My short answer is that for controlled blocked factorial experiments where =
interactions are important and where you have planned contrasts - since you=
designed it you should know what the important questions are - I'm not awa=
re of any tool except ANOVA that will suffice. You simply get much more ban=
g for the buck. Also, despite what might seem obvious, determining whether =
your data are ordinal or something else may not always simple once you set =
up a design and a response variable. That said, you should use the correct =
statistical tool but, where you have choices, ANOVA seems to be the most ef=
ficient.=0A=0A=0A----- Original Message ----=0AFrom: Swalker <[EMAIL PROTECTED]
COM>=0ATo: [EMAIL PROTECTED]: Monday, March 12, 2007 11:30:3=
9 AM=0ASubject: Re: [ECOLOG-L] Dealing with non-normal, ordinal data for 2-=
way ANOVA with interactions=0A=0A=0AThis is an interesting discussion.=0A=
=0AWhy do we want to put a square peg into a round hole? So despite the =
=0Afact that ANOVA is robust to all of these problems with normality and =
=0Avariance heterogeneity, why use it in this case? There are lots of =0At=
echniques for modeling ordinal or categorical data (e.g. log-linear =0Amod=
els, logistic regression etc.). These won't pretend the response =0Avaria=
ble is continuous (like ANOVA or Regression would) and, I'm =0Acertain wi=
th binomially distributed data, logistic regression is much =0Amore powerf=
ul than the arc-sine sqrt transformed ANOVA. Also, with the =0Aavailabili=
ty of generalized linear models in many different statistical =0Apackages =
(e.g. R, SAS, etc..) there's no need to try and force things =0Ato fit int=
o an ANOVA framework when the data clearly don't.=0A=0ACheers,=0A=0ASean=0A=
=0A=0A=0A=0A=0A=0AOn Mar 11, 2007, at 4:29 PM, Highland Statistics Ltd. wro=
te:=0A=0A> At 16:19 11/03/2007, John Gerlach wrote:=0A>=0A>> After lengthly=
reviews of the literature drilling down through the=0A>> numerous citation=
s that all cite secondary sources, I found that all=0A>> of the statements =
that ANOVA is robust to normality or homogeneity=0A>> were based on a coupl=
e of early simulations using one-way models.=0A>> All bets are off once you=
leave the simplistic realm of one-way ANOVA.=0A>=0A> Similar statements ar=
e made within linear regression (and anova is=0A> linear regression)..... M=
ontgomery and Peck (2002?).=0A>=0A>> In my analysis the distributions of no=
rmality or homogeneity=0A>> patterns across the data structure were critica=
lly important for=0A>> interpreting effects. After a lot of pain, including=
failing to get=0A>> proc GLM to run without crashing,=0A>=0A> If a GLM fai=
ls (in whichever package) I would rather try to=0A> understand why it fails=
. To me, that is more a warning that something=0A> "funny" goes on with you=
r data. Perhaps a certain combination of=0A> factors with not enough observ=
ations?=0A>=0A> Alain=0A>=0A>> I went with a weighted ANOVA approach for Ca=
se 2 and for Case 1 I'll=0A>> probably use a detection limit approach that =
is used to analyze=0A>> water quality data - failure time approaches don't =
lend themselves=0A>> to factorial ANOVA.=0A>>=0A>> John Gerlach=0A>>=0A>>=
=0A>>=0A>> ----- Original Message ----=0A>> From: Highland Statistics Ltd. =
<[EMAIL PROTECTED]>=0A>> To: [EMAIL PROTECTED]>> Sent: Sunda=
y, March 11, 2007 4:38:10 AM=0A>> Subject: Re: [ECOLOG-L] Dealing with non-=
normal, ordinal data for=0A>> 2-way ANOVA with interactions=0A>>=0A>> On We=
d, 7 Mar 2007 16:19:31 -0500, Ryan Earley <[EMAIL PROTECTED]>=0A>> wrot=
e:=0A>>=0A>>> Help with stubbornly non-normal data....=0A>>>=0A>>> We have =
a data set with 2 independent variables and 1 dependent =0A>>> (Gosner=0A>=
>> stage for amphibian larvae).=0A>>=0A>> Hello,=0A>> Normality is less imp=
ortant. What about homogeneity?=0A>>=0A>> We have tried every creative way =
to transform=0A>>> the data=0A>>=0A>> a waste of your time I am afraid=0A>>=
=0A>>> and end up with significant deviation from normality each time.=0A>>=
=0A>> Just make a histogram or QQ plot, and judge by eye. Normality is not =
=0A>> soo=0A>> important....compared to independence and homogeneity. But =
it also =0A>> depends=0A>> on sample size, whether the data are balanced a=
nd how significant your=0A>> results are. And perhaps your non-normality is=
caused by an improper =0A>> model?=0A>> See also:=0A>> <http://www.spring=
er.com/0-387-45967-7>www.springer.com/0-387-45967-7>=0A>> for possible solu=
tions.=0A>>=0A>>> What we'd like to ultimately do is test both main effects=
and their=0A>>=0A>> testing the main efffects while the interaction is sig=
nificant??? =0A>> There is=0A>> a whole discussion on this topic. See Unde=
rwood (200-something).=0A>>=0A>>> interaction (which effectively eliminates=
the use of two =0A>>> Kruskal-Wallis=0A>>> tests or Friedman's two-way AN=
OVA). We would be indebted to anyone =0A>>> who=0A>> might=0A>>=0A>> Is yo=
ur response (dependent) ordinal??? Then I guess it has only a few=0A>> unqi=
ue values....? No wonder it is not normal. In thas case, have a =0A>> look=
=0A>> at multinomial logistic regression (MLR). There is also an =0A>> "ex=
tension" of=0A>> MLR that takes into account the fact that the data are ord=
inal. See:=0A>>=0A>> Kleinbaum DG Klein M (2002) Logistic Regression A Self=
-Learning Text. =0A>> New=0A>> York: Springer-Verlag=0A>>=0A>>=0A>> Alain=
=0A>>=0A>> Dr. Alain F. Zuur=0A>> First author of:=0A>>=0A>> Analysing Ecol=
ogical Data (2007). Zuur, AF, Ieno, EN and Smith, GM.=0A>> Springer. 680 p=
.=0A>> URL: =0A>> <http://www.springer.com/0-387-45967-7>www.springer.com/=
0-387-45967-7>=0A>>=0A>> Analysing Ecological data using GLMM and GAMM in R=
. (2008). Zuur, AF,=0A>> Ieno, EN, Walker, N and Smith, GM=0A>> Springer.=
=0A>>=0A>> Other books:=0A>> <http://www.brodgar.com/books.htm>http://www.b=
rodgar.com/books.htm=0A>>=0A>> Statistical consultancy, courses, data analy=
sis and software=0A>> Highland Statistics Ltd.=0A>> 6 Laverock road=0A>> UK=
- AB41 6FN Newburgh=0A>> Tel: 0044 1358 788177=0A>> Email: [EMAIL PROTECTED]
at.com=0A>> URL: <http://www.highstat.com>www.highstat.com>=0A>> URL: <http=
://www.brodgar.com>www.brodgar.com>=0A>>=0A>>=0A>>=0A>>=0A>>=0A>>=0A>>=0A>>=
=0A>>> have a suggestion on how to proceed statistically. Thanks for your =
=0A>>> help=0A>> in=0A>>> advance.=0A>>=0A>>=0A>>=0A>>=0A>>>=0A>>> Best,=
=0A>>> Ryan L. Earley & Foung Vang=0A>>> Cal State Fresno=0A>>> =3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D =0A>>> =3D=3D=3D=3D=0A>>=
=0A>> No virus found in this incoming message.=0A>> Checked by AVG Free Edi=
tion.=0A>> Version: 7.5.446 / Virus Database: 268.18.8/718 - Release Date:=
=0A>> 11/03/2007 09:27=0A>=0A> Dr. Alain F. Zuur=0A> First author of:=0A>=
=0A> Analysing Ecological Data (2007). Zuur, AF, Ieno, EN and Smith, GM.=
=0A> Springer. 680 p.=0A> URL: www.springer.com/0-387-45967-7=0A>=0A> Analy=
sing Ecological data using GLMM and GAMM in R. (2008). Zuur, AF,=0A> Ieno, =
EN, Walker, N and Smith, GM=0A> Springer.=0A>=0A> Other books: http://www.b=
rodgar.com/books.htm=0A>=0A> Statistical consultancy, courses, data analysi=
s and software=0A> Highland Statistics Ltd.=0A> 6 Laverock road=0A> UK - AB=
41 6FN Newburgh=0A> Tel: 0044 1358 788177=0A> Email: [EMAIL PROTECTED]
=0A> URL: www.highstat.com=0A> URL: www.brodgar.com
