[R-sig-ME] lme vs paired t-test

Federico Calboli f.calboli at imperial.ac.uk
Tue Jun 17 17:22:24 CEST 2008

Hello everyone,

to keep on the line of my pesky questions/irritating questions, I did  
one simple analysis for a colleague and got some unexpected results.

In the analysis I had to model size over selection -- two selection  
regimes, big and small. Nested withing selection there are 2  
replicated lines for each selection regime. The experiment had been  
replicated 4 independent times.

My model is:

agmod = lme(Ag_size ~ selection , random = ~1|rep.sel/block_sep, agsize)

with rep.sel being the nested replicated lines and block_sep the 4  
independent replicates. Since my colleague cares about the effect of  
selection I did an anova of the model:

             numDF denDF  F-value p-value
(Intercept)     1   128 693.5251  <.0001
selection       1     2  35.5191   0.027

This is all fine and dandy, but my colleague expected a much stronger  
selection effect, he did a paired t-test on the means of each  
replicated selection line:

mat = matrix(tapply(agsize$AG_size, agsize$rep.sel, mean), ncol = 2)
 > mat
          [,1]      [,2]
[1,] 15224.03  9143.403
[2,] 16418.50 10729.206
 > t.test(mat[,1], mat[,2], paired = T)

	Paired t-test

data:  pio[, 1] and pio[, 2]
t = 30.0763, df = 1, p-value = 0.02116
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
  3398.768 8371.155
sample estimates:
mean of the differences

Now the pesky question: the value from a rough and ready t-test is  
not all that different from the linear model... what's going on? I  
would have though that all the extra data in the lme model would make  
it much more sensitive. Where are my conjectures wrong?



PS the data I used, not being mine, cannot bet just posted for  
everyone to test my assumptions, sorry.

Federico C. F. Calboli
Department of Epidemiology and Public Health
Imperial College, St. Mary's Campus
Norfolk Place, London W2 1PG

Tel +44 (0)20 75941602   Fax +44 (0)20 75943193

f.calboli [.a.t] imperial.ac.uk
f.calboli [.a.t] gmail.com

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