\documentclass[11pt]{article}
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%>Sweave("Sweave_example.Rnw")
\usepackage{url}
\usepackage{moreverb}
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\SweaveOpts{prefix.string=CFRIeg1}
\SweaveOpts{eps=TRUE,pdf=FALSE}

\title{A Simple Example Sweave Report}
\author{Elizabeth G. Hill \\ Hollings Cancer Center Biostatistics Shared Resource}
\date{\today}
\begin{document}
\maketitle

\section{Airquality data desciption}
The data set \texttt{airquality} provides air quality measurements 
in New York from May to September in 1973.  We wish to investigate
the association between month of the year and ozone levels.  
The median ozone
level for the five-month period was \Sexpr{median(airquality$Ozone,na.rm=TRUE)}
(interquartile range = \Sexpr{quantile(airquality$Ozone,probs=0.25,na.rm=TRUE)} 
to \Sexpr{quantile(airquality$Ozone,probs=0.75,na.rm=TRUE)}).  
Average ozone for the five month
period was \Sexpr{round(mean(airquality$Ozone,na.rm=TRUE),2)} 
(SD = \Sexpr{round(sd(airquality$Ozone,na.rm=TRUE),2)}).
Figure \ref{ozhist} shows the distribution of ozone is positively skewed.  
(Of course, we could tell that anyway by inspection of the 
mean and standard deviation.)  Figure \ref{ozqq} shows a quantile-quantile 
plot of ozone indicating the data are not normally distributed.
Therefore, we will use a non-parametric approach to assess the association 
between ozone level and month.

\begin{figure}[ht]
\begin{center}
<<ozonehist, echo=FALSE, fig=TRUE>>= 
hist(airquality$Ozone,main="",xlab="Ozone")
@
\caption{Histogram of ozone.}
\label{ozhist}
\end{center}
\end{figure}

\begin{figure}[ht]
\begin{center}
<<ozoneqq, echo=FALSE, fig=TRUE>>= 
qqnorm(airquality$Ozone)
qqline(airquality$Ozone)
@
\caption{Quantile-quantile plot of ozone.}
\label{ozqq}
\end{center}
\end{figure}

\section{Association of ozone with month}

<<ozboxplots,echo=FALSE,fig=TRUE,include=FALSE>>=
boxplot(Ozone ~ Month, data = airquality,xaxt="n")
axis(side=1,at=1:5,labels=c("May","June","July","Aug","Sept"))
@
Figure \ref{newozbox} shows boxplots of ozone by month.  

\begin{figure}[ht]
\begin{center}
\includegraphics[width=5in,height=3in]{CFRIeg1-ozboxplots}
\caption{Boxplot of ozone by month of year.}
\label{newozbox}
\end{center}
\end{figure}

\subsection{Analysis using Kruskal-Wallis test}

<<kw>>=
kw.out <- kruskal.test(Ozone ~ Month, data=airquality)
kw.out
pval <- round(kw.out$p.value,6)
@
Based on the results of the Kruskal-Wallis test, ozone differs
significantly by month (p = \Sexpr{pval}).

\subsection{Analysis using ANOVA}

Let's revisit this analysis using ANOVA.  We'll perform a logarithmic 
transformation of the ozone
values to facilitate transformation to approximate normality.

<<histtransf,echo=FALSE,fig=TRUE,include=FALSE>>=
hist(log(airquality$Ozone),xlab="log(Ozone)")
@

<<qqtransf,echo=FALSE,fig=TRUE,include=FALSE>>=
qqnorm(log(airquality$Ozone))
qqline(log(airquality$Ozone))
@

Figure \ref{transf} shows histogram and quantile-quantile plots of log-transformed
ozone values.  Based on these empirical results, we are comfortable with approximate
normality and proceed with inference using ANOVA.

\begin{figure}[ht]
\begin{center}
\includegraphics[width=3in,height=3in]{CFRIeg1-histtransf}
\includegraphics[width=3in,height=3in]{CFRIeg1-qqtransf}
\caption{Histogram of log transformed ozone.}
\label{transf}
\end{center}
\end{figure}

<<>>=
lm.out <- lm(log(Ozone)~as.factor(Month),data=airquality)
summary(lm.out)
@

By default, comparisons are performed relative to May ozone levels, 
the first level of the factor.  Suppose we'd like to perform all 
pairwise comparisons.  Table \ref{pairwise} shows p-values associated 
with all pairwise comparisons of ozone levels across months.

<<contrasts,echo=FALSE,results=hide>>=
#MAY COMPARISONS
p.may.june <- summary(lm.out)$coefficients[2,4]
p.may.july <- summary(lm.out)$coefficients[3,4]
p.may.aug <- summary(lm.out)$coefficients[4,4]
p.may.sep <- summary(lm.out)$coefficients[5,4]
#JUNE COMPARISIONS
library(gmodels)
contrast.june.july <- estimable(lm.out, c(0, 1, -1, 0, 0))
p.june.july <- contrast.june.july$Pr

contrast.june.aug <- estimable(lm.out, c(0, 1, 0, -1, 0))
p.june.aug <- contrast.june.aug$Pr

contrast.june.sep <- estimable(lm.out, c(0, 1, 0, 0, -1))
p.june.sep <- contrast.june.aug$Pr
#JULY COMPARISONS
contrast.july.aug <- estimable(lm.out, c(0, 0, 1, -1, 0))
p.july.aug <- contrast.july.aug$Pr

contrast.july.sep <- estimable(lm.out, c(0, 0, 1, 0, -1))
p.july.sep <- contrast.july.sep$Pr

#AUGUST COMPARISONS
contrast.aug.sep <- estimable(lm.out, c(0, 0, 0, 1, -1))
p.aug.sep <- contrast.aug.sep$Pr
@

\begin{table}
\caption{All pairwise comparisons.}
\begin{center}
\begin{tabular}{rccccc} \\ \hline
Month &May &June &July &August &September \\ \hline
May &&\Sexpr{round(p.may.june,3)} &\Sexpr{round(p.may.july,3)} 
&\Sexpr{round(p.may.aug,3)} &\Sexpr{round(p.may.sep,3)} \\
June &\Sexpr{round(p.may.june,3)} &&\Sexpr{round(p.june.july,3)} 
&\Sexpr{round(p.june.aug,3)} &\Sexpr{round(p.june.sep,3)}\\
July &\Sexpr{round(p.may.july,3)} &\Sexpr{round(p.june.july,3)} 
&&\Sexpr{round(p.july.aug,3)} &\Sexpr{round(p.july.sep,3)}\\
August &\Sexpr{round(p.may.aug,3)} &\Sexpr{round(p.june.aug,3)} 
&\Sexpr{round(p.july.aug,3)} &&\Sexpr{round(p.aug.sep,3)}\\
September &\Sexpr{round(p.may.sep,3)} &\Sexpr{round(p.june.sep,3)} 
&\Sexpr{round(p.july.sep,3)} &\Sexpr{round(p.aug.sep,3)} & \\ \hline
\end{tabular}
\end{center}
\label{pairwise}
\end{table}

\section{Source code for this report}
\verbatimtabinput{Sweave_example.Rnw}

\end{document}