I need help with designing an experiment. Suppose I am testing 2 fertility programs against a control in Lettuce, for a total of 3 groups (Program A, Program B, and Untreated Control). Let's assume that the field has no noticeable differences in factors that could influence yield.
If I were to do a Latin square, that would be 9 experimental units with 3 replications for each group. Now, compare that to a randomized complete block design (RCBD) with 4 replications of each group.
Would the Latin Square actually be more robust because I would be evaluating the treatments against each other both by row and column, even though there are less replicates? Seems to me that the row and column evaluations for 3 treatments in a latin square would be allow for more comparisons between treatments (row x 3 and column x 3) than a 4-repetition RCBD.
Am I missing something? If you were a researcher or evaluating this experiment, which would you consider more robust and why?