Lec15.ANOVA - Analysis of Variance (ANOVA) One-way ANOVA,...

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Unformatted text preview: Analysis of Variance (ANOVA) One-way ANOVA, KNNL Chp. 16 Two-way ANOVA, KNNL Chp. 19 Poplar Trees Marathon Times Single-Factor (One-way) ANOVA Treatment None Fertilizer Irrigation Both Weight (kg) Poplar Trees 0.15 0.02 0.16 0.37 0.22 1.34 0.14 0.02 0.08 0.08 0.23 0.04 0.34 0.16 0.05 2.03 0.27 0.92 1.07 2.38 n 5 5 5 5 mean 0.184 0.332 0.164 1.334 standard deviation 0.127 0.565 0.126 0.859 Data (poplar.trees.txt) poplar.trees weight.kg treatment 1 0.15 none 2 0.02 none 3 0.16 none 4 0.37 none 5 0.22 none 6 1.34 fertilizer 7 0.14 fertilizer 8 0.02 fertilizer 9 0.08 fertilizer 10 0.08 fertilizer 11 0.23 irrigation 12 0.04 irrigation TULIP POPLAR Liriodendron tulipifera Questions Do fertilizer and irrigation affect tree growth? Which treatment has the greatest effect? What is the magnitude of that effect? Splus/R summaries tapply(poplar.trees$weight.kg,poplar.trees$treatment,le ngth) none fertilizer irrigation both 5 5 5 5 tapply(poplar.trees$weight.kg,poplar.trees$treatment,me an) none fertilizer irrigation both 0.184 0.332 0.164 1.334 tapply(poplar.trees$weight.kg,poplar.trees$treatment,st dev) none fertilizer irrigation both 0.1270039 0.5650841 0.1262141 0.8590285 both fertilizer irrigation none treatment 0.0 0.5 1.0 1.5 2.0 2.5 weight.kg Analysis of Variance Table value P Fstat ErrorMS ErrorDF ErrorSS GroupMS GroupDF GroupSS TotalDF TotalSS- . .. . .. i ij i ij Y Y Y Y Y Y Error Group Total- +- =- + = Analysis of Variance Table value P Fstat ErrorMS ErrorDF ErrorSS GroupMS GroupDF GroupSS TotalDF TotalSS- summary(aov(weight.kg~treatment,data=poplar.trees) ) Df Sum of Sq Mean Sq F Value Pr(F) treatment 3 4.682415 1.560805 5.731353 0.007348294 Sums of Squares, Degrees of Freedom ( 29 ( 29 ( 29 1 1 2 .. 2 . 2 .. .- =- =- =- =- =- = T T ij T E i ij R i i n df Y Y SSTO r n df Y Y SSE r df Y Y n SSR summary(aov(weight.kg~treatment,data=poplar.trees) ) Df Sum of Sq Mean Sq F Value Pr(F) treatment 3 4.682415 1.560805 5.731353 0.007348294 predict(poplar.aov) resid(poplar.aov) 0.2 0.4 0.6 0.8 1.0 1.2-1.0-0.5 0.0 0.5 1.0 No Transformation predict(poplar.log.aov) resid(poplar.log.aov)-2.0-1.5-1.0-0.5 0.0-2-1 1 2 Log Transformation predict(poplar.sqrt.aov) resid(poplar.sqrt.aov) 0.4 0.6 0.8 1.0-0.6-0.2 0.2 0.6 Sqrt Transformation Which transformation would you choose? poplar.sqrt.aov= aov(sqrt(weight.kg) ~treatment, data=poplar.trees) summary(poplar.sqrt.aov) Df Sum of Sq Mean Sq F Value Pr(F) treatment 3 1.784770 0.5949233 6.167209 0.005471173 Residuals 16 1.543449 0.0964656 0.2 0.4 0.6 0.8 1.0 1.2 1.4 both fertilizer irrigation none Square Root Transformation summary(poplar.sqrt.aov)summary(poplar....
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This note was uploaded on 04/17/2010 for the course STSCI 3200 taught by Professor Sullivan during the Spring '10 term at Cornell University (Engineering School).

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Lec15.ANOVA - Analysis of Variance (ANOVA) One-way ANOVA,...

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