of =
=0A> the ex=3D=0A> permient from using space at a field site or on a lab be=
nch =0A> efficiently, th=3D=0A> e cost in time and money of putting the exp=
eriment in the ground, the =0A> amoun=3D=0A> t of useful data that the expe=
riment produces, your ability to say =0A> somethin=3D=0A> g interesting abo=
ut the data. the time involved in analyzing the data, =0A> the =3D=0A> time=
involved in writing it up, etc.=3D0A=3D0AWith regard to planned =0A> contr=
asts.=3D=0A> If you designed the experiment right and you have some experi=
ence =0A> with the=3D=0A> study system significant main effects and intera=
ctions are a given. =0A> What y=3D=0A> ou really want to know is are your s=
pecific hypotheses correct. Things =0A> such=3D=0A> as in environment 1 A>=
B>C and in environment 2 C>B>A are the critical =0A> thin=3D=0A> gs that yo=
u want to know. Perhaps I have not been schooled properly =0A> but the=3D=
=0A> se sorts of questions seem easier to answer using the ANOVA tool =0A> =
followed b=3D=0A> y planned contrasts.=3D0A =3D0A=3D0A =3D0A----- Original =
Message ----=3D0AFrom: =0A> Highl=3D=0A> and Statistics Ltd. <[EMAIL PROTECTED]
STAT.COM>=3D0ATo: =0A> [EMAIL PROTECTED]> =3D0ASent: Tuesday,=
March 13, 2007 4:39:29 PM=3D0ASubject: Re: [ECOLOG-L] =0A> Deali=3D=0A> ng=
with non-normal, ordinal data for 2-way ANOVA with =0A> interactions=3D0A=
=3D0A=3D0A=3D=0A>> Date: Mon, 12 Mar 2007 15:35:18 -0700=3D0A>From: J=
ohn Gerlach =0A>> <gerlach=3D=0A> [EMAIL PROTECTED]>=3D0A>Subject: Re: Dealing =
with non-normal, ordinal data =0A> for 2-=3D=0A> way ANOVA =3D0Awith intera=
ctions=3D0A=3D0A>My short answer is that for =0A> controlled=3D=0A> blocke=
d factorial experiments where =3D3D=3D0A>interactions are important =0A> an=
d =3D=0A> where you have planned contrasts - since you=3D3D=3D0A>designed i=
t you =0A> should k=3D=0A> now what the important questions are - I'm not a=
wa=3D3D=3D0A>re of any =0A> tool exc=3D=0A> ept ANOVA that will suffice.=3D=
0A=3D0A=3D0AAm I missing something here?? =0A> ANOVA is=3D=0A> linear regr=
ession...linear =3D0Aregression is GLM (generalised linear =0A> modell=3D=
=0A> ing)....if you can set up =3D0Ayour explanatory variables in an ANOVA =
=0A> context=3D=0A> (for interactions with =3D0Aplanned contrasts), you ca=
n do the same in =0A> a log=3D=0A> istic regression =3D0Acontext, and for o=
rdinal data. The only thing that =0A> is c=3D=0A> hanging is the =3D0Aexact=
interpretation of the parameters if you swap =0A> famili=3D=0A> es, but th=
at =3D0Ashouldn't be a problem? We all seem to agree that the =0A> logis=3D=
=0A> tic =3D0Aregression (or better: its extension to ordinal data) is a =
=0A> better =3D=0A> =3D0Aapproach for your ordinal data. If your GLM softwa=
re crashed for =0A> your =3D=0A> =3D0Adata, then there is something wrong w=
ith your data or model, not =0A> with =3D=0A> =3D0Athe software (provided i=
t is decent software like SAS or =0A> R).=3D0A=3D0A=3D0A>up=3D=0A> a desig=
n and a response variable. That said, you should use the =0A> correct =3D=
=0A> =3D3D=3D0A>statistical tool but, where you have choices, ANOVA seems t=
o be =0A> the =3D=0A> most ef=3D3D=3D0A>ficient.=3D0A=3D0AWhat is your defi=
nition of "efficient"? I =0A> have=3D=0A> n't seen many examples =3D0Afor =
which all the assumptions of linear =0A> regressio=3D=0A> n/ANOVA were met.=
My =3D0Abelief is that everything in ecology is =0A> heterogeneo=3D=0A> us=
....hence the =3D0Aonly thing I do is mixed modelling (or GLS). =0A> Hetero=
genei=3D=0A> ty is part of =3D0Athe nature of the data, and should be taken=
into =0A> account..=3D=0A> ..not =3D0Ahidden behind a transformation. Chap=
ter 5 in Pinheiro and =0A> Bates gi=3D=0A> ves =3D0Aa good intro.=3D0A=3D0A=
As to one of the other respondents to this =0A> postin=3D=0A> g.....6-8 wee=
ks ago =3D0Athere was a posting on the statistical =0A> newsgroup all=3D=0A=
> stat that =3D0Asummarised 10-20 replies on the significance of main =0A> =
terms if =3D=0A> the =3D0Ainteraction is also significant. It is not that t=
rivial. I =0A> don't hav=3D=0A> e =3D0Agood email access this week, hence c=
an't provide the URL for the =0A> =3D0Asu=3D=0A> mmary posting on allstat ;=
just google on "allstat significance main =0A> terms"=3D=0A> =3D0A=3D0AAla=
in=3D0A=3D0A=3D0A=3D0ADr. Alain F. Zuur=3D0AFirst author =0A> of:=3D0A=3D0A=
Analysing =3D=0A> Ecological Data (2007). Zuur, AF, Ieno, EN and Smith, GM=
. =0A> =3D0ASpringer. 680=3D=0A> p.=3D0AURL: www.springer.com/0-387-45967-=
7=3D0A=3D0AAnalysing Ecological =0A> data us=3D=0A> ing GLMM and GAMM in R.=
(2008). Zuur, AF, =3D0AIeno, EN, Walker, N and =0A> Smith,=3D=0A> GM=3D0A=
Springer.=3D0A=3D0AOther books: =0A> http://www.brodgar.com/books.htm=3D0A=
=3D0ASta=3D=0A> tistical consultancy, courses, data analysis and software=
=3D0AHighland =0A> Statis=3D=0A> tics Ltd.=3D0A6 Laverock road=3D0AUK - AB4=
1 6FN Newburgh=3D0ATel: 0044 1358 =0A> 78817=3D=0A> 7=3D0AEmail: [EMAIL
PROTECTED]
ighstat.com=3D0AURL: www.highstat.com=3D0AURL: =0A> www.brodgar=3D=0A> .com
