Question

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?

Answer 1

Clearly the design is RBD (Randomized Block Design). Where the blocks are nothing but 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 III	2	2	2
Soil IV	2	2	2

The 5 rows are nothing but five blocks for five soil combination type.Each cell consists of 2 tomato plants such that there were an equal number of plants grown under each combination.i.e 30 tomatoes are equally distributed in each cell.

Explanation why the above model is RBD (Randomized Block Design)??

Definition: With a randomized block design, the experimenter divides subjects into subgroups called blocks, such that the variability within blocks is less than the variability between blocks. Then, subjects within each block are randomly assigned to treatment conditions.

Model for a randomized block design

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

where

Y_ij is any observation

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

T_i is the effect for being in treatment i (Fertilizer)

B_j is the effect for being in block j (Type of Soil)