StatsOneWeek1.tex

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\begin{document}
\tableofcontents
\newpage
%------------------------------------------------------%
\section{Statistics One -Lecture Topics}

\begin{description}
\item [Lecture 1:] Experimental research 

\item [Lecture 2:] Correlational research 

\item [Lecture 3:] Variables, distributions, and scales 

\item [Lecture 4:] Summary statistics 

\item [Lecture 5:] Correlation 

\item [Lecture 6:] Measurement 

\item [Lecture 7:] Introduction to regression 

\item [Lecture 8:] Null hypothesis significance testing 

\item [Lecture 9:] The central limit theorem 

\item [Lecture 10:] Confidence intervals

\item [Lecture 11:] Multiple regression 

\item [Lecture 12:] The general linear model

\item [Lecture 13:] Moderation 

\item [Lecture 14:] Mediation 

\item [Lecture 15:] Student’s t-test 

\item [Lecture 16:] Analysis of variance (ANOVA) 

\item [Lecture 17:] Factorial ANOVA 

\item [Lecture 18:] Repeated measures ANOVA 

\item [Lecture 19:] Chi-square tests

\item [Lecture 20:] Binary logistic regression 

\item [Lecture 21:] Assumptions revisited

\item [Lecture 22:] Non-parametric statistics 

\item [Lecture 23:] Generalized linear model 

\item [Lecture 24:] Course summary
\end{description}


 
%------------------------------------------------------%
\section{Statistics One - Lab Topics}

\begin{description}
\item[ Lab 1:] Introduction to R 

\item[ Lab 2:] Histograms and summary statistics           

\item[ Lab 3:] Scatterplots and correlations          

\item[ Lab 4:] Regression 

\item[ Lab 5:] Confidence intervals 

\item[ Lab 6:] Multiple regression 

\item[ Lab 7:] Moderation and mediation 

\item[ Lab 8:] Group comparisons (t-tests, ANOVA, post-hoc tests) 

\item[ Lab 9:] Factorial ANOVA 

\item[ Lab 10:] Chi-square 

\item[ Lab 11:] Non-parametric tests 

\item[ Lab 12:] Non-linear regression
\end{description}
%------------------------------------------------------%
\newpage
\section{Statistics One - Week 1}
\subsection{Using Packages}

\begin{itemize}
\item \texttt{install.packages()}
\item \texttt{library()}
\end{itemize}

Suppose we wish to use the \textbf{\emph{caret}} package for some statistical analyses.
As this package is not part of the base \texttt{R} installation, we must install it. 
We use the \texttt{install.packages()} command to perform this operation. (N.B. notice the use of the plural packages,as this function may be used for downloading several packages simultaneously, and also the use of the quotation marks.)
\bigskip

Some options will be presented to the user, in particular, the choice of CRAN mirror. 
Simply select the mirror of the country you are in, or nearest too.
\bigskip

Some packages require the last version of \texttt{R} to be installed. This problem is usually avoided by regularly updating your version of \texttt{R} on an ongoing basis.
\bigskip

The package may be installed on your PC, but that does not mean that \texttt{R} may use that package. The package must be called using the \texttt{library()} command (this time not using quotation marks)


\begin{framed}
\begin{verbatim}
install.packages("caret")
library(caret)
\end{verbatim}
\end{framed}


\subsection{What packages are avaiulable?}
Q3 : What should you type in the R console to check what packages you have installed and loaded on your computer?

To check what packages you have installed and \textbf{loaded} on your computer, you would use the \texttt{search()} command, with no additional arguments.

\begin{framed}
\begin{verbatim}

library()
installed.packages()
search()
\end{verbatim}
\end{framed}

\begin{verbatim}
> search()
 [1] ".GlobalEnv"        "package:nlme"      "package:stats"    
 [4] "package:graphics"  "package:grDevices" "package:utils"    
 [7] "package:datasets"  "package:methods"   "Autoloads"        
[10] "package:base" 
\end{verbatim}




\subsection{Getting Help}
The command to get help about an object, data set or function is simply \texttt{help()}.
%Q4 : What should you type to get help about the “data.frame” function?

\begin{framed}
\begin{verbatim}
help(sort)
help(list)
help(iris)

?sort
?list
?iris
\end{verbatim}
\end{framed}
\subsection{Sequences}

\begin{framed}
\begin{verbatim}
1:10
seq(1,10)
10:20
seq(1,10,length=3)
seq(1,10,by=1.5)
\end{verbatim}
\end{framed}

\begin{verbatim}
> 1:10
 [1]  1  2  3  4  5  6  7  8  9 10
> seq(1,10)
 [1]  1  2  3  4  5  6  7  8  9 10
>
> 10:20
 [1] 10 11 12 13 14 15 16 17 18 19 20
> 20:10
 [1] 20 19 18 17 16 15 14 13 12 11 10
>
> seq(1,10,length=3)
[1]  1.0  5.5 10.0
> seq(1,10,by=1.5)
[1]  1.0  2.5  4.0  5.5  7.0  8.5 10.0
\end{verbatim}

\subsection{data Frames}
Q5 : Create two vectors, the first one named "numbers" including all natural numbers from 1 to 10, and the second one named "words" containing the following series:"One", "Two", "Three", "Four", "Five", "Six", "Seven", "Eight", "Nine", "Ten". 

\begin{framed}
\begin{verbatim}
words <-c("One", "Two", "Three", "Four", "Five", "Six", "Seven", "Eight", "Nine", "Ten")
\end{verbatim}
\end{framed}
From these two vectors, create a dataframe "nw" with each vector as a separate column. What should you type to check the attributes of "nw"?

\subsection{attributes of a data frame}

The \texttt{attribute()} function can  access an object's attributes, and returns the object's attribute list. The following code demonstrates how to obtain details on attributes for the iris and Titanic data sets.
\begin{framed}
\begin{verbatim}
attributes(iris)
attributes(Titanic)

\end{verbatim}
\end{framed}
The output for the Titanic data set should look like this.
\begin{verbatim}
> attributes(Titanic)
$dim
[1] 4 2 2 2

$dimnames
$dimnames$Class
[1] "1st"  "2nd"  "3rd"  "Crew"

$dimnames$Sex
[1] "Male"   "Female"

$dimnames$Age
[1] "Child" "Adult"

$dimnames$Survived
[1] "No"  "Yes"

$class
[1] "table"
\end{verbatim}
\newpage
%-----------------------------------------------------------------%
\subsection{Accessing Cells Rows and Columns of a data frame}
Q6 : Question 6
What command should you type to get R to return the number “8” from the dataframe "nw"?

Question 7
What command should you type to get R to return the word “eight” from the dataframe "nw"?

\subsection{Matrices}
Question 8
%What should you type to create a matrix “a” comprising all natural numbers from 1 to 10, with 2 rows and 5 columns.

In this following example, we will 
create a matrix Mat1 comprising all natural numbers from 1 to 12 in order, structured with 2 rows and 5 columns.

\begin{verbatim}
dozen <- 1:12
Mat1 <- matrix(dozen, nrow=2)

Mat2 <- matrix(1:12, ncol=4)
\end{verbatim}


%------------------------------------%
\newpage
\subsection{Combining Vectors}

\begin{itemize}
\item \texttt{rbind()} combine several vectors by row
\item \texttt{cbind()}  combine several vectors by column
\end{itemize}

%Question 9
Create a vector "x" comprising all natural numbers from 1 to 6 and another vector "y" comprising all natural numbers from 5 to 10. What should you type to combine them in a matrix of 2 rows and 6 columns?
%Question 10
Create a vector "x" comprising all natural numbers from 1 to 6 and another vector "y" comprising all natural numbers from 5 to 10. What should you type to combine them in a matrix of 6 rows and 2 columns?

\begin{framed}
\begin{verbatim}
x <- 1:6
y <- 5:10

cbind(x,y)
rbind(x,y)
\end{verbatim}
\end{framed}
%---------------------------------------------------%
\begin{verbatim}
> cbind(x,y)
     x  y
[1,] 1  5
[2,] 2  6
[3,] 3  7
[4,] 4  8
[5,] 5  9
[6,] 6 10
>
> rbind(x,y)
  [,1] [,2] [,3] [,4] [,5] [,6]
x    1    2    3    4    5    6
y    5    6    7    8    9   10
\end{verbatim}


%-----------------------------------------------%


%-------------------------------------------------------------%
\section{Statistics One - Week 2 Exercise}

\subsection{Inspecting a Data frame}
%Question 1
How many rows of data are in the data file?
Answer for Question 1

\subsection{Column names}
%Question 2
What is the name of the dependent variable?
Answer for Question 2

\subsection{The summary of a dataframe}
%Question 3
What is the mean of SR across all subjects?
Answer for Question 3

\subsection{Using the psych package}
%Question 4
What is the variance of SR across all subjects?
Answer for Question 4

%Question 5
What is the mean of SR for all subjects at pretest?
Answer for Question 5

%Question 6
What is the standard deviation of SR for all subjects at posttest?
Answer for Question 6

%Question 7
What is the median of SR for all subjects at posttest?
Answer for Question 7

\subsection{groups}
%Question 8
Which group has the highest mean at posttest?
Answer for Question 8

\subsection{Testing Normality}

\begin{itemize}
\item QQ-plots
\item Skew and Kurtosis
\end{itemize}

%Question 9
Which one best approximates a normal distribution?
- WM group at pretest
- WM group at postest
- PE group at pretest
- PE group at posttest
- DS group at pretest
- DS group at postest

Question 10
Which group showed the biggest gains in SR?
Answer for Question 10



\end{document}