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Unformatted text preview: MAT 3378 3X  Spring 2010 Assignment 3  Solution Total = 18 points Question 1: 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 three levels each. Randomization was used in assigning four volunteers to each of the nine treatments. The data on hours of relief follow. The data is found in the tab delimited file: hayfever.txt . The columns are respectively: hours of relief, Factor A (ingredient 1), Factor B (ingredient 2). The codes in the case of both factors represent: 1=low, 2=medium, 3=high. 1. Write down the twofactor ANOVA model to represent these data. 2. Fit the model and produce a QQplot of the residuals. Does the normality assumption appear to be reasonable here? 3. Produce a scatter plot of the residuals against the fitted values. Compare the within treatment variability. Does the variance constancy assumption appear to be reasonable here? 4. Produce an interaction plot. Does your graph suggest that any factor effects are present? Explain. Does your graph suggest that the factors interact? Explain. 5. Test whether or not the two factors interact. Use α = 5%. State the null and alternative hypotheses. Compute the pvalue and give the conclusion. 6. Perform a posthoc analysis to describe the effects. Hint: Consider a cell means model. Solution: 1. It is a two factor study. The corresponding ANOVA model is Y ijk = μ ·· + α i + β j + ijk , where the random error ijk are independent N (0 ,σ 2 ) and a X i =1 α i = 0 , b X j =1 β j = 0 , a X i =1 ( αβ ) ij = 0 and b X j =1 ( αβ ) ij = 0 . Here a = 3 and b = 3. 1 2. Using the following GLM procedure, we obtained the residuals and the fitted values in the output data set called HAYFEVEROUT. proc glm data=hayfever; class ing1 ing2; model relief = ing1 ing2; output out=hayfeverout r=residual p=fitted; run; Using the CAPABILITY procedure, we produced the following QQplot of the residuals. The tendency appears to be linear. We do not have strong evidence against the normality assumption. 3. Below we find a plot of the residuals against the fitted values. The within treatment variability appear to be similar. It seams reasonable to assume that the constancy of error variance assumption holds. 2 4. Using the SAS output delivery system (ODS) with the GLM procedure we obtain the following interaction plot....
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This note was uploaded on 12/22/2011 for the course MAT 3378 taught by Professor G.lamothe during the Spring '11 term at University of Ottawa.
 Spring '11
 G.Lamothe
 Math

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