[R] ANOVA and lmer

From: Eric Imbert <eric.imbert_at_univ-montp2.fr>
Date: Thu, 07 Feb 2008 22:43:32 +0100

I am analyzing from a very simple experiment. I have measured plants of two different colours (yellow and purple) in 9 different populations.

So, I have two different factors : a fixed effect (Colour with two levels) and a random one (Population with 9 levels).

I first analyzed the data with the aov function LargS is the variable

aov(formula = LargS ~ Col + Error(Col/Pop))

Terms:

                    Col
Sum of Squares  3.440351
Deg. of Freedom        1

Estimated effects are balanced

Stratum 2: Col:Pop

Terms:

                Residuals
Sum  of Squares   3017.112
Deg. of Freedom        16

Residual standard error: 13.73206

Stratum 3: Within

Terms:

                Residuals
Sum of Squares   3347.385
Deg. of Freedom       302

To test for the interaction Col*Pop, I used the following F-ratio = (3017/16)/(3347/302) = 188. Highly significant !

Now, let's go to the analysis performed by lmer - First I do the linear model without the Col*Pop interaction :
m3=lmer(LargS ~ Col + (1 | Pop)

And next with the interaction : m2=lmer(LargS ~ Col + (Col | Pop))

Comparing both models : anova(m2,m3) :

   Df     AIC     BIC  logLik  Chisq Chi Df Pr(>Chisq)
m3  3 1710.67 1721.97 -852.33                         
m2  5 1714.59 1733.43 -852.30 0.0746      2     0.9634

=> Conclusion : the interaction Col*Pop is not significant !

I guess I am missing something.
Who can help ?

Eric

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