tapply.txt

\subsection{A Quick remark about Logic Values}
Why use TRUE/FALSE and not T/F in \texttt{R} programming?
\begin{verbatim}
> # Why use TRUE/FALSE and not T/F in #RStats?
> x<-1:2
> x[c(T,F)]
[1] 1
> F<-TRUE
> x[c(T,F)]
[1] 1 2
\end{verbatim}

X <- rnorm(100,mean=100,sd=15)

Grp1 <- gl(4,10,labels=c("A","B","C","D"))
Grp2 <- gl(4,1,40,labels=c("W","X","Y","Z"))

\begin{verbatim}
> Grp1 <- gl(4,10,labels=c("A","B","C","D"))
> Grp2 <- gl(4,1,40,labels=c("W","X","Y","Z"))
>
> Grp1
 [1] A A A A A A A A A A B B B B B B B B B B C C C C C C C
[28] C C C D D D D D D D D D D
Levels: A B C D
> Grp2
 [1] W X Y Z W X Y Z W X Y Z W X Y Z W X Y Z W X Y Z W X Y
[28] Z W X Y Z W X Y Z W X Y Z
Levels: W X Y Z
>
> table(Grp1,Grp2)
    Grp2
Grp1 W X Y Z
   A 3 3 2 2
   B 2 2 3 3
   C 3 3 2 2
   D 2 2 3 3
> 
\end{verbatim}


\begin{framed}
\begin{verbatim}

X <- rnorm(100,mean=100,sd=10)
GrpA <- gl(4,25,labels=c("A","B","C","D"))
GrpB <- gl(4,1,100,labels=c("W","X","Y","Z"))

DF <- data.frame(Score=X,GrpA=GrpA,GrpB=GrpB)

attach(DF)
aggregate(Score,by=list(GrpA,GrpB),mean)
\end{verbatim}
\end{framed}


%------------------------------------------------------------------%
\subsection{Correlation with Missing Values}
To compute the correlation coefficient, the command is simply \texttt{cor()}, specifying the name of the variables.

\begin{verbatim}
>  # mtcars data set is attached
>  # attach(mtcars)
> cor(hp,wt)
[1] 0.6587479
\end{verbatim}
Importantly there are no missing values in the mtcars data set. Suppose you are trying to compute the correlation
coefficient when some values are missing. Running the function would result in an "NA" value (see code below).

If the argument \texttt{use} has the value "pairwise.complete.obs" then the correlation or 
covariance between each pair of variables is computed using all \textbf{complete} pairs 
of observations on those variables. 


\begin{framed}
\begin{verbatim}
attach(airquality)

cor(Ozone,Wind) # NA as answer
cor(Ozone,Wind,use = "pairwise.complete.obs")
cor(Ozone,Wind,use = "complete.obs")

detach(airquality)
\end{verbatim}
\end{framed}

\begin{verbatim}
> cor(Ozone,Wind) # NA as answer
[1] NA
> cor(Ozone,Wind,use = "pairwise.complete.obs")
[1] -0.6015465
> cor(Ozone,Wind,use = "complete.obs")
[1] -0.6015465

\end{verbatim}


%------------------------------------%
\subsection{Simple Frequency Tables}
\begin{verbatim}
> attach(mtcars)
> table(vs)
vs
 0  1 
18 14
> 
> table(vs,am)
   am
vs   0  1
  0 12  6
  1  7  7
\end{verbatim}
%------------------------------------%
\begin{framed}
\begin{verbatim}
#attach the mtcars data set
#save a lot of typing.

attach(mtcars)
tapply(hp,cyl,mean)
\end{verbatim}
\end{framed}


\begin{framed}
\begin{verbatim}
> attach(mtcars)
> tapply(hp,cyl,mean)
        4         6         8 
 82.63636 122.28571 209.21429 

\end{verbatim}
\end{framed}

The mean horsepower for 4 cylinder cars is 82.64cc.
The mean horsepower for 6 cylinder cars is 122.29cc.



%---------------------------------------%
The levels of the \textbf{am} are 0 (i.e automatic) and 1 (i.e. manual)

\begin{framed}
\begin{verbatim}
tapply(hp,list(cyl,am),mean)
\end{verbatim}
\end{framed}

\begin{verbatim}
> tapply(hp,list(cyl,am),mean)
          0        1
4  84.66667  81.8750
6 115.25000 131.6667
8 194.16667 299.5000
\end{verbatim}

Grouping by more than one categorical variable.
\begin{verbatim}
> tapply(hp,list(VS=vs,AM=am),sd)
   AM
VS         0        1
  0 33.35984 98.81582
  1 20.93186 24.14441
\end{verbatim}
%----------------------------------------%
%---------------------------------------%