IGNOU MST 5 2018 - Below is given the plan and yields of 22 factorial experiment involvin

Question

Below is given the plan and yields of 22 factorial experiment involving 2 factors A and B each at two levels 0 and 1:

Block I

(1)

117

b

106

ab

129

a

124

Block II

ab

124

(1)

120

b

117

a

124

Block III

(1)

111

a

127

b

114

ab

126

Block IV

ab

125

a

131

b

112

(1)

108

Block V

ab

95

b

97

(1)

73

a

128

Block VI

a

158

(1)

81

ab

125

b

117

Analyse the design. Does treatment effects A differ from treatment effect B significantly?

16 Feb 2018

Answer :

Word Count : 422

It looks like you have a \( 2^2 \) factorial experiment with two factors, \( A \) and \( B \), each at two levels (0 and 1). Your data is provided in blocks, and you need to numerically solve for the factorial effects. I'll compute the main effects and interaction effect using the standard \( 2^2 \) factorial experiment analysis. ### Step 1: Define the Notation Each treatment combination is represented as: - \( (1) \) → \( A_0 B_0 \) - \( a \) → \( A_1 B_0 \) - \( b \) → \( A_0 B_1 \) - \( ab \) → \( A_1 B_1 \) We will calculate: - Main Effect of \( A \): Difference between average response when \( A=1 \) vs. when \( A=0 \). - Main Effect of \( B \): Difference between average response

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Stratum II :	8 8 12 16 16 18
Stratum III :	16 16 18 22 22 26