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

[Federico Calboli]

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:

anova(agmod)
             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
                5884.962

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?

Cheers,

Federico

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