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Lec15.ANOVA

# Lec15.ANOVA - Analysis of Variance(ANOVA One-way ANOVA KNNL...

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Analysis of Variance (ANOVA) One-way ANOVA, KNNL Chp. 16 Two-way ANOVA, KNNL Chp. 19 Poplar Trees Marathon Times

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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 13      0.34 irrigation TULIP POPLAR Liriodendron tulipifera

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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

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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 - + - = - + =

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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

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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 0 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

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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)

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Lec15.ANOVA - Analysis of Variance(ANOVA One-way ANOVA KNNL...

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