The inclusion of R codes is a work in progress. Initially I aimed to create resources for the more complex multivariate statistical procedures that I am unable to program myself. Eventually I aim to supplement most programs in StatsToDo with R codes and examples, using resources provided by CRAN if they are available, or to rewrite my programs using R if the progam cannot be found in CRAN. The initiative began in April 2020, so not all algorithms will be accompanied by R codes for some time

The R codes in StatsToDo are basic, simple, and the minimum necessary to conclude an initial analysis. It is aimed to create a shallow learning curve for those with no great statistical experience, to explore his/her data, and to provide the minimum results that are required by most clinical journals for publication. In most cases they merely repeat the programs written in php or Javascript for the web page, and no more than a validation of the algorithm. Most experienced statisticians will find the details provided incomplete, or even insufficient, as the safeguards and complete descriptions of the results are often not provided. Although references will be provided for users to obtain further information and resources. Inexperienced users are strongly urged to seek advice from experienced statisticians before drawing conclusions from the results obtained.

All data in the examples are computer generated, to demonstrate the analysis and interpretation. Although attempts were made to produce results that are plausible and easy to understand, users should realise that the data are artificial and do not represent reality. Given that I had a background in obstetrics, the examples are mostly issues in childbirth and hospitals. The interests are mostly clinical, towards classification, survey, quality control, clinical discovery and trials.

Format

Three colors are used, to clarify the intent of the text

• Maroon color is used to represent R codes
• Navy blue color is used to show results generated by R in the console
• Black is used for explanations and descriptions

All R programs in StatsToDo assume no missing data. How to handle missing data is described in the Missing Data panel of this page

Setting up R and RStudio

RStudio

Anatomy of RStudio :

• The bottom left panel is called the console. we start here because you can analyse data just using the console. Commands can be typed into the console and run interactively. The console is also where the results of calculations (other than graphics) are displayed
• The top left panel is called the source. This is essentially a text editor, where files can be loaded in, edited, and saved. Part or all of the codes in the source can also be marked by the mouse, and on clicking the run button the output will be displayed in the console. Please note that the example codes from this site is intended to be copied and pasted into this source panel, and run from here
• The top right panel is called environment and history. This provides a list of variables and procedures created and run during a session in the console. The idea is that these are saved when exiting RStudio, and reloaded in future sessions to provide continuity. This panel is not used in these pages
• The right bottom panel is called the viewer which contained a number of sub-panels. This is where packages and help can be viewed. Graphical output is also displayed in this panel

Packages

Required packages are included in the example codes. The install.packages("PackageName") command is usually commented out, as once installed it is always available.

The Explanation and resources available for eack package, once installed, can be accessed by the ??"PackageName" command typed into the console

How to use the example codes

1. Activate RStudio
2. Copy and paste the example codes (in Maroon) into the source panel, in the same order that they are presented in the web page
3. Mark the codes and click run at the top right corner of the source panel
4. Check that the program runs as intended
5. Replace example names and data with the user's own
6. Add, delete, or edit codes as appropriate
7. Mark and run again to produce the results required

Help and further information

• help(thesubject) will bring up explanations of the subject in the right bottom panel (help)
• ??packagename will bring up documentation of the package in the right bottom panel (help)

• https://cran.r-project.org/doc/manuals/R-intro.html An Introduction to R from CRAN
• https://cran.r-project.org/doc/contrib/Short-refcard.pdf Reference card cheat sheet for R
• An R Companion for the Handbook of Biological Statistics by Salvatore S. Mangiafico. This is a textbook like site and provides resources for many commonly used statistical procedures in bio-medical statistics
• Summary and Analysis of Extension Program Evaluation in R by Salvatore S. Mangiafico. This is a textbook like site providing resources for the more advanced statistical procedures commonly used in complex data analysis

• R for Dummies by Vries and Meys. John Wiley & Son's Inc. ISBN 978-1-119-05580-9. This is good for the novice with no prior experience of R.
• R Cookbook by Teetor. O'Reilly Media Inc ISBN 978-93-5023-379-5. This takes the user step by step learning how to use and program R, and introduces the basic R resources
• R Graphics Cookbook by Chang. O'Reilly Media Inc ISBN 978-1-449-31695-2. This is an excellent book providing detailed instructions on how to do graphics using R

Dataframe

The first step in any analysis is therefore converting the table of data into a dataframe, which R can then analyse. The standard data table has columns for variables and rows for subjects. The first row containing the name of each column. The table can then be imported into R using one of the following methods

Direct data I/O

myTxt = ("
Col1  Col2  Col2	  
A     1     2
B     3     4
C     5     6
")                       # Example data in text
myDF <- read.table(textConnection(myTxt),header=TRUE)      
                         # Make data frame
#myDF             # Optional show dataframe in console  

• The table, in text, is in between (" and ")
• The first row contains the column names
• The columns are separated by spaces or tabs
• The values of Col1 are text, which R called factors, and those of Col2 and Col3 are numerical. Please Note: the type of values in each column must be consistent.

Files

getwd()
list.files()

Comma delimited (.csv) files

myDF <- read.csv("myCsvIn.csv") 
#myDF  

• myCsvIn.csv is the name of the comma delimited file containing the data table.
• The first line reads the table to the dataframe
• The second line is optional display of the dataframe

write.csv(myDF, "myCsvOut.csv", row.names = FALSE)

• myDF is the name of the dataframe to be saved to the .csv. It should already exist
• myCsvOut.csv is the name of the output comma delimited (.csv) file. User should change this name to one that is appropriate
• If row.names= False is not used, then a first column containing row number will be included
• If the named .csv file pre-exists and is closed, it will be overwritten. Attempt to write to an open file with the same name will fail and flag an error message

Excel worksheet (.xlsx) files

For data input

#install.packages("xlsx")             #use only if the library is not already installed
library("xlsx")     
myDF <- read.xlsx("myXlsxIn.xlsx", sheetName="mySheet")
#myDF                                         

• The xlsx package needs to be already installed once in a computer
• The library xlsx must be called
• myXlsxIn.xlsx is the name of the excel .xlsx file to be read. User should change this to his/her own file name
• mySheet is the name of the worksheet to be read. This can be the name of the sheet, or a number (without the quotes) counting from 1
• When testing, uncomment the last command (remove #) to see if the correct data has been read

lbrary("xlsx")
write.xlsx2(myDF, "myXlsxOut.xlsx", sheetName = "mySheet", 
            row.names = FALSE, append=TRUE)

• The package xlsx must be pre-installed and is called
• myDF is a dataframe to be saved to file, a table with columns and rows.
• myXlsxOut.xlsx is the name of the excel workbook to be saved to. Users should change this to his/her own file name
• mySheet is the name of the sheet to save the data to
• If row.names= False is not used, then a first column containing row number will be included
• If the file pre-exists, it must be closed. Attempt to write to an open file will crash the program
• If the append option is FALSE, any existing file containing a wroksheet with the same name will be overwritten
  If the append option is TRUE and no worksheet with the same name exists, a new worksheet with the name will be created and the data written to it
  If the append option is TRUE and a worksheet with the same name already exists, write to the worksheet will fail and the program crashes

Creating a report of analysis using Knit

Once a set of R codes are tested and found to be satisfactory, at the menu bar on the top of RStudio,

click File->Knit Document
select type of file, msWord is recommended as this is the easiest to edit afterwards

Please note: The knit program is quite temperamental, and have the following problems

• It can be incompatible with some other packages, especially those that read or write to files or produce graphics. The program merely crashes without too much explanation. An example is that knit will crash when trying to read from or write to excel worksheets.
• In some graphics programs, the labeling for the axis may be misplaced or absent in the report file

1:Data Frames and Matrices

Template 1.1: Convert a text fields into a matrix. This is done by firstly import the text field (all columns must be numerical values) into a data frame, then convert the data frame into the matrix

txt = ("
Col1  Col2  Col3	  
7     1     2
8     3     4
9     5     6"
)                       
df <- read.table(textConnection(txt),header=TRUE)      
mx <- data.matrix(df)
colnames(mx) <- NULL    # optional removing column names
mx

> mx
     [,1] [,2] [,3]
[1,]    7    1    2
[2,]    8    3    4
[3,]    9    5    6

txt = ("
Col1  Col2  Col3	  
A     1     2
B     3     4
C     5     6"
)                       
df <- read.table(textConnection(txt),header=TRUE)      
#df              # data frame
mx <- matrix(c(df$Col2,df$Col3), ncol=2)
mx

> mx
     [,1] [,2]
[1,]    1    2
[2,]    3    4
[3,]    5    6

# Input 3. matrix to data frame
#mx = matrix(c(1,2,3,4,5,6,7,8,9,10,11,12),nrow=4)  # alternative method to create matrix
col1 <- c(1,2,3,4)
col2 <- c(5,6,7,8)
col3 <- c(9,10,11,12)
mx <- cbind(col1, col2, col3)
mx         #matrix
# turn matrix into data frame
df = as.data.frame(mx)
df
# add another column to existing data frame
df$col4 <- c(20,21,22,23)             # method 1
df
ar <- c(30,31,32,33)                  # method 2
df$col5 <- ar
df

> df
  col1 col2 col3
1    1    5    9
2    2    6   10
3    3    7   11
4    4    8   12
> # add another column to existing data frame
> df$col4 <- c(20,21,22,23)             # method 1
> df
  col1 col2 col3 col4
1    1    5    9   20
2    2    6   10   21
3    3    7   11   22
4    4    8   12   23
> ar <- c(30,31,32,33)                   # method 2
> df$col5 <- ar
> df
  col1 col2 col3 col4 col5
1    1    5    9   20   30
2    2    6   10   21   31
3    3    7   11   22   32
4    4    8   12   23   33
> 

2:Arrays

# create an array with contents
ar <- c(1,2,3,4)
ar

[1] 1 2 3 4

# Create an array with sequence
start = 1
finish = 10
increment = 2
ar <- seq(start, finish, by=increment)
ar

[1] 1 3 5 7 9

# Create an empty vector
ar <- vector()

# Create vector of defined length
default = 5
siz = 3
ar <- array(default,siz)
ar

[1] 5 5 5

# Operations
ar1 <- c(1,2,3)
ar2 <- c(4,5,6)

# add
ar1 + ar2

[1] 5 7 9

#subtract
ar2 - ar1

[1] 3 3 3

#multiply elements
ar1 * ar2

[1]  4 10 18

# multiply vectors col by row # default is column
ar1 %*% t(ar2)

     [,1] [,2] [,3]
[1,]    4    5    6
[2,]    8   10   12
[3,]   12   15   18

#multiply row by col
t(ar1) %*% ar2

     [,1]
[1,]   32

3:Matrices

#matrix with values
ar <- c(1,2,3,4,5,6)
mx <- matrix(data=ar, nrow=2,ncol=3) #byrow=FALSE is default
mx 
mx <- matrix(data=ar, nrow=2,ncol=3, byrow=TRUE)
mx

> mx <- matrix(data=ar, nrow=2,ncol=3) #byrow=FALSE is default
> mx 
     [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6
> mx <- matrix(data=ar, nrow=2,ncol=3, byrow=TRUE)
> mx
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    4    5    6

# matrix with default value
default = 5
mx <- matrix(data=default, nrow=2,ncol=3)
mx

> mx
     [,1] [,2] [,3]
[1,]    5    5    5
[2,]    5    5    5

#matrix joining two arrays
a1 <- c(1,2,3)
a2 <- c(4,5,6)
mx <- matrix(data=c(a1,a2), nrow=2,ncol=3, byrow=TRUE)
mx
mx <- matrix(data=c(a1,a2), nrow=3,ncol=2)
mx

> mx <- matrix(data=c(a1,a2), nrow=2,ncol=3, byrow=TRUE)
> mx
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    4    5    6
> mx <- matrix(data=c(a1,a2), nrow=3,ncol=2)
> mx
     [,1] [,2]
[1,]    1    4
[2,]    2    5
[3,]    3    6

# rows
mx[1,]
mx[2,]
mx[3,]
#cols
mx[,1]
mx[,2]

> # rows
> mx[1,]
[1] 1 4
> mx[2,]
[1] 2 5
> mx[3,]
[1] 3 6
> #cols
> mx[,1]
[1] 1 2 3
> mx[,2]
[1] 4 5 6

# operations
mx1 <- matrix(c(c(3,5,1,2),c(4,1,3,1),c(2,3,1,1)),nrow=4,ncol=3)
mx1
mx2 <- matrix(c(c(1,2,1),c(2,3,1)),nrow=3,ncol=2)
mx2

> mx1
     [,1] [,2] [,3]
[1,]    3    4    2
[2,]    5    1    3
[3,]    1    3    1
[4,]    2    1    1
> mx2
     [,1] [,2]
[1,]    1    2
[2,]    2    3
[3,]    1    1

# transpose
mx3 <- t(mx1)
mx1
mx3

> mx1
     [,1] [,2] [,3]
[1,]    3    4    2
[2,]    5    1    3
[3,]    1    3    1
[4,]    2    1    1
> mx3
     [,1] [,2] [,3] [,4]
[1,]    3    5    1    2
[2,]    4    1    3    1
[3,]    2    3    1    1

# add
mx1 + mx1

> mx1 + mx1
     [,1] [,2] [,3]
[1,]    6    8    4
[2,]   10    2    6
[3,]    2    6    2
[4,]    4    2    2

# subtract
mx2 - mx2

> mx2 - mx2
     [,1] [,2]
[1,]    0    0
[2,]    0    0
[3,]    0    0

# multiply elements
mx2 * mx2

> mx2 * mx2
     [,1] [,2]
[1,]    1    4
[2,]    4    9
[3,]    1    1

#multiply matrices
mx1 %*% mx2

> mx1 %*% mx2
     [,1] [,2]
[1,]   13   20
[2,]   10   16
[3,]    8   12
[4,]    5    8

#division by elements
mx1 / mx1

> mx1 / mx1
     [,1] [,2] [,3]
[1,]    1    1    1
[2,]    1    1    1
[3,]    1    1    1
[4,]    1    1    1

# transpose
t(mx2)

> t(mx2)
     [,1] [,2] [,3]
[1,]    1    2    1
[2,]    2    3    1

# square matrix
mx <- matrix(c(c(4,2,3,2),c(2,5,3,1),c(3,3,6,2),c(2,1,2,3)),nrow=4,ncol=4)
mx

> mx
     [,1] [,2] [,3] [,4]
[1,]    4    2    3    2
[2,]    2    5    3    1
[3,]    3    3    6    2
[4,]    2    1    2    3

# invert
solve(mx)

> solve(mx)
            [,1]        [,2]        [,3]        [,4]
[1,]  0.50000000 -0.07142857 -0.14285714 -0.21428571
[2,] -0.07142857  0.29591837 -0.12244898  0.03061224
[3,] -0.14285714 -0.12244898  0.32653061 -0.08163265
[4,] -0.21428571  0.03061224 -0.08163265  0.52040816

# Rank
qr(mx)$rank  # uses qr decomposition

[1] 4

# Determinant
det(mx)

> det(mx)
[1] 98

# Eigen values and matrices
eigenResults <- eigen(mx)
eigenResults

> eigenResults
$values
[1] 11.501474  3.143052  2.000000  1.355473
$vectors
           [,1]        [,2]       [,3]        [,4]
[1,] -0.4779381 -0.36246433  0.3779645  0.70522169
[2,] -0.4961149  0.76831305  0.3779645 -0.14390264
[3,] -0.6487310 -0.05918796 -0.7559289 -0.06493346
[4,] -0.3234090 -0.52422462  0.3779645 -0.69118597

#Square root of matrix after obtaining eigen
sr <- eigenResults$vectors %*% diag(sqrt(eigenResults$values)) %*% solve(eigenResults$vectors)
sr

> sr
          [,1]      [,2]      [,3]      [,4]
[1,] 1.7886506 0.3942986 0.6321685 0.4956015
[2,] 0.3942986 2.1073918 0.6176967 0.1479165
[3,] 0.6321685 0.6176967 2.2465112 0.4147301
[4,] 0.4956015 0.1479165 0.4147301 1.6001559

# Validate square root matrix
sr %*% sr

> sr %*% sr
     [,1] [,2] [,3] [,4]
[1,]    4    2    3    2
[2,]    2    5    3    1
[3,]    3    3    6    2
[4,]    2    1    2    3