# Experimental design with two factorial treatment and blocks of the treatment combination

I am going to do an experiment with planting seeds involving 2 factorial treatments. There are 4 families of seeds: F1, F2, F3, F4 and 3 foliar seed treatments: T1, T2, T3. There will be 160 seeds for each treatment combination. I will then plant these seeds in 4 separate boxes, with each box containing 40 seeds. The total number of boxes is 48. These boxes will be placed randomly in the growth room in 6 rows and 8 columns regardless of the treatment combination (meaning that there will be no group placement of the treatment combination). When sampling, for each type of analysis, 5 plants from each box of treatment combination will be taken, to make the total sample size of 20 plants for each analysis for each treatment combination.

What is the name of this design? I'm not sure if it is a complete randomized block design or a split-plot design. Do you have to include the "boxes" random factor when doing the statistical analysis later?

• First think about the structure of the experimental units. Seeds in the same box will share common characteristics from that box, so they are nested in box, and thus box as random effect. The boxes are independent, as long as random allocation of which box gets which seeds. Since only one family in each box, you can conceptualize it as each box having its mean analyzed. Treatments are 4x3=12 and 4 replicates, so 48 means. You could run a 2-way general linear model if using the means, or a mixed-effects with box=random if using plant measurements as data. Feb 23, 2023 at 9:23
• Because there are no treatment differences within box, I wouldn't call it a randomized block design. It's also not split-plot because treatments are applied only at one level (box). Feb 23, 2023 at 9:23