I am designing an experiment that will include an assay on a 96 well plate and could use some advice on the optimal layout.
In our experiment we have 12 biological replicates, and each replicate has been given each of two treatments. We are measuring our primary outcome on a single plate with 4 technical replicates for each measurement (12x2x4=96).
I suspect (and have some evidence) for row and column effects for this assay, and so row and column balance seems important.
My thought was to alias biological replicates with columns as blocks, since the comparison is being made within biological replicates, and then apply either a complete randomised block design (shuffling the eight technical replicates within the block) or to restrict the permutations using something like an extended Latin square so that the treatment was perfectly balanced across both rows and columns.
Option 1: Each column is a biological replicate, four treatment A technical reps and four treatment B technical reps shuffled within each column. This I think is easy to analyse, but possibly unbalanced across rows.
Option 2 - as before but with the restriction that treatments are balanced across rows (something like this - but built on Latin squares rather than just shuffled columns and rows as I've done it here). This option is balanced but I think harder to analyse.
So my question are whether these designs make sense at all, whether the first or second approach would be better (and possibly whether I'm overthinking the whole thing).