This lab is expected to be self-paced and make sure that everyone is familiar with R and RStudio. This is a long lab, but we expect that for everyone, parts of this will be review and parts will be new. All of these concepts will continue to be reinforced in future labs.

While we give “Exercises”, nothing needs to be turned in – they are just for checking your understanding. Go at your own pace, and only do the exercises if they add to your understanding. Notice the table of contents on the left-hand side. These will allow you to efficiently navigate through the document, and if you click on one, it will open up into more detailed sub-sections.

Data 8 Students / Python Users For Data 8 students working in R and R Studio will be new. You will find that the basic concepts from python will transfer over, and you just need to concentrate on figuring out the difference in syntax. For those students who are more familiar with python, there are special notes about how R commands compare to python commands that look like this:

Python Users: An example of python note!

If you’re coming from STAT 20, you can ignore the comments and code with a green background.

Stat 20 Students / R users For Stat 20 students this will feel very familiar, but some of the programming concepts, like how to write your own function and for-loops may be new. (Data 8 students will be familiar with these concepts, but should focus on the syntax in R). Please slowly go over these sections and if you are not clear ask for help in lab or do some outside google searches to find further tutorials on these concepts.

For additional R support, see https://epurdom.github.io/Stat131A/RSupport/RResources.html

Getting RStudio

RStudio is an open-source Integrated Development Environment (IDE) which provides many user-friendly features. We will use RStudio throughout the rest of the course. RStudio can be started from the desktop (i.e. your computer) or through logging into a website and accessing a web server. The user interface is generally the same for the two.

We will use the web version for labs, since this makes it easier and quicker to get going during labs – by clicking on the links to the lab we provide you on bcourses, it will necessary additional files for the lab into your workspace.

We give brief instructions below for both methods, but for following this lab (and future labs), you should use the web version. For other assignments, you may find it easier to use RStudio on your own computer. In fact, we strongly recommend for your own convenience that if you have your own computer you should download and install R and do assignments (other than the labs) on your own machine.

Web Version

A RStudio server can be accessed via a web browser for this class. All the data storage and computation are done remotely on the server (similar to what you may have experienced in Data 8 or Stat 20).

Log In

To login in to the server, open the url for this lab here. Once successfully authenticated, you will see the following RStudio interface.

A screen shot of Rstudio on initial startup The files you see in the lower left corner may look different, but you should see the folder “Stat131LabsPublic”. This will be where the necessary files for the lab will be located (e.g. data files, code files, etc.). We will explore this more below.

Desktop Version

The layout looks similar to that of the web version. The installation of R and RStudio is straightforward, just as installing other applications in your computer. We strongly recommend for your own convenience that if you have your own computer, download and install R and do assignments (other than the labs) on your own machine.

To install R on your computer (legally for free!), go to the home website of R https://cran.r-project.org/ and choose the platform (Mac, Windows or Linux) corresponds to your own divice.
After successfully installing R, you can https://www.rstudio.com/products/rstudio/download3/ according to your platform.

Introduction to RStudio

Working Directory

Your working directory is the folder on your computer in which you are currently working. When you ask R to open a certain file, it will look in the working directory for this file, and when you tell R to save a data file or figure, it will save it in the working directory.

Before you start working, please set your working directory to where all your data and script files are or should be stored. You can browse and choose working directory by going to Session -> Set working directory -> Choose directory ... as follows.

For this lab, change your working directory to where the uploaded lab 00 files should be:

Stat131Public -> lab00

After doing this, you should see that the tab in the lower right marked files should show the files that were automatically imported when you clicked on the link to start this session:

These are the files you will be using in this lab, and you can create more during this lab (this is your personal working space…)

Your first command in the console

The main window is the “Console” on left panel. The symbol > is a command prompt. And this is where R evaluate your commands. For example, type the following commands in the console:

a = 1:5
a

You should see something like this:

Your first command in the R console

R print the outputs (except figures) in the console, right below your commands. You might notice that after you excute the command, vector a appears in the upper right environment window. In fact, you can always check all the value of objects you created in the environment window. Now you may try to explore how to execute commands in the console yourself.

Create an Rscript to store your commands.

R allows you to go back to previous commands using up and down arrow in your keyboard. However, often times you would like to store R commands in a file. To do so, you can create an R Script by clicking File -> New File -> R Script with the menu bar in the top. R will create an R script with the file extention .R and the editor window will be invoked. R scripts is a file type that stores only R commands and comments.

Type the same commands from above into the R script.

To run one line or several line of code in an R script, put your cursor in that line or select mulitple lines, and then click the Run botton.

Create an R script

RStudio Layout

The RStudio interface contains several component:

Console window (bottom left)

This is where you can type simple command after the the prompt “>”. R will excute your current command and return the output in this window.

Editor window (top left)

This window will contain the files you are working on, and is hidden on initial startup. This will show you files that you have opened or created. You will want to have separate files where you will save commands for editing and future use.

If you do not have any files open, this editor may not show up (like when you first opened RStudio). You can make this window appear by creating a new document (e.g. with the menu bar in the top File -> New File -> R Script.) or opening a file ( File -> Open file ...). The editor supports multiple file type, including R script, R markdown, R notebooks, and Sweave files.

For example, open the R script example.R in the lab 0 folder (under Stat131APublic/2019Fall/Labs/lab00) and try to run the code (you don’t have to understand the code). You can run the code by either cutting and pasting into the console, or highlighting the code and clicking Run button.

Try adding the following code to the example.R file and running it:

D<-data.frame(a=1:3, b=2:4)

You can also run all the code in the file by clicking on the source button.

The red font with * at the end of the file name shows that the current changes are not saved. While you are working in a file, you should save it frequently to avoid losing data unexpectedly.

Environment / history window (Top right).

In the environment window you can see the data, values and functions you created or loaded. You can view the data by clicking on them. In the example below, if you click the data frame D you created, you can see the data on the editor window. The history window shows the commands which has been excuted.

files/plots/packages/help tabs (Bottom right)

files: By double clicking the file name, you can open files, then view and edit them in the editor. You can upload files from your own device to the server by clicking the Upload botton. To download files from server, check the box before that file and go to More -> Export. This is useful, for example, if you are working on the web server, and then want to move your files to your own computer and work on your desktop version of R.

After changing your working directory, you should see the files that were imported

plot: The plots tab will display the graphs. It allows you to go back to pervious plots (by clicking on the left-arrow icon) and export plot as image or pdf. If you highlight the following code and click Run you should see a histogram come up in this tab.

C=rnorm(1000)
hist(C)

packages: install and load packages.
help: search and view the help document.

Packages

R can do many statistical and data analyses. They are organized in packages.

To get a list of all installed packages, go to the packages window or type library() in the console window. If the box in front of the package name is ticked, the package is loaded (activated) and can be used.

To install a package to your computer For example, if we want to install a package named ggplot2, click install packages in the packages window and type ggplot to search and install. Or you can type install.packages("ggplot2") in the console.
To load an installed package for current use Once a package is installed, you have to “load” it to you current working environment in order to be able to actually use it. You can check box in front of geometry or type library("geometry") in the command window.

Python Users: In python you would bring in modules with the command import to bring in other code; packages or libraries are the equivalent idea in R, and the command library is like that of import. A big difference is that in python you can also use import to bring in arbitrary code that you have written that is saved in a script file (e.g. functions you have written and saved in a .py file). In R the library command is only for bringing in bundled packages; this means mean code that has been developed and distributed in a particular format and has been installed into your R system on your computer. To read in arbitrary code in a script .R file you would use the function source.

Introduction to R Markdown

While R Scripts contains only R code, R Markdown enable us to create dynamic documents with embedded chunks of R code. Meaning you can write text and also have code that you want to describe in the same document. The R Markdown document can be converted to other formats such as HTML and PDF to have a “published” version. So you can develop a published report with the code embedded within it, ensuring that you can always recreate your work. This is opposed to, for example, cutting and pasting figures or results into a text editor like Word.

Python Users: The relationship between R Scripts (*.R) and R Markdown (*.Rmd) is similar to the relationship between Python scripts (*.py) and IPython Notebooks (*.ipynb).

To create an R Markdown file, click on File -> New File -> R Markdown. You should now see a dialog as shown below. Select ‘Document’ in the left panel and fill in title and author field and hit ‘OK’.

You should now have a document which looks like this:

RStudio has already populated the file with example text and code to get you started (which you would obviously delete for a real assignment). The code is contained within “chunks”, which start with ```{r} and end with ``` (each on their own line):

Extra options can be added in the ```{r} code. In the above example, this code chunk has been given a descriptive name (“cars”), via ```{r cars}

To add new code chunks into the document, click in the document where you want the code chunk to go and click add chunk icon . Try to add a code chunk after the “cars” chunk that is already there. It should look like this

Add the following code into your chunk,

a=c(pi, 2, 4)
b=1:3
a>b

so that it looks like this

Running code

If you click on the run icon at the top right of the chunk (green triangle), the entire chunk will be run and the output will either show the results below

or will show them in the console which look like this:

Python Users: Beneath the code is similar to how IPython notebooks work

You can change between these two options under the “gear” button:

Similar as in R script file, you can instead run one or several lines of code from the R Markdown. To run several lines of code, You may select a piece of code as follows:

Click Run and get a drop-down menu about what you want to run (there are simple key short-cuts that will show up there, but they differ on different operating systems).

Publishing (compiling) your document

To generate an HTML file of the entire document, click on the icon .

It should generate the HTML in the same folder as the R Markdown file.

The above code chunk will look as follows in the HTML file:

Compiling the entire document will run all the commands from the beginning in a fresh environment. You will often discover mistakes when you do this, even if you think you have been testing your code interactively the whole time. Running everything fresh ensures that you have reproducible code, meaning someone else can start with just this document and recreate everything you show in your report.

For example, suppose your code ran fine, you changed something, but didn’t hit run. Or if you move a chunk around and don’t realize that you moved it after another chunk that depends on the results of that chunk – if you run the chunks in the right order, you won’t get an error. But when you compile it from top to bottom, it won’t work.

You should always give yourself time to test your assignment before the due date. Furthermore, it is wise as you finish one section/question of your assignment to compile the entire document and see if you get what you expect, rather than waiting until you are completely finished.

Please refer to an introduction of Markdown Basics on how to add headers, lists and images on the markdown file and generally formatting your text.

R Notebooks (optional)

You also have an option to create a R notebook. R notebooks create a R markdown file on your computer so they’re not so different, but R Studio treats them a little bit differently.

Create a new R Notebook (under File/New… again). It should create a file that again is populated with example code. Go to the first chunk (plot(cars)) and hit the Run triangle for that chunk. You should see the plot appear under the code:

When you when save this notebook, it will save both the .Rmd file and also a html file with extension .nb.html.

You can see this file by going to the “Preview” button at the top (which will force you to save the file)

In the Viewer tab, you should see a html come up with the results. You can see the code and plot below, and this html has the option to hide your code.

This html file is not like the html file from our simple R markdown from before. Before, with a simple R markdown, when we “knit” our .Rmd file, it reran all of our code from scratch and created a html of the output. This means that all the code has to be able to run in sequence correctly.

With the .nb.html that is created, it is just a html file that mimics what actually have on your screen, namely the output of the chunk when it was last run by you in your editor is displayed.

Add the following code to your R notebook below the plot code but don’t run it

a=1:3
a<1

If you hit the preview button, you can scroll down and see this new code, but the actual results will not show:

If you do run the code and hit preview, you’ll see the results now show up:

This can be convenient to be able to see (and save) exactly where you are in terms of what you have tested and run. It is also much quicker than compiling the whole document if you just want to quickly see how the html (i.e. text) will look at the end. It also allows a preview, even if part of your code isn’t finished.

Warning But it also means that you could have broken code that you haven’t run and this preview will not let you know that.

So while this preview can be handy, you still need to be able to compile it completely from scratch to know that everything works. The preview button has a drop down menu that gives you the option to do this (i.e. compile them like standard .Rmd documents)

By clicking “Knit to html” (or pdf) you can make sure the entire thing compiles fresh from the beginning (which is what we will do in testing that your code works).

A Note on This Lab

This tutorial is compiled from a Rmarkdown document, but is a little bit complicated as an introduction to Rmarkdown because of the screenshots and python comments that we have added.

In future labs, your labs will be Rmarkdown documents. You will open them up and interact with the code directly in the Rmarkdown file we have given you as part of the lab. You will turn in your modified Rmarkdown, along with a compiled pdf version as your solution to gradescope.

But for this lab (where you do not need to turn in anything), you will need to cut and paste (or type!) the commands from the html version of this lab into your console.

Introduction to R language

In what follows, we will move away from Rmarkdown, and just show you the R code. You can type this directly into the console, or (better!) use the R script document we were working with above.

Assigning values

Here we do a simple assignment of a number to a variable called val:

val <- 3
print(val)

## [1] 3

Val <- 7 # case-sensitive!
print(Val)

## [1] 7

print(val)

## [1] 3

Val-val #you don't really need the print statement

## [1] 4

Notice the assignment operator <-, which consists of the two characters < (“less than”) and - (“minus”), and must be strictly side-by-side and ‘point’ to the object receiving the value of the expression. R expression is case sensitive, which means A and a are different symbols and would refer to different variables.

The = operator can be used as an alternative (like in python).

val = 3
print(val)

## [1] 3

Val = 7 # case-sensitive!
print(Val)

## [1] 7

You can use either one, and you should be comfortable reading code with either one.

Arithmetic Operators

Let’s learn basic arithmetic operators

Python Users: While in Python we import math or numpy packages to do calculations such as square root and log, in R these are built-in functionalities and can be applied directly.

# add numbers
2 + 3

## [1] 5

# powers
3^4

## [1] 81

# square root
sqrt(4^4)

## [1] 16

# 21 mod 5
21 %% 5

## [1] 1

# take log
log(10)

## [1] 2.302585

# exponential
exp(2)

## [1] 7.389056

# mathematical constant pi
2*pi

## [1] 6.283185

# absolute value
abs(-2)

## [1] 2

# scientific notation
5000000000 * 1000

## [1] 5e+12

# scientific notation
5e9 * 1e3

## [1] 5e+12

Python Users: The following would be the corresponding code in python for these arithmetic operations:

# python code:
import math
import numpy as np

print(2 + 3) # add numbers
print(3**4) # powers
print(pow(3, 4)) # powers
print(math.sqrt(4**4)) # functions
print(21 % 5) # 21 mod 5
print(math.log(10)) # take log
print(math.exp(2)) # exponential
print(np.abs(-2)) # absolute value
print(2*math.pi) # mathematical constant

# scientific notation
print(5000000000 * 1000)
print(5e9 * 1e3)

Exercise 1. You’ve seen the probability density function of Normal distribution $N(\mu, \sigma^2)$ in Data8 or Stat 20 as follows:

\[p(x)=\frac{1}{\sqrt{2\sigma^2\pi}}\exp{-\frac{(x - \mu)^2}{2\sigma^2}}\]

Now let $\mu = 1$, $\sigma^2 = 2$, and calculate the value of the density function at $X = 0$. Finish the chunk below

mu <- 1
sig.sq <- 2
x <- 0
# insert code here to calculate this value

You can check that you got the right answer by making sure that it is the same as the following (built-in) function in R that calculates this quantity:

dnorm(0, mean=1, sd=sqrt(2))

## [1] 0.2196956

Data Types

R has similar data types as in python: numeric values, integer values, characters (i.e. strings), and logicals (i.e. booleans or TRUE/FALSE).

Python Users: In R the boolean value is TRUE or FALSE (all caps), while in Python it would be True or False

In R we can generally test what something is using functions like is.X

is.numeric("my name is")

## [1] FALSE

is.character("my name is")

## [1] TRUE

is.numeric(5)

## [1] TRUE

is.integer(5) #This is false! you have to specify values to be integers, other wise they are saved as numeric (i.e. decimal valued)

## [1] FALSE

is.character(TRUE)

## [1] FALSE

is.logical(TRUE)

## [1] TRUE

Relational operators and logical operators

Logical values generally arise from comparisons. Here we will review operators for comparing values in R.

The basic numerical comparisons are <, <=, >, >=. To do put together multiple comparisons we can require both logical statements to be true (&) or at least one (|)

Python Users: In python, the equivalent of & is and and of | would be or, i.e. python uses the words for these operations.

(1 > 0) & (3 <= 5)

## [1] TRUE

(1 < 0) | (3 > 5)

## [1] FALSE

(3 == 9/3) | (2 < 1)

## [1] TRUE

!(2 != 4/3)

## [1] FALSE

Python Users: The above would be the corresponding code in python for these logical operations:

print((1 > 0) and (3 <= 5))
print((1 < 0) or (3 > 5))
print((3 == 9/3) or (2 < 1) )
print(not(2 != 4/3))

Exercise 2 We want to use R and the function dnorm that evaluates the normal density to answer the following questions. Recall that dnorm(x,mean=1,sd=2) is the value of the normal density with mean 1 and standard deviation 2 evaluated at x.

The density of N(1,2) is larger than the density of N(0,2) at X=0. Assign your TRUE/FALSE answer to variables result1.
The density of N(1,2) at X=0 is larger than 0.2 and less than 0.3. Assign your TRUE/FALSE answer to variables result2.

mu1 <- 1
mu2 <- 0
sig.sq <- 2
x <- 0
# Add code with result saved as `result1`

# uncomment to print annswer
# print(result1)

# Add code with result saved as `result2`

# uncomment to print annswer
# print(result2)

Vectors

Vectors store a series of values that are of the same data type in R.

There are several ways to create an vector in R.

You can enter in comma-separated values with the function c

# set up a vector
a <- c(0.125, 4.75, -1.3)
a

## [1]  0.125  4.750 -1.300

Python Users: In python this would be equivalent to:

a = [0.125, 4.75, -1.3]
#Or a numpy array
a = np.array([0.125, 4.75, -1.3])

We can also use c to combine together existing vectors

# set up another vector
b <- c(0, 1, -1, pi, exp(1))
b

## [1]  0.000000  1.000000 -1.000000  3.141593  2.718282

newVector <- c(a, b)
newVector

## [1]  0.125000  4.750000 -1.300000  0.000000  1.000000 -1.000000  3.141593
## [8]  2.718282

Python Users: In python this would be equivalent to

a = [0.125, 4.75, -1.3]
b = [0, 1, -1, math.pi, math.e]
print([a, b])
print(np.concatenate((a,b)))

Vectors can also hold logical or character values

bools <- c(TRUE, FALSE, TRUE)
bools

## [1]  TRUE FALSE  TRUE

mystring <- c("Hello", ",", " ", "world", "!")
mystring

## [1] "Hello" ","     " "     "world" "!"

If we have a vector of strings, we can put them together into a single string (concatenate them) with the function cat or the function paste to have finer control of how we combine them (cat always puts a space between each value)

cat(mystring)

## Hello ,   world !

paste(mystring,collapse="")##i.e. put nothing between the values

## [1] "Hello, world!"

Creating sequences with `seq`

The function seq generates sequences of numbers with a similar pattern. Usually it has three parameters: from, to, and by, which stands for the starting value, ending value and increment of the sequence.

seq1 <- seq(from=4, to=9, by=1)
seq1

## [1] 4 5 6 7 8 9

seq2 <- seq(1.1, 11.1, by = 2)
seq2

## [1]  1.1  3.1  5.1  7.1  9.1 11.1

Python Users: Notice the difference with np.arange, where then end value given to np.arrange (given by stop) is one past the value you want:

>>> np.arange(start=4,stop=10,step=1)
 array([4, 5, 6, 7, 8, 9])

You can also write function seq(from=a, to=b, by=1) as a:b

seq3 <- 1:6
seq3

## [1] 1 2 3 4 5 6

Getting Help More parameters are available for seq – how to figure out how to use them? R provides easy accessible documents to search for help for functions, datasets and packages. Before asking others for help, it will always be helpful to read the documents. Documentation for a function usually includes description, usages, arguments and examples. For example, there are two ways to access the document of the function seq: ?seq and help(seq).

Exercise 3 To create a vector with replicates, we usually use rep as follows. Look at the documentation of rep and figure out what these arguments do

seq4 <- rep(4, times=6)

seq5 <- rep(1:2, times=5)

seq6 <- rep(1:2, each = 5)

Vectorized calculations

In R, mathematical operations on vectors are usually done element-wise, meaning the operation is done on each element of the vector.

Let $x=(x_1,x_2,\ldots,x_n$ and $y=(y_1,y_2,\ldots,y_n)$ Then x*y will return the vector \[(x_1 y_1, x_2 y_2,\ldots,x_n y_n)\]

Note: For those that are familiar with vector operations this means that x*y for vectors in R is NOT the inner product, but element wise, and ditto for matrices.

And it’s similar for other operators. Look at how these mathematical operations work on vectors:

vec1 <- 1:5
vec2 <- seq(0.1, 0.5, by = 0.1)
vec1 + vec2

## [1] 1.1 2.2 3.3 4.4 5.5

vec2^vec1

## [1] 0.10000 0.04000 0.02700 0.02560 0.03125

vec1 > vec2

## [1] TRUE TRUE TRUE TRUE TRUE

vec1 < 5 & vec2 > 0.3

## [1] FALSE FALSE  TRUE  TRUE FALSE

vec1 < 5 | vec2 > 0.3

## [1] TRUE TRUE TRUE TRUE TRUE

Exercise 4

Create the following vectors.

vec1: (20, 18,…, 2, 0)

# Insert code here

vec2: $(2, \frac{2^2}{2}, \frac{2^3}{3}, \cdots, \frac{2^{10}}{10})$”

# Insert code here

vec3: A True/False vector indicating which element in vec2 is larger than 10 and less than 50.

# Insert code here

vec4: $(2, 4, 5, 2, 4, 5, \cdots, 2, 4, 5, 2)$, where there are 11 occurrences of 2 and 10 occurrences of 4 and 5.

# Insert code here

vec5 = (1, 1,…, 1, 2, 2, …, 2, …, 10, 10, …, 10) where there are 5 occurrences of each number from 1 to 10.

# Insert code here

Indexing and subsetting Vectors

Python Users: Python and R have similar subsetting options, but have small differences in indexing for which you should take care! Please read this carefully!

Let’s use a integer vector example to show the differences.

You can retrieve elements based on their position in the vector, starting with the first element being 1

vector1 <- 8:17
# the first element 
vector1[1]

## [1] 8

vector1[10]

## [1] 17

Python Users: R starts at 1 while Python starts at 0. In python you would say vector1[0] to get the first element and vector1[9] to get the 10th value of the vector

A negative index value means to remove that element

vector1[-1]

## [1]  9 10 11 12 13 14 15 16 17

Python Users: Python uses negative indexing differently. For example, somevector[-1] refers to the last element of the vector. However, negative index in R returns the vector with indicated elements DELETED. In python the R code above would be give the last element, not delete the first one:

>>> vector1[-1]
10

You can get a range of values using the a:b notation

vector1[3:6]

## [1] 10 11 12 13

Python Users: When subsettting an vector using a:b, R subsets b-a+1 (i.e. includes all of the elements a through b) elements while Python takes out b-a elements (includes elements a+1 through b). In python you would need to do vector1[2:6] to get these same values.

Further subsetting

You can subset using non-consecutive integer vectors in the same way

# pull out the 1st and 5th elements of the vector
vector1[c(1, 5)]

## [1]  8 12

Python Users: In python you would do vector1[[0, 4]] to get these same values.

And using negative indices works the same way for vectors – this example removes the 1st and 5th element

# subsetting, noting (1, 5) here indicating the index instead of the values.\n",
vector1[-c(1, 5)]

## [1]  9 10 11 13 14 15 16 17

You can also subset based on logical values as well, meaning if you have a logical vector of the same length as another vector, you can use it to subset to only the TRUE values of your vector.

mylogical<-c(rep(TRUE, 3), rep(FALSE, 3), rep(TRUE, 4))
vector1[mylogical]

## [1]  8  9 10 14 15 16 17

Since vector1 > 5 creates a logical vector, I can use this to pull out entries of my vector greater than 5

# indexing using boolean operators
vector1[vector1 > 5]

##  [1]  8  9 10 11 12 13 14 15 16 17

Python Users: In python you would do similar indexing, vector1[vector1>5]

Alternatively, you can also find the indices of the vector that satisfy the logical using the which function. Here I find which of my vector values are even using %%

whEven<-which(vector1 %%2 ==0)
print(whEven)

## [1] 1 3 5 7 9

I can then index with this vector of indices

vector1[whEven]

## [1]  8 10 12 14 16

Note that I don’t have to have unique indices – I repeat the indices to get replicates of the values of the vector:

vector1[c(3,3,2,1,4,2,2)]

## [1] 10 10  9  8 11  9  9

The same indexing method works when assigning values, namely you can assign values to only a subset of the vector.

vector1 <- 1:10
vector1[1] <- 5
vector1[3:6] <- c(8, 8, 8, 8)
vector1

##  [1]  5  2  8  8  8  8  7  8  9 10

You can also give names to each entry of your vector

vector1<-1:3
names(vector1)<-c("A","B","C")
vector1

## A B C 
## 1 2 3

I can then subset the vector by a vector of characters giving the names I want

vector1["A"]

## A 
## 1

vector1[c("B","C")]

## B C 
## 2 3

Some basic functions on vectors

Random sampling: We can sample with and without replacement with the function sample. We give the function a vector of values we want to sample from, the size of the sample we want, and whether we want to sample with or without replacement. We also use the argument set.seed so that in fact our random numbers will be the same every time we rerun this code, rather than varying.

# Can put any arbitrary integer in set.seed and the random code that follows will always be the same:
set.seed(27489)
# random sample 10 number from integers 1 to 10.
x<-1:100
# WITH replacement
samples <- sample(x, size=500, replace = TRUE)
# WITHOUT replacement
sample.withoutrep <- sample(x, size=10)

The length of a vector

length(samples)

## [1] 500

Simple summary statistics of the data stored in a vector: max, min, mean, median, var, sum

min(samples)

## [1] 1

max(samples)

## [1] 100

mean(samples)

## [1] 51.136

median(samples)

## [1] 53

var(samples)

## [1] 845.3041

sd(samples)

## [1] 29.07411

summary(samples)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1.00   25.75   53.00   51.14   76.00  100.00

Factors

Factors in R are vectors especially for storing categorical variable. While factors can seem like they are vectors of character values, in fact they are treated very different by R. By storing the values in a factor we are telling R to treat the values as categorical values, not as arbitrary strings. The implicit assumption is that there are only small set of discrete values the vector take on (small relative to the size of the data). The possible values that a categorical variable takes on are called levels in statistics.

It is very important for summarizing information and plot. Both numeric and character variables can be made into factors by the function factor.

Here’s an example where we take character-valued vectors and change them into a factor.

# Create character vector
vec2 <- c('Fri', 'Thur', 'Mon', 'Tue', 'Wed', 'Thur', 'Mon', 'Mon', 'Tue', 'Wed', 'Wed', 'Tue', 'Fri')
summary(vec2)

##    Length     Class      Mode 
##        13 character character

# Create character vector
vec2.fac <- factor(vec2)
summary(vec2.fac)

##  Fri  Mon Thur  Tue  Wed 
##    2    3    2    3    3

Notice how R treats the variable differently now that it’s a factor – the function summary gives entirely different results for the factor vector as it does the character vector. In fact, summary for a factor works like the function table, which simply counts the number of times each unique entry is present.

# table of factor
table(vec2.fac)

## vec2.fac
##  Fri  Mon Thur  Tue  Wed 
##    2    3    2    3    3

# table of character
table(vec2)

## vec2
##  Fri  Mon Thur  Tue  Wed 
##    2    3    2    3    3

# table of numeric
table(c(1,4,2,4,2,1))

## 
## 1 2 4 
## 2 2 2

We can also create factors from numeric vectors. This may not feel intuitive – character values feel like they are naturally categorical. However, many times categorical variables might be encoded as numeric (e.g. 1=No, 2=Maybe, 3=Yes )

# Create numeric variable
vec1 <- c(3, 2, 3, 2, 1, 3, 2, 3, 1, 1, 2)
vec1

##  [1] 3 2 3 2 1 3 2 3 1 1 2

summary(vec1)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   1.500   2.000   2.091   3.000   3.000

Now convert it to a factor

# Convert it to a factor
vec1.fac <- factor(vec1)
vec1.fac

##  [1] 3 2 3 2 1 3 2 3 1 1 2
## Levels: 1 2 3

summary(vec1.fac)

## 1 2 3 
## 3 4 4

Again, notice how R treats the variable differently now that it’s a factor. This is important, because it doesn’t make sense to take the mean of categorical variables, even if they are encoded as numbers.

I can also give more informative labels to my factor:

# Convert it to a factor
vec1.fac <- factor(vec1, labels=c("No","Maybe","Yes"), levels=c(1,2,3))
vec1.fac

##  [1] Yes   Maybe Yes   Maybe No    Yes   Maybe Yes   No    No    Maybe
## Levels: No Maybe Yes

summary(vec1.fac)

##    No Maybe   Yes 
##     3     4     4

We can check what the possible levels are and how many:

# give the levels of the factor
levels(vec1.fac)

## [1] "No"    "Maybe" "Yes"

# give the number of levels of the factor
nlevels(vec1.fac)

## [1] 3

To count the number of occurrence of each level, we use function table

table(vec1.fac)

## vec1.fac
##    No Maybe   Yes 
##     3     4     4

Note that you can also apply table to non-factor vectors, and that works – the function transforms them to factors first, but without our nice mapping of the values to their labels that we created above.

table(vec1)

## vec1
## 1 2 3 
## 3 4 4

table(vec2)

## vec2
##  Fri  Mon Thur  Tue  Wed 
##    2    3    2    3    3

Data frames

You can think data frame as a collection of vectors, each element of the vectors holding different types of data collected on the same observations. Data frames can be a mix of types of vectors (e.g. numbers and characters) and they are the main way to store data in R. Data frames can be manually created with the function data.frame as shown in the following examples. But usually, we would read them from an external file files, as we’ll do later.

Python Users: A Data frame in R is very similar to Table in Python.

We will use examples of demonstrated in Data 8 below (LAB 3 and LAB 4)

When not specified, the function data.frame will coerce all character variables to factors, which is usually right for characters. If you want to keep the strings as character variables, you need to specify stringsAsFactors = FALSE.

# Create a data frame from scratch (unusual)
imdb <- data.frame(Votes = c(1498733, 1027398, 692753),
        Rating = c(9.2, 9.2, 9.0),
        Title = c('The Shawshank Redemption (1994)', 'The Godfather (1972)', 
                  'The Godfather: Part II (1974)'),
        Year = c(1994, 1972, 1974),
        Decade = c(1990, 1970, 1970), stringsAsFactors = FALSE)
imdb

##     Votes Rating                           Title Year Decade
## 1 1498733    9.2 The Shawshank Redemption (1994) 1994   1990
## 2 1027398    9.2            The Godfather (1972) 1972   1970
## 3  692753    9.0   The Godfather: Part II (1974) 1974   1970

The data.frame is generally thought of like a matrix, where the vectors (the different variables or attributes) are stored as columns and the observations in the rows.

# Get number of rows (observations)
nrow(imdb)

## [1] 3

# Get number of columns (attributes)
ncol(imdb)

## [1] 5

You can index them like a matrix too:

imdb[1:2,]

##     Votes Rating                           Title Year Decade
## 1 1498733    9.2 The Shawshank Redemption (1994) 1994   1990
## 2 1027398    9.2            The Godfather (1972) 1972   1970

imdb[,c(3,5)]

##                             Title Decade
## 1 The Shawshank Redemption (1994)   1990
## 2            The Godfather (1972)   1970
## 3   The Godfather: Part II (1974)   1970

But in fact they are not matrices, and they have some indexing options that don’t work for matrices. In particular, you can call up a column using a $ and the name of the column

imdb$Title

## [1] "The Shawshank Redemption (1994)" "The Godfather (1972)"           
## [3] "The Godfather: Part II (1974)"

All the tricks about indexing vectors will work for data frames (and matrices). For example, what do the following snippets do (in words)?

imdb[imdb$Rating > 9.0 & imdb$Decade == 1990, ]

##     Votes Rating                           Title Year Decade
## 1 1498733    9.2 The Shawshank Redemption (1994) 1994   1990

oldest_rating <- max(imdb$Year)
imdb$Title[imdb$Year==oldest_rating]

## [1] "The Shawshank Redemption (1994)"

Plotting

We will go through a couple of basic plotting commands here. Specific types of plots have different commands, but most plotting commands share basic arguments for certain aspects of the plot, such as axis labels, titles, and so forth. Here are some important ones:

main: Title of the plot
sub: subtitle for plot (below x-axis)
xlab/ylab: x/y axis label
xlim/ylim: the limits (starting and ending values) for the x/y axis”,
las the orientation of the axis labels
lty the type of line (e.g. solid, dashed, dotted)
lwd the width of lines (>1 increases size, <1 decreases)
pch the type of point (see help of points for the many options)
col color of the plotted images (e.g. “red”, “blue” – colors() prints out all possible character names of colors you can give)
cex the relative size of plotting (>1 increases size, <1 decreases)

A full set of the parameters can be found in the help for par (?par).

Not all of these parameters are applicable for any plot, often because they don’t make sense.

Plotting commands in R are generally of two kinds, the main plotting command, that sets up the axes, labels, etc and draws the plot and then plotting commands that can add on top of the existing plot.

Common main plotting commands are

plot – for scatterplots (and plotting of other objects)
boxplot – boxplots
hist – histograms
barplot – barplots
curve – draw a function

Common commands for adding features to a plot are:

lines – drawing lines connecting points (input vectors x and y and draw lines between each (x[i],y[i]) and (x[i+1],y[i+1]), in the order they are listed in the vector)
points – drawing points (input vectors x and y and draw point for each (x[i],y[i]) pair)
legend – add legend to plot
abline – draw a line on a plot based on an equation for a line. Useful for horizontal and vertical plots, but can draw arbitrary intercept and slope too.
title – add x/y labels, titles, subtitles, etc on top of existing plot
axes – add axes (tick marks and their labels) to plot

We will go through three common examples, and you will see many more in future labs

Histograms

The file baby.csv contains data on a random sample of 1,174 mothers and their newborn babies. The column birthwt contains the birth weight of the baby, in ounces; gest_days is the number of gestational days, that is, the number of days the baby was in the womb. There is also data on maternal age, maternal height, maternal pregnancy weight, and whether or not the mother was a smoker.

We will read this data in

baby <- read.csv('baby.csv', header = TRUE)
head(baby)

##   X Birth.Weight Gestational.Days Maternal.Age Maternal.Height
## 1 1          120              284           27              62
## 2 2          113              282           33              64
## 3 3          128              279           28              64
## 4 4          108              282           23              67
## 5 5          136              286           25              62
## 6 6          138              244           33              62
##   Maternal.Pregnancy.Weight Maternal.Smoker
## 1                       100           FALSE
## 2                       135           FALSE
## 3                       115            TRUE
## 4                       125            TRUE
## 5                        93           FALSE
## 6                       178           FALSE

The command hist is used to create histograms.

hist(baby$Birth.Weight, 
     col="darkblue", # histogram color,
     main = "Birth weights of babies",# plot title,
     xlab = "Birth weights (in ounces)", # x axis label,
     xlim = c(40, 180) # x axis range
     )

I can also add a vertical line showing where the mean and median are on this histogram using abline and the argument v, for “vertical” (notice that I have to repeat the hist command from above. This is because you can’t spread plotting commands across R chunks in a rmarkdown. If I was typing into a console, I could just type in the abline command after my previous hist command)

hist(baby$Birth.Weight, 
     col="darkblue", # histogram color,
     main = "Birth weights of babies",# plot title,
     xlab = "Birth weights (in ounces)", # x axis label,
     xlim = c(40, 180) # x axis range
     )
abline(v=c(mean(baby$Birth.Weight), median(baby$Birth.Weight)), lty=c("solid","dashed"), col=c("red","orange"))
legend("topright", legend=c("Mean","Median"), lty=c("solid","dashed"),col=c("red","orange"))

Notice in abline I could give a vector of values I want for my vertical lines, and it makes a separate vertical line for each. Notice also that lty and col defines the type and color of the lines, and that by giving a vector to lty and col, the first value of lty and col is for the first vertical line in the v argument, etc.

The legend’s first argument is the location (e.g. “topright”, “center”, “bottomright” etc). The second argument is the vector of characters that gives the text you want in the legend, and then the remaining commands describe what you want in front of this text. In this case, we want the text to correspond to different line types and colors, so we give it our lty and col values for each text element, and it draws lines with those colors.

** Exercise** Plot a histogram of the birth weights of the babies of the smokers, with meaningful labels, title etc.

Scatter plots

We create scatter plots using the plot command.

plot(x=baby$Maternal.Pregnancy.Weight, y=baby$Birth.Weight, 
    pch=19, #colored in points
    cex=.75, #smaller points
    col="grey",
    xlab="Maternal Pregnancy Weight (in lbs)", 
    ylab="Birth Weight (in ounces)")

I could chose to color some points differently. I could do this in two ways. The first is to give a vector of colors, equal to the length of x and y for each point. Here I give an example of plotting different colors based on the variable Maternal.Age

First I will make a variable that divides Maternal.Age into three categories, <21, 21-35, 35+. I will use the function cut

ageBinned<-cut(baby$Maternal.Age, c(0,21,35,100))
summary(ageBinned)

##   (0,21]  (21,35] (35,100] 
##      194      852      128

class(ageBinned)

## [1] "factor"

Notice that the resulting variable, ageBinned, is now a factor variable, classifying each observation into three categories.

Now I can use that to define colors. Suppose I want the colors for (0,21] to be red, (21,35] black and (35,100] green. If I make a variable with the three colors, in the order of the levels of my factor variable ageBinned, I can do the following

levels(ageBinned)

## [1] "(0,21]"   "(21,35]"  "(35,100]"

ageColors<-c("red","black","green")
head(ageBinned)

## [1] (21,35] (21,35] (21,35] (21,35] (21,35] (21,35]
## Levels: (0,21] (21,35] (35,100]

head(ageColors[ageBinned])

## [1] "black" "black" "black" "black" "black" "black"

The vector ageColors[ageBinned] has taken the vector of colors and repeated it for every value that matches it’s level (it’s using ageBinned to do the repeated indices trick from above and so get replicated values of the colors in the right order). I can use this vector to tell the plot command what colors to give to each observations.

plot(x=baby$Maternal.Pregnancy.Weight, y=baby$Birth.Weight, 
    pch=19, #colored in points
    cex=.75, #smaller points
    col=ageColors[ageBinned], 
    xlab="Maternal Pregnancy Weight (in lbs)", 
    ylab="Birth Weight (in ounces)")
legend("bottomright",legend=levels(ageBinned),fill=ageColors, title="Age of Mother")

Another way to change something about a small number of points, is to use the points function to add points to the existing plot. Because it plots over the existing points, it will effectively replot the points you request. It’s a little less elegant, but can be useful to highlight a subset of values.

Here I will plot differently points with birth weight under 60oz. First I need to identify those points, using the function which

whLowBirth<-which(baby$Birth.Weight<60)
length(whLowBirth) #check how many observations that is

## [1] 2

baby[whLowBirth, ]

##       X Birth.Weight Gestational.Days Maternal.Age Maternal.Height
## 860 860           58              245           34              64
## 923 923           55              204           35              65
##     Maternal.Pregnancy.Weight Maternal.Smoker
## 860                       156            TRUE
## 923                       140           FALSE

This gives me the indices of the observations with low birth weight

plot(x=baby$Maternal.Pregnancy.Weight, y=baby$Birth.Weight, 
    pch=19, 
    cex=.75, 
    col="grey",
    xlab="Maternal Pregnancy Weight (in lbs)", 
    ylab="Birth Weight (in ounces)")
points(x=baby$Maternal.Pregnancy.Weight[whLowBirth], y=baby$Birth.Weight[whLowBirth], 
    pch=19, 
    cex=2, # Make the points BIG
    col="red")
title(sub="Highlighting in red low weight babies")

Reading and Saving Files

Reading in text files with data

However, usually we do not create data frame manually by typing the information. We read data from external files.

A common task is to read in comma-deliminated files with read.csv:

# Read csv files
twitter_follows <- read.csv("twitter_follows.csv")
twitter_follows

##       Screen.name Followers Friends
## 1     LeoDiCaprio  14082200     142
## 2     SteveCarell   4607580      48
## 3     MarkRuffalo   2165110    1178
## 4      amyschumer   3452330    1931
## 5   TherealTaraji   3960390     702
## 6 Racheldoesstuff     31996    3341
## 7 IAMQUEENLATIFAH   6890940     458

We can also read tab-deliminated with read.delim (these are often saved as .txt files, but can sometimes be .tsv)

# Read tab-delinated files
twitter_info <- read.delim("twitter_info.txt")
twitter_info

##                Name     Screen.name Gender Medium
## 1 Leonardo DiCaprio     LeoDiCaprio      M   Film
## 2      Steve Carell     SteveCarell      M   Both
## 3      Mark Ruffalo     MarkRuffalo      M   Film
## 4       Amy Schumer      amyschumer      F   Both
## 5  Taraji P. Henson   TherealTaraji      F   Both
## 6       Aziz Ansari      azizansari      M     TV
## 7      Rachel Bloom Racheldoesstuff      F     TV
## 8     Queen Latifah IAMQUEENLATIFAH      F   Both

R can handle any kind of delimination via read.table (both read.csv and read.delim are just special cases of read.table), and has many options for dealing with common formatting problems.

Joining (or merging) datasets

We can also join data frames together that have at least one shared data attributes. In this case, both datasets have twitter information about actors, and we can match the actors in different datasets based on the attribute Screen.name

# join the data frame info and follows into one data frame called twitter
twitter = merge(twitter_info,twitter_follows,by="Screen.name")
twitter

##       Screen.name              Name Gender Medium Followers Friends
## 1      amyschumer       Amy Schumer      F   Both   3452330    1931
## 2 IAMQUEENLATIFAH     Queen Latifah      F   Both   6890940     458
## 3     LeoDiCaprio Leonardo DiCaprio      M   Film  14082200     142
## 4     MarkRuffalo      Mark Ruffalo      M   Film   2165110    1178
## 5 Racheldoesstuff      Rachel Bloom      F     TV     31996    3341
## 6     SteveCarell      Steve Carell      M   Both   4607580      48
## 7   TherealTaraji  Taraji P. Henson      F   Both   3960390     702

Notice that one of the observations in twitter_info was not in twitter_follows and was silently dropped. We could ask that all entries in either dataset be kept by setting all=TRUE:

# join the data frame info and follows into one data frame called twitter
twitter = merge(twitter_info,twitter_follows,by="Screen.name", all=TRUE)
twitter

##       Screen.name              Name Gender Medium Followers Friends
## 1      amyschumer       Amy Schumer      F   Both   3452330    1931
## 2      azizansari       Aziz Ansari      M     TV        NA      NA
## 3 IAMQUEENLATIFAH     Queen Latifah      F   Both   6890940     458
## 4     LeoDiCaprio Leonardo DiCaprio      M   Film  14082200     142
## 5     MarkRuffalo      Mark Ruffalo      M   Film   2165110    1178
## 6 Racheldoesstuff      Rachel Bloom      F     TV     31996    3341
## 7     SteveCarell      Steve Carell      M   Both   4607580      48
## 8   TherealTaraji  Taraji P. Henson      F   Both   3960390     702

In this case, R adds in NA values for the missing entries.

There are many options for merge, including if the two datasets have different names for the same attribute.

Writing data to a text file

We can also write data frames to a file using write.table. We can make them tab or comma deliminated by setting the option sep, but there is a special function write.csv for the special case of comma-deliminated.

# Write a data frame to csv
write.csv(twitter_follows, 
          file = "twitter_follows.csv",
          row.names = FALSE)
# Write a data frame to tab-deliminated
write.table(twitter_follows, sep="\t", 
            file = "twitter_follows.txt", 
            col.names=FALSE,
            row.names = FALSE )

Saving and loading R objects

R provide another method for saving and loading R data. You can save(load) several R objects to(from) at the same timea binary file with the extension .RData . And load them when you start a new R session in the future.

x <- 1:3
y <- list(a = 1, b = TRUE, c = "oops")
# save x, y
save(x, y, file = "xy.RData")
# load x, y
load("xy.RData")

R provides methods to save the environment (all data, values, functions, etc.) in RData for future use. You could excute the code as follows, or click the save botton in the environment window to save and click the RData files in the file window to load them.

# save the environment
save.image("myenv.RData")
# load the environment
load("myenv.RData")

Writing functions

While R comes with many functions, you can actually write your own functions.

You define a function in R using the command function. The format is

nothing <- function(){
        x = 4
        return(x)  
    }

Python Users: Unlike python, R is not sensitive to white space. Meaning you can tab or not as you like (though indenting is recommended for readability). Instead the brackets { } define the limits of the function

You can now call your function

nothing()

## [1] 4

Python Users: The same function in python would be defined as:

def nothing():
    x = 4
    return x

output = nothing()

Often you will want your function to take information from the user. This is done by defining arguments that the user can give in the function(...) part of the call.

randMean <- function(data){
        x = sample(data, size=50, replace=FALSE)
        return(mean(x))  
}
set.seed(915820)
randMean(data=samples)

## [1] 54.28

Notice how I can use the variable data in my function as if it has been defined – it will be whatever data the user gives.

I can also have multiple arguments. Here I will allow the user to also determine the sample size; only this time I will give a default value in my definition of the function.

randMean <- function(data, sampleSize=50){
        x = sample(data, size=sampleSize, replace=FALSE)
        return(mean(x))  
}
set.seed(915820)
randMean(data=samples) #should be same as above

## [1] 54.28

randMean(data=samples, sampleSize=20)

## [1] 51.35

Notice how because I set the seed I get the same answer (when sampleSize=50) as before, even though I have a “random” sample.

Conditional Statements

In my function above, I have a problem – what if the data the user gives me is less than length 50? Since I’m sampling without replacement, this will be a problem. So I can add error handling using conditional statements. An “if statement” will evaluate a logical expression and do a series of actions if the expression is true; I can add an “else” which tells what to do if the expression is false.

randMean <- function(data, sampleSize=50){
    if(length(data) < sampleSize){
        stop("Input to argument data must be of length at least ", sampleSize)
    }
    else{
        x = sample(data, size=sampleSize, replace=FALSE)
        return(mean(x))          
    }
}
set.seed(915820)
randMean(data=samples)

## [1] 54.28

randMean(data=samples[1:10])

## Error in randMean(data = samples[1:10]): Input to argument data must be of length at least 50

Notice the function stop – it will produce an error and kill the function. You can also use warning to give warnings – notice the difference in the next function and how I changed the conditional statements:

randMean <- function(data, sampleSize=50){
    if(length(data) < sampleSize){
        warning("Input to argument data is longer than requested sample size. Will set to default of ", length(data))
        sampleSize<-length(data)
    }
    x = sample(data, size=sampleSize, replace=FALSE)
    return(mean(x))          
}
set.seed(915820)
randMean(data=samples)

## [1] 54.28

randMean(data=samples[1:10])

## Warning in randMean(data = samples[1:10]): Input to argument data is longer than
## requested sample size. Will set to default of 10

## [1] 55.4

For-loops and Iteration

Often we will want to repeat an expresion over and over again, but change the input into it each time. This is called iteration, and for-loops are a standard programming device for doing so. The basic idea is that you give a vector of values to the for loop, and for each element in the vector, the for loop will evaluate the expression on that element.

Here is a for-loop in R

for(animal in c('cat', 'dog', 'rabbit')){
    print(animal)    
}

## [1] "cat"
## [1] "dog"
## [1] "rabbit"

Python Users: This for-loop in python would be defined as:

for animal in make_array('cat', 'dog', 'rabbit'):
    print(animal)

This means that for every element in the vector c('cat', 'dog', 'rabbit'), the variable animal was given the value of the element of the vector, and then the code beween the { } is executed.

Here’s a more complex for-loop, that determines the sum and product of the numbers 1-10. It does this by defining variables it will at each iteration add (or multiple) the new integer to.

sum_10 = 0
prod_10 = 1
#loop over the integers 1-10:
for (i in 1:10){
    sum_10 = sum_10 + i
    prod_10 = prod_10 * i
}
print(sum_10)

## [1] 55

print(prod_10)

## [1] 3628800