Question

what is the additional major assumption that is needed in RBD and not needed in an ordianry 2 factor study?

Answer 1

The assumptions of RBD are as follows :

1. Assumption of Independence

[ The samples from the populations under consideration are independent within each block. ]

2. Normality Assumption  

[ The populations under consideration are normally distributed. ]

3. Homogeneity of Variances Assumption

[ The standard deviations of the populations under consideration are equal; that is they are all the same value, σ. ]

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Answer :

The first Assumption is an additional assumption that is needed in RBD i.e. the independence assumption which states that in RBD it is assumed that the samples from the populations under consideration are independent within each block.

Explanation:

Therefore the randomization on the factor occurs within the levels of the blocking variable and thus this concept focuses on creating homogeneous blocks of the experimental units in the design.

(i.e. the treatment is allocated randomly in each block )

Whereas in Two factor study the interaction term is also taken into count and in the experimental population the sample is simply randomized into the cells of the two factor design. This is used to access whether the effect of the factor differs across the blocks .

Hence the RBD is an additive model whereas a 2 factor study involves the term describing the interaction and hence is not a additive model but an interaction model.