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Setup: A research laboratory was developing a new compound for the relief of severe cases of hay fever. In an experiment with 36 volunteers, the amounts of the two active ingredients (Factors A and B) in the compound were varied at four levels for A, and three levels for B. Randomization was used in assigning four volunteers to each of the twelve treatments. The data on hours of relief follow (dataset in the file “relief.csv" where the columns represent Hours of Relief; Factor A Level; Factor B Level; Subject). Factor B (Ingredient 2) j = 2 j=3 (Ingredient 1) | Low Medium High 3.7 Factor A j = 1 i = 1 Placebo 1.4 3.1 0.8 3.3 3.6 0.9 2.9 3.6 1.1 3.0 3.9 i = 2 Low 2.4 4.6 4.8 2.7 4.2 4.5 2.3 4.9 4.4 4.6 9.1 2.5 4.7 i = 3 Medium 5.8 8.9 5.2 9.1 9.3 5.5 8.7 8.7 5.3 9.0 9.4 i = 4 High 6.1 9.9 13.5 5.7 10.5 13 5.9 10.6 13.3 6.2 10.1 13.2 For the following, assume a FIXED effects model is appropriate.

Setup: A research laboratory was developing a new compound for the relief of severe cases of hay fever. In an experiment with 36 volunteers, the amounts of the two active ingredients (Factors A and B) in the compound were varied at four levels for A, and three levels for B. Randomization was used in assigning four volunteers to each of the twelve treatments. The data on hours of relief follow (dataset in the file “relief.csv" where the columns represent Hours of Relief; Factor A Level; Factor B Level; Subject). Factor B (Ingredient 2) j = 2 j=3 (Ingredient 1) | Low Medium High 3.7 Factor A j = 1 i = 1 Placebo 1.4 3.1 0.8 3.3 3.6 0.9 2.9 3.6 1.1 3.0 3.9 i = 2 Low 2.4 4.6 4.8 2.7 4.2 4.5 2.3 4.9 4.4 4.6 9.1 2.5 4.7 i = 3 Medium 5.8 8.9 5.2 9.1 9.3 5.5 8.7 8.7 5.3 9.0 9.4 i = 4 High 6.1 9.9 13.5 5.7 10.5 13 5.9 10.6 13.3 6.2 10.1 13.2 For the following, assume a FIXED effects model is appropriate.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Setup: A research laboratory was developing a new compound for the relief of severe cases of hay fever. In an experiment with 36 volunteers, the amounts of the two active ingredients (Factors A and B) in the compound were varied at four levels for A, and three levels for B. Randomization was used in assigning four volunteers to each of the twelve treatments. The data on hours of relief follow (dataset in the file "relief.csv" where the columns represent Hours of Relief; Factor A Level; Factor B Level; Subject). Factor B (Ingredient 2) j = 1 j = 2 Medium High Factor A j = 3 (Ingredient 1) i = 1 Placebo Low 1.4 3.1 3.7 0.8 3.3 3.6 0.9 2.9 3.6 1.1 3.0 3.9 i = 2 Low 2.4 4.6 4.8 2.7 4.2 4.5 2.3 4.9 4.4 2.5 4.7 4.6 i = 3 Medium 5.8 8.9 9.1 5.2 9.1 9.3 5.5 8.7 8.7 5.3 9.0 9.4 i = 4 High 6.1 9.9 13.5 5.7 10.5 13 5.9 10.6 13.3 6.2 10.1 13.2 For the following, assume a FIXED effects model is appropriate. Questions: 1. Is this setup an observational study or an experiment? Write down the statistical model with interaction effects and necessary assumptions. Interpret the cell mean Hij.
Transcribed Image Text:Setup: A research laboratory was developing a new compound for the relief of severe cases of hay fever. In an experiment with 36 volunteers, the amounts of the two active ingredients (Factors A and B) in the compound were varied at four levels for A, and three levels for B. Randomization was used in assigning four volunteers to each of the twelve treatments. The data on hours of relief follow (dataset in the file "relief.csv" where the columns represent Hours of Relief; Factor A Level; Factor B Level; Subject). Factor B (Ingredient 2) j = 1 j = 2 Medium High Factor A j = 3 (Ingredient 1) i = 1 Placebo Low 1.4 3.1 3.7 0.8 3.3 3.6 0.9 2.9 3.6 1.1 3.0 3.9 i = 2 Low 2.4 4.6 4.8 2.7 4.2 4.5 2.3 4.9 4.4 2.5 4.7 4.6 i = 3 Medium 5.8 8.9 9.1 5.2 9.1 9.3 5.5 8.7 8.7 5.3 9.0 9.4 i = 4 High 6.1 9.9 13.5 5.7 10.5 13 5.9 10.6 13.3 6.2 10.1 13.2 For the following, assume a FIXED effects model is appropriate. Questions: 1. Is this setup an observational study or an experiment? Write down the statistical model with interaction effects and necessary assumptions. Interpret the cell mean Hij.
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