1 ANOVA Homework Solutions EPP 245/298 Statistical Analysis of Laboratory Data.

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1 ANOVA Homework Solutions EPP 245/298 Statistical Analysis of Laboratory Data

November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 2 Exercise 6.1 > library(ISwR) Loading required package: survival Loading required package: splines > data(zelazo) > zelazo $active [1] $passive [1] $none [1] $ctr.8w [1]

November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 3 > age.walk <- c(zelazo$active,zelazo$passive,zelazo$none,zelazo$ctr.8w) > group <- rep(c("active","passive","none","ctr.8w"),c(6,6,6,5)) > group <- as.factor(group) > group [1] active active active active active active passive passive passive [10] passive passive passive none none none none none none [19] ctr.8w ctr.8w ctr.8w ctr.8w ctr.8w Levels: active ctr.8w none passive > anova(lm(age.walk ~ group)) Analysis of Variance Table Response: age.walk Df Sum Sq Mean Sq F value Pr(>F) group Residuals > plot(age.walk ~ group)

November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 4

November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 5 > mgroup <- rep(c("active","passive","none"),c(6,6,11)) > mgroup <- as.factor(mgroup) > anova(lm(age.walk ~ mgroup)) Analysis of Variance Table Response: age.walk Df Sum Sq Mean Sq F value Pr(>F) mgroup Residuals Signif. codes: 0 `***' `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 > t.test(zelazo$active,c(zelazo$none,zelazo$ctr.8w)) Welch Two Sample t-test data: zelazo$active and c(zelazo$none, zelazo$ctr.8w) t = , df = 9.327, p-value = alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: sample estimates: mean of x mean of y

November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 6 Exercise 6.2 Lung data set has columns –volume = measured lung volume –method = method of measurement –subject = subject Compare the methods. Are they different? Which ones differ?

November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 7 > attach(lung) > lm(volume ~ method + subject) Call: lm(formula = volume ~ method + subject) Coefficients: (Intercept) methodB methodC subject2 subject3 subject subject5 subject > lung.lm <- lm(volume ~ method + subject) > anova(lung.lm) Analysis of Variance Table Response: volume Df Sum Sq Mean Sq F value Pr(>F) method * subject * Residuals Signif. codes: 0 `***' `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 8 > tapply(volume,method,mean) A B C > tapply(volume,subject,mean) > diff(sort(tapply(volume,method,mean))) B C > plot(volume ~ method) > plot(lung.lm) Hit to see next plot: > help(plot.lm) > plot(lung.lm$resid ~ method)

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November 10, 2004EPP 245 Statistical Analysis of Laboratory Data 16 > anova(lung.lm) Analysis of Variance Table Response: volume Df Sum Sq Mean Sq F value Pr(>F) method * subject * Residuals > diff(sort(tapply(volume,method,mean))) B C