[edit : because my question was ambiguous, I decided to rewrite it entirely, with some simplification but a lot more details on the experimental design]
Four independent 10m*10m plots each received sewage sludge from the same water treatment facility (this is precisely where pseudoplication occurs).
After a year of waiting, one "representative" 1kg soil sample was sampled from each plot.
Ten 1g-sub-samples were sampled from each soil sample, then suspended in 10ml water and agitated for 2 days in order to "equilibrate".
Only then, 1 (arbitrary) unit of labeled molecule was added into each soil suspension.
We want to follow the decrease of labeled molecule quantity as time goes on.
After 1 min of agitation, remaining labeled molecule in water of one soil suspension was measured destructively, giving a value "v" between 0 and 1. The value of w = 1-v was recorded.
Same after 2, 3, 4, 5, 6, 7, 8, 9 and 10 minutes of agitation.
So far, we have recorded 10 w values for each soil sample.
plot of w with time of agitation :
Because v decreases with time, w is increasing with time and can be efficiently modeled by the following model equation :
w ~ a * time^b
This model was fit onto each of the 4 sets of 10 w values, giving four sets of (a,b) parameters.
My problem is : How to calculate / estimate a set of global (a,b) parameters ?
I think calculating average of each parameter (=> a_mean and b_mean) is not right. Fitting a model on all pooled 40 w values is no more right.
NB : As a side note, if I had one, and only one, parameter of interest (for example, a maximum value, or a mean) by soil sample, one good option would be to average those four values into one global average.