本文是實驗設計與分析（第6版，Montgomery著，傅玨生譯) 第5章析因設計引導5.7節思考題5.6 R語言解題。主要涉及方差分析，正態假設檢驗，殘差分析，交互作用圖，等值線圖。

dataframe <-data.frame(

strength=c(109,110,110,112,116,114,110,115,110,111,112,115,108,109,111,109,114,119,110,108,114,112,120,117),

machine=gl(4,6,24),

operator=gl(3,2,24))

summary (dataframe)

dataframe.aov2 <- aov(strength~operator*machine,data=dataframe)

summary (dataframe.aov2)

> summary (dataframe.aov2)

???????????????? Df Sum Sq Mean Sq F value?? Pr(>F)???

operator????????? 2 160.33?? 80.17? 21.143 0.000117 ***

machine?????????? 3? 12.46??? 4.15?? 1.095 0.388753???

operator:machine? 6? 44.67??? 7.44?? 1.963 0.150681???

Residuals ???????12? 45.50??? 3.79????????????????????

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Signif. codes:? 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

with(dataframe,interaction.plot(machine,operator,strength,type="b",pch=19,fixed=T,xlab="operator",ylab="strength"))

plot.design(strength~machine*operator,data=dataframe)

fit <-lm(strength~operator*machine,data=dataframe)

anova(fit)

> anova(fit)

Analysis of Variance Table

Response: strength

???????????????? Df? Sum Sq Mean Sq F value??? Pr(>F)???

operator????????? 2 160.333? 80.167 21.1429 0.0001167 ***

machine?????????? 3? 12.458?? 4.153? 1.0952 0.3887526???

operator:machine? 6? 44.667?? 7.444? 1.9634 0.1506807???

Residuals??????? 12? 45.500?? 3.792?????????????????????

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Signif. codes:? 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

summary(fit)

> summary(fit)

Call:

lm(formula = strength ~ operator * machine, data = dataframe)

Residuals:

?? Min???? 1Q Median???? 3Q??? Max

? -2.5?? -1.0??? 0.0??? 1.0??? 2.5

Coefficients:

???????????????????? Estimate Std. Error t value Pr(>|t|)???

(Intercept)???????? 1.095e+02? 1.377e+00? 79.527?? <2e-16 ***

operator2?????????? 1.500e+00? 1.947e+00?? 0.770?? 0.4560???

operator3?????????? 5.500e+00? 1.947e+00?? 2.825?? 0.0153 *?

machine2??????????? 3.000e+00? 1.947e+00?? 1.541?? 0.1493???

machine3?????????? -1.000e+00? 1.947e+00? -0.514?? 0.6169???

machine4?????????? -5.000e-01? 1.947e+00? -0.257?? 0.8017???

operator2:machine2 -3.500e+00? 2.754e+00? -1.271?? 0.2278???

operator3:machine2 -4.500e+00? 2.754e+00? -1.634?? 0.1282???

operator2:machine3? 8.808e-14? 2.754e+00?? 0.000?? 1.0000???

operator3:machine3? 2.500e+00? 2.754e+00?? 0.908?? 0.3818???

operator2:machine4? 2.500e+00? 2.754e+00?? 0.908?? 0.3818???

operator3:machine4? 4.000e+00? 2.754e+00?? 1.453?? 0.1720???

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Signif. codes:? 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.947 on 12 degrees of freedom

Multiple R-squared:? 0.827,???? Adjusted R-squared:? 0.6684

F-statistic: 5.214 on 11 and 12 DF,? p-value: 0.004136

par(mfrow=c(2,2))

plot(fit)

par(mfrow=c(2,2))

plot(as.numeric(dataframe$machine), fit$residuals, xlab="machine", ylab="Residuals", type="p", pch=16)

plot(as.numeric(dataframe$operator), fit$residuals, xlab="operator", ylab="Residuals", pch=16)