A total of 30 tomato plants were grown in a greenhouse under various conditions consisting of combinations of soil type (I, II, III, IV, and V), and fertilizer type (A,B,C). There were an equal number of plants grown under each combination. After a fixed period of time, the yield (in kilograms) of tomatoes from each plant was measured. What type of experimental design is this?

Going by the question, the design is RBD (Randomized Block Design). Where the blocks are nothing but a Combination of Soil Types(I, II, III, IV and V).So here we have seen 5 blocks.Fertilizers can be considered as treatments(A,B and C).

Fertilizer A Fertilizer B Fertilizer C

Soil I 2 2 2

Soil II 2 2 2

Soil III 2 2 2

Soil IV 2 2 2

Model for a randomized block design

The model for a randomized block design with one nuisance variable is

[tex]Y_{ij}=\mu +T_{i}+B_{j}+\mathrm {random\ error}[/tex]

where

is any observation

μ is the general location parameter (i.e., the mean)

is the effect for being in treatment i (Fertilizer)

[tex]B_j[/tex] is the effect for being in block j (Type of Soil)