I would like to design a randomized complete block design experiment (RCBD). Let's say I have 3 treatments and 10 logical groupings of my experimental units (EUs) which are the blocks. If each of my 10 blocks has 3 EUs, I can easily use a RCBD by assigning the 3 treatments randomly within each block. However, each of my 10 blocks varies in size, and they won't necessarily be divisible by three. For example, block 1 could have 3 EUs, but block 2 could have 10 EUs. I could fall back on a completely randomized design by ignoring the blocks and randomly assigning all EUs to one of 3 treatments, but I'd like to make use of the natural blocking structure to reduce variance. I see two potential routes:
- Completely randomized design - ignore blocks and assign EUs to the 3 treatment groups. The subsequent ANOVA could include a control variable for the blocks (I just won't have efficiently taken advantage of the groupings in my design)
- CRBD - is it okay to just randomly assign EUs within the blocks? I.e., block 2 could end up with a 3/3/4 treatment1/treatment2/treatment3 split, or depending on how I randomize could even be something like 2/2/6
p.s. this isn't quite an incomplete block design - it's sort of the opposite, where I have more EUs per block than treatments, and it's not quite a repeated measures design because all of the EUs are unique subjects.