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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Civil and Environmental Engineering 1.017/1.010 Computing and Data Analysis for Environmental Applications / Uncertainty in Engineering Problem Set 9: Two-way ANOVA and Regression (Solutions provided at end of each problem) Due: Tuesday, Dec. 2, 2003 Please turn in a hard copy of your MATLAB program as well as all printed outputs (tables, plots, etc.) required to solve the problem. Problem 1 Continue your investigation of Massachusetts Water Resources Authority (MWRA) Boston Harbor data by carrying out a two factor ANOVA which considers both rainfall and date. For Factor A (rainfall) your treatments should be the same three rainfall intensity categories used in Problem Set 8. For Factor B (date) use two treatments: 1) dates through 1991 and 2) dates after 1991. The dates are included in the file lowercharles.txt that you used in Problem Set 8 . You should use the internal MATLAB function ANOVA2 to carry out your two-factor analysis. This function can handle treatments that have different numbers of replicates. However, if you prefer to adopt the equal replicate assumption, you can force each treatment to have the same number of replicates (as assumed in the lecture notes) by randomly selecting the same number of measurements from the coliform population available for each treatment combination. As before, convert the coliform count C to the transformed count C T = ln ( C +1) and check for normality. Present the two factor ANOVA table, report the p value, and discuss the significance of your results. Problem 1 Solution % Problem Set 9 -- Problem 1 clear all close all % edited lowercharles3 in excel: deleted unnecessary columns % replaced blank rain with zeros load lowercharles3.txt; date=lowercharles3(:,1); coli=log(lowercharles3(:,2)+1); rain=lowercharles3(:,3);
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p=1; q=1; r=1; s=1; u=1; v=1; for i=1:length(coli) if rain(i)==0&date(i)<33790 T1(p)=coli(i); p=p+1; elseif rain(i)==0&date(i)>=33790 T4(s)=coli(i); s=s+1; elseif (rain(i)>0&rain(i)<=0.25)&date(i)<33790 T2(q)=coli(i); q=q+1; elseif (rain(i)>0&rain(i)<=0.25)&date(i)>=33790 T5(u)=coli(i); u=u+1; elseif rain(i)>.25&date(i)<33790 T3(r)=coli(i); r=r+1; elseif rain(i)>.25&date(i)>=33790 T6(v)=coli(i); v=v+1; end end number=min([(length(T1)), (length(T2)), (length(T3)),(length(T4)), (length(T5)), (length(T6))]); index1=randperm(length(T1)); ctreat1=T1(index1(1:number)); index2=randperm(length(T2));
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This note was uploaded on 11/29/2011 for the course CIVIL 1.00 taught by Professor Georgekocur during the Spring '05 term at MIT.

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