assessing treatment effect in field trial and pseudo-replication

[vstorme]

I want to assess a treatment effect. I have a field trial with 9 treatment plots(=rep 1,...,9). There are 3 different treatments, each treatment is replicated 3 times. Within each treatment plot, 150 plants are measured over time (5 measurements, factor week). Each plant in the field has a unique plantID. I analysed the data as follows:

proc mixed data = plot  scoring=1 order=internal;
class rep plantID treatment week;
model length = treatment|week / ddfm=kr  singular=1e-11 ;
repeated week /subject=plantID(rep) type=un r rcorr;
random intercept / subject=rep ;
run;

Am I correctly taking into account pseudo-replication with this model. Examples in "contemporary statistical models for the Plant and Soil sciences" from Schabenberger, seem to calculate first the plot average, in which case the analysis becomes:

proc means data=plot;
class rep week treatment;
var length;
output out = means;
run;
data input;
set means;
where _TYPE_=7 and _STAT_= "MEAN";
run;
title 'pseudo-rep';
proc mixed data = input  scoring=1 order=internal;
class rep  treatment week;
model length = treatment|week / ddfm=kr  singular=1e-11 ;
repeated week /subject=rep type=ar(1) r rcorr;
random intercept / subject=rep ;
run;
title;

due to the much lower dendf, I have much larger p-values. Which analysis isto be preferred?

Thanks for any input, Veronique

[sld]

If WEEK is a classification variable, and if you are thinking of REP as the replicating experimental unit for TREATMENT and of PLANTID as subsamples within each REP, and if you want to avoid pseudoreplication, then I concur with the code from Schabenberger and Pierce.

Although you don't derive any denominator df benefits from all those individual plots within a REP, the subsamples still have value: the mean computed over 150 plants is a better metric, with a smaller variance, than the value from a single plant.