Dear Friends,
A few days ago I posted a question on the best way to analyse some data.
Below I summaryze the answers I received, and my original message. Thank you
for your interest!
ORIGINAL MESSAGE
Date: Sun, 26 Mar 2006 08:18:19 -0300
From: Alexandre Souza <[EMAIL PROTECTED]>
Subject: Conflicting Results of Contrasts vs. GLM: what do you think about that?
Dear Friends,
I have recently posted the messaged you can read below. Unfortunately, in
that moment I forgot to substitute the Issue field with an appropriate title,
so many of you probably did not read it. Here it goes again.
Dear Friends,
I am performing na analysis and would like to hear your opinion about
it.
The System
A subtropical riparian forest
Dependent Variable: density of trees with diameter at 1.3 m height >= 5
cm
Management: most of the forest has been continuously exposed to cattle
grazing, but a small portion has been protected by fencing for the last 35
years.
Sampling design: 5 x 5 m plots
A variable number of 5 x 5 m plots was established in 5 distinct areas
of the forest: one area in the exclosure and four areas in the grazed part of
the forest. A larger number of areas could not be sampled in the exclosure due
to its restricted size. I know that this characterize pseudoreplication of the
excluded factor, but at the moment we have no alternatives, although we are
seeking them.
Areas A, B, C, D are grazed. Area E is the exclosure.
Approaches to Analysis (using Systat)
ANOVA plus Planned Contrasts
Dep Var: RAIZNIND N: 198 Multiple R: 0.369 Squared multiple R: 0.136
Analysis of Variance
Source Sum-of-Squares df Mean-Square F-ratio P
Regression 9.177 4 2.294 7.614 0.000
Residual 58.149 193 0.301
-------------------------------------------------------------------------------
Durbin-Watson D Statistic 1.896
First Order Autocorrelation 0.041
Hypothesis Testing
Contrast between Areas A, B, C and D versus Areas E: 1 1 1 1 -4
Test for effect called: AREA$
A Matrix
1 2 3 4 5
0.000 5.000 5.000 5.000 5.000
Test of Hypothesis
Source SS df MS F P
Hypothesis 2.695 1 2.695 8.945 0.003
Error 58.149 193 0.301
According to this approach, the exclosures is different from the grazed areas
GLM with explanatory variables manajement (grazed x exclosure) and area
Categorical values encountered during processing are:
MANAGEMENT$ (2 levels)
PASTEJADA, PROTEGIDA
AREA$ (5 levels)
A, B, C, D, E
The following effects have lost degrees of freedom.
Initial Lost Final
Effect df df df
AREA$ 4 1 3
Dep Var: RAIZNIND N: 198 Multiple R: 0.369 Squared multiple R: 0.136
Analysis of Variance
Source Sum-of-Squares df Mean-Square F-ratio P
MANAGEMENT$ 0.802 1 0.802 2.663 0.104
AREA$ 6.917 3 2.306 7.653 0.000
Error 58.149 193 0.301
>From this, we conclude that there is no difference between the grazed and
>non-grazed areas, although there is considerable heterogeneity between the
>grazed areas.
I could not find help in Zar or Sokal and Rohlf, as well as in Systat's help.
What do you think about this?
Thanks in advance,
Alexandre
ANSWER 1
Alexandre,
Basically you are asking two questions with one data set. The first is on the
importance of grazing. The second is whether grazed sites differ. The first
question is easy to answer - grazed are different. The second is different and
for which, you do NOT need to include the ungrazed (if fact, you should NOT
include it) plot to test for differences in the grazed plot. So, the first
test, Dunnet's, compares a control with treatments, and basically asks if the
treatments are different from the control. The second its a typical ANOVA,
testing for differences among treatments, and can use a Tukey test to
distinguish between treatments, but leaving the control out. In fact, the
control makes no sense with this question.
Does that make sense?
Cheers,
ANSWER 2
Alexandre,
It looks to me like you have confounded effects in the GLM. All of
the variability explained by the MANAGEMENT predictor is also
explained by the AREA predictor (as the difference between (A,B,C,D)
and E. Perhaps you should try to run the GLM with AREA nested within
MANAGEMENT. That is, test for differences between A, B, C, and D
(the grazed treatments) and also test for differences between all
those groups and E (the fenced treatment). I suspect you will find
almost the same result as in your ANOVA, since ANOVA and GLM are
essentially the same procedure. Unfortunately I don't use Systat, so
I can't help with specific recommendations.
Best wishes,
Dr. Alexandre F. Souza
Programa de Pós-Graduação em Biologia (Diversidade e Manejo da Vida Silvestre)
Universidade do Vale do Rio dos Sinos
Av. UNISINOS 950 - C.P. 275
São Leopoldo 93022-000
RS - Brasil
Telefone: (051)3590-8121 ramal 1263
[EMAIL PROTECTED]
http://www.unisinos.br/laboratorios/lecopop
