Question

(a) What expelimental design would be the best to use in the following sit-
uation? Be specific. Explain the good features of your proposed design.
A taste panel will convene this afternoon to compare six different brands
of ice cream. The panel is comprised of 10 persons who are expert
tasters. The maximum number of different brands that an individual
taster will taste is 3.
(b) What would you do if three of the expert tasters failed to come this
afternoon because of illness, so that you could not run the design rec-
ommended in (a) above?

Answer 1

a)

The design is BIBD ( balanced incomplete block design ) because here we know only three can be tasted with each tasters so the design can be incomplete. It contain block factors hence it's a block design it is also balanced because only one missing value there is by column and row so each pair of treatments appear together 2 times , then the values are ,

a = number of elements

a = 6

b = number of blocks

b = 10

K = block size or number of points in the block

K = 3

r = number of block containing a given point .

r = 5

= number of blocks containing any 2 distinct points .

= 2

b)

If three of the experts failed to come then we would have the values as ,

a = 6

b = 7

K = 3

And we would not be able to have treatment i occur in r blocks it says that the balance will be changed or can be break and also we know that the number 10 is the lowest number of person that can satisfy that ,

a r = b k and is the integer. So the design of the given data will change in to unbalanced incomplete block design .