Dear List,

I am using a random effects model of the following form to analyse data from a field experiment in lmer:
Response~Treatment+(1|Block)+(1|family)
where family is the full-sib family that the plants belong to and block is the field block that the plants were in.

There are 4 treatments. I would like to fit contrasts to test whether the mean of Treatment C = the average of Treatments A and B, and whether the mean of Treatment D = average of Treatments A and B.

I am not sure if I can use the random effects model to fit contrasts like this?

If not, would it be appropriate to account for the pseudoreplication involved in using full sibs by using the number of families (not the number of observations) as the df for the t-test of the contrast? I have between 44 and 47 observations per treatment, there are 181 observations, consisting of 104 families (some families are only represented by 1 individual), and 48 field blocks. Data are normal.

Any advice would be much appreciated,

Thank you,

Rebecca Ross
University of Oxford

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