Why do I get a diffirent answer from book in this ANOVA question?

Question

From Design and Analysis of Experiments, by Douglas C Montgomery,

An example for ANOVA is given using the following data set,

With a conclusion being

But I am having a lot of trouble trying to do this myself.

I understand the results using manual calculations, but I want to do it in R.

What I did in R was as follows

data<-c(160,160,160,160,160,180,180,180,180,180,200,200,200,200,200,220,220,220,220,220) Etch160<-c(575,542,530,539,570) Etch180<-c(565,593,590,579,610) Etch200<-c(600,651,610,637,629) Etch220<-c(725,700,715,685,710) response<-c(Etch160,Etch180,Etch200,Etch220) dataframe<-data.frame(response,data) t<-aov(data~response,data=dataframe) summary(t)

For which I get a completely different answer and form.

I am wondering firstly, why? Secondly, how can I get a table like the book did using R? Is there some function I am missing? Where is my mistake?

Running my code gives

Answer 1

The correct code you need to replicate the anova table you provided is as follows:

data<-c(160,160,160,160,160,180,180,180,180,180,200,200,200,200,200,220,220,220,220,220)

Etch160<-c(575,542,530,539,570)
Etch180<-c(565,593,590,579,610)
Etch200<-c(600,651,610,637,629)
Etch220<-c(725,700,715,685,710)

response<-c(Etch160,Etch180,Etch200,Etch220)

dataframe<-data.frame(response,data)

dataframe$data <- factor(dataframe$data)

t <- aov(response ~ data,data=dataframe)

summary(t)

Your first mistake was in mis-specifying the formula used inside the aov() function. This formula is of the form outcome ~ factor. In your case, the factor is RF Power - this factor has 4 levels, hence the 4 - 1 = 3 degrees of freedom listed next to it in the anova table. The 4 levels are 160, 180, 200 and 220.

Your second mistake was in not converting the RF Power variable (which you called "data") to a factor using the factor() function.

Addendum:

To check the normality assumption for the one-way ANOVA analysis you performed, simply use the R code below:

t <- aov(response ~ data,data=dataframe)

r <- residuals(t) 

par(mfrow=c(1,3))
hist(r, main="Histogram of Residuals", xlab="Residual") 
plot(density(r), main="Density Plot of Residuals")
qqnorm(r, main="Normal Quantile-Quantile Plot \nof Residuals")
qqline(r)

This code will produce the histogram of the residuals, the density plot of the residuals and the normal quantile-quantile plot of the residuals. You can examine these plots to see if the residuals look like they come from a normal distribution.

Rather than using aov() to conduct the one-way ANOVA, you could use the lm() command as follows:

m <- lm(response ~ data,data=dataframe)

anova(m) 

Then you could check the normality assumption for your linear model like so:

r <- residuals(m) 

par(mfrow=c(1,3))
hist(r, main="Histogram of Residuals", xlab="Residual") 
plot(density(r), main="Density Plot of Residuals")
qqnorm(r, main="Normal Quantile-Quantile Plot \nof Residuals")
qqline(r)

So both aov() and lm() use the same syntax in the case of one-way ANOVA: outcome ~ factor.