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?