Contrast anova multi factor

?Dear Thierry,

That is the problem. I read that interpretation is the same, but the
Intercept value of summary is different:

The mean of level "a" of f1 and level "I" of f2 (first level of each
factor) is 0.7127851.

When I run model with interaction term:

summary.lm(aov(y~f1*f2,data=dt))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   0.7128     0.2884   2.471   0.0484 *
f1b           1.0522     0.4560   2.307   0.0605 .
f2II         -0.6787     0.4560  -1.488   0.1872
f1b:f2II     -1.1741     0.6449  -1.821   0.1185

I check that Intercept is mean of level "a" of f1 and level "I" of f2.

But when I run the model without interaction term, the Intercept value is
different:

summary.lm(aov(y~f1+f2,data=dt))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   0.9476     0.2976   3.185   0.0154 *
f1b           0.4651     0.3720   1.251   0.2513
f2II         -1.2658     0.3720  -3.403   0.0114 *

I do not know what is Intercept value in this case. I expected that it is
mean of level "a" of f1 and level "I" of f2, but not.

Best regards,

Mario


On 26 April 2015 at 12:30, Thierry Onkelinx <thierry.onkelinx at inbo.be>
wrote:

Dear Mario,

The interpretation is the same: the average at the reference situation
which is the group that has f1 == "f1 level1" and f2 == "f2 level1".

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature

and

Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to

say

what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of

data.

~ John Tukey

2015-04-26 17:12 GMT+02:00 Mario Jos? Marques-Azevedo <
mariojmaaz at gmail.com>:

Hi all,

I am doing anova multi factor and I found different Intercept when model
has interaction term.

I have the follow data:

set.seed(42)
dt <- data.frame(f1=c(rep("a",5),rep("b",5)),
                 f2=rep(c("I","II"),5),
                 y=rnorm(10))

When I run

summary.lm(aov(y ~ f1 * f2, data = dt))

The Intercept term is the mean of first level of f1 and f2. I can

confirm

that with:

tapply(dt$y, list(dt$f1, dt$f2), mean)

I know that others terms are difference of levels with Intercept.

But I do not know what is Intercept when the model do not have

interaction

term:

summary.lm(aov(y ~f1 + f2, data = dt))

I know that I can create a specific contrast table, by I would like
understand the default R output.

I read contrast sub-chapter on Crawley 2012 (The R book) and in his
example
the Intercept is different when model has or not interaction term, but

he

explain that Intercept is mean of first level of the factors.

Best regards,

Mario

.............................................................
Mario Jos? Marques-Azevedo
Ph.D. Candidate in Ecology
Dept. Plant Biology, Institute of Biology
University of Campinas - UNICAMP
Campinas, S?o Paulo, Brazil

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