A 2 factorial design has the following factors: Temperature (A), Pressure (B), and Time (C). The...

 

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A 2³ factorial design has the following factors: Temperature (A), Pressure (B), and Time (C). The response is the variable Yield. The analysis of the data for this experiment, with a single replication, gave the following results: Treatment Combinations (1) a b ab C ac bc abc Mean Effect Estimate: Sum of Squares: I d) A Answer: 33.8 -0.5 0.5 f) g) B a) Fill in the column for BC using + and - signs. b) Calculate the mean effect estimate for the interaction BC Answer: Factorial Effects AB C AC -9.5 4.5 2.5 -3.5 2.5 180.5 40.5 12.5 24.5 60.5 12.5 BC ABC Yes c) Just by looking at the Sum of Squares values, which factor(s) and/or interactions you think are significant? Answer: How many degrees of freedom will have an F-test for the BC interaction? Numerator: Denominator: e) If you need to arrange this design into four blocks of size 2 using 1 = AB and I = AC find the treatment combinations that belong to each block. Block | = Block II = Block III = Block IV = Which effects are confounded with blocks? Answer: Would you recommend this blocking procedure? No Yield 32 35 28 31 48 39 28 29 A 2³ factorial design has the following factors: Temperature (A), Pressure (B), and Time (C). The response is the variable Yield. The analysis of the data for this experiment, with a single replication, gave the following results: Treatment Combinations (1) a b ab C ac bc abc Mean Effect Estimate: Sum of Squares: I d) A Answer: 33.8 -0.5 0.5 f) g) B a) Fill in the column for BC using + and - signs. b) Calculate the mean effect estimate for the interaction BC Answer: Factorial Effects AB C AC -9.5 4.5 2.5 -3.5 2.5 180.5 40.5 12.5 24.5 60.5 12.5 BC ABC Yes c) Just by looking at the Sum of Squares values, which factor(s) and/or interactions you think are significant? Answer: How many degrees of freedom will have an F-test for the BC interaction? Numerator: Denominator: e) If you need to arrange this design into four blocks of size 2 using 1 = AB and I = AC find the treatment combinations that belong to each block. Block | = Block II = Block III = Block IV = Which effects are confounded with blocks? Answer: Would you recommend this blocking procedure? No Yield 32 35 28 31 48 39 28 29

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a The BC column can be filled in using the signs of the interactions with factors B and C as follows ... View the full answer