Paired t-test with subsamples in R?

Question

I've been trying to find a similar "problem", but I didn't, so I'm going to try to explain what am I looking for.

I have for different sites A,B,C and D. In each site I have a forest and a fallow=> AFo, AFa, BFo,BFa... In each forest and fallow I have 4 quadrates: AFo1, AFo2, AFo3, AFo4, AFa1,...

I measured different variables such as pH, electric conductivity, total phosphorus, etc in all quadrates. My aim is to compare the forests to the fallows, but I have to take into account the variability between the sites and the quadrates.

I have made a two way crossed ANOVA, but my teacher told me that I should do a t-test which takes into account the subsamples (the quadrates). My fixed factor would be forest/fallow, and my random factor the sites.

Can anyone help me, please? :)

Thank you very much in advance!

Lili

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More or less, but normally she wants me to perform a t-test on all the AFo-s , while taking into account the subsamples 1,2,3 and 4.

Because what I would like to do is not to compare the quadrate1 from the forest with quadrate 1 from the fallow, but the mean of the 4 quadrates of the forest with the mean of the 4 quadrates of the fallow. Hm. don't know whether I'm expressing myself clearly..

Answer 1

The paired t test takes advantage of natural pairings of observations between samples. In this case the pairs would be one measurement in a forest quadrate and the same measurement in the corresponding fallow quadrate, for example, pH in AFo1 and pH in AFa1. For any type of measurement (pH, conductivity, etc.) this gives you a data matrix / table like

$$ \left[ \begin{array}{cc} AFo1 & AFa1 \\ AFo2 & AFa2 \\ \vdots & \vdots \\ DFo4 & DFa4 \end{array} \right] $$

Then you would perform a paired t-test with the first column as one sample and the second column as the other (so each row would be a pair).