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

[Martin Henry H. Stevens]

Hi Frederico,
I assume that your ability to test "selection" is limited by the  
number of blocks, not the total number of reps. If If I am right,  
this is actually reassuring that the mixed model is not anti- 
conservative.
Hank
On Jun 17, 2008, at 11:22 AM, Federico Calboli wrote:
> 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
>
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

Dr. Hank Stevens, Associate Professor
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Miami University
Oxford, OH 45056

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