Introduction to R

Mathematical operations in R

Many familiar operators work in R, allowing you to work with numbers like you would in a calculator. Operators such as inequalities also work, returning “TRUE” if the proposed logical expression is true and “FALSE” otherwise.

2+4 #addition

[1] 6

2-4 #subtraction

[1] -2

2*4 #multiplication

[1] 8

2/4 #division

[1] 0.5

2^4 #exponentiation

[1] 16

log(2) #the default log base is the natural log

[1] 0.6931472

2 < 4

[1] TRUE

2 > 4

[1] FALSE

2 >= 4 #greater than or equal to 

[1] FALSE

2 == 2 #is equal to (notice that there are two equal signs, as a single equal sign denotes assignment)

[1] TRUE

2 != 4 #is not equal to 

[1] TRUE

2 != 4 | 2 + 2 == 4 #OR

[1] TRUE

2 != 4 & 2 + 2 == 4 #AND

[1] TRUE

"Red" == "Red"

[1] TRUE

Objects

In addition to being able to work with actual numbers, R works in objects, which can represent anything from numbers to strings to vectors to matrices. Everything in R is an object. The best practice for assigning variable names to objects is the “<-” operator. After objects are created, they are stored in in the “Environment” tab in your RStudio console and can be called upon to perform different operations.

R has many data structures, including:

• atomic vector
• list
• matrix
• data frame
• factors

R has 6 atomic vector types, or classes. Atomic means that a vector only contains elements of one class (i.e. the elements inside the vector do not come from mutliple classes).

• character
• numeric (real or decimal)
• integer
• logical (TRUE or FALSE)
• complex (containing i)

a <- 2
b <- 3
a + b

[1] 5

class(a) #the "class" function tells you what class of object a is

[1] "numeric"

d <- c(1,2,3,4,5) #the "c" function concatenates the arguments contained within it into a vector
d

[1] 1 2 3 4 5

d <- c(d, 1) #The "c" function also allows you to append items to an existing vector
d

[1] 1 2 3 4 5 1

class(d)

[1] "numeric"

d[3] #brackets allow you index vectors or matrices. Here, we call the third value from our d vector.

[1] 3

#Matrices are just like vectors, but with two dimensions
my_matrix <- matrix(seq(1:9), ncol = 3)
my_matrix

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

#vectors and matrices can only contain objects of one class. If you include objects of multiple types into the same vector, R will perform coersion to force all the objects contained in the vector into a shared class
x <- c(1.7, "a")
x

[1] "1.7" "a"  

class("a")

[1] "character"

class(1.7)

[1] "numeric"

class(x)

[1] "character"

y <- c(TRUE, 2)
y

[1] 1 2

z <- c("a", TRUE)
z

[1] "a"    "TRUE"

#If you would like to store objects of multiple classes into one object, a list can accomodate such a task.
x_y_z_list <- list(x,y,z)
x_y_z_list

[[1]]
[1] "1.7" "a"  

[[2]]
[1] 1 2

[[3]]
[1] "a"    "TRUE"

#to index an element in a list, use double brackets [[]]. You can further index elements within an element of a list.
x_y_z_list[[1]]

[1] "1.7" "a"  

x_y_z_list[[1]][2]

[1] "a"

#elements in a list can be assigned names
x_y_z_list <- list(a=x, b=y, c=z)
x_y_z_list

$a
[1] "1.7" "a"  

$b
[1] 1 2

$c
[1] "a"    "TRUE"

#Dataframes are a very commonly used type of object in R. You can think of a dataframe as a rectangular combination of lists.
#The below code stores the stated values in a dataframe which contains employee ids, names, salaries, and start dates for 5 employees
emp.data <- data.frame(
   emp_id = c (1:5), 
   emp_name = c("Rick","Dan","Michelle","Ryan","Gary"),
   salary = c(623.3,515.2,611.0,729.0,843.25), 
   
   start_date = as.Date(c("2012-01-01", "2013-09-23", "2014-11-15", "2014-05-11",
      "2015-03-27")),
   stringsAsFactors = FALSE
)

emp.data

  emp_id emp_name salary start_date
1      1     Rick 623.30 2012-01-01
2      2      Dan 515.20 2013-09-23
3      3 Michelle 611.00 2014-11-15
4      4     Ryan 729.00 2014-05-11
5      5     Gary 843.25 2015-03-27

emp.data$emp_id #the $ operator calls on a certain column of a dataframe

[1] 1 2 3 4 5

class(emp.data$emp_id) #As noted earlier, a dataframe can be thought of as a rectangular list, combining different data classes together, each in a different column.

[1] "integer"

class(emp.data$salary)

[1] "numeric"

emp.data$emp_name[emp.data$salary > 620] #You can combine logical operators, brackets, and the $ sign to subset your dataframe in any way you choose! Here, we print out all the employee names for employees who have a salary greater than 620.

[1] "Rick" "Ryan" "Gary"

ls() #ls lists all the variable names that have been assigned to objects in your workspace

[1] "a"          "b"          "d"          "emp.data"   "my_matrix" 
[6] "x"          "x_y_z_list" "y"          "z"         

Using Packages in R

In addition to the basic functions provided in R, oftentimes we will be working with packages that contain functions written by other people to perform common tasks or specific analyses. Packages can also contain datasets. We can load these packages into our R environment after installing them in R.

usePackage <- function(p) 
{
  if (!is.element(p, installed.packages()[,1]))
    install.packages(p, dep = TRUE)
  require(p, character.only = TRUE)
}

usePackage("gapminder")#This code installs the gapminder packages, which contains vital statistics data from multiple countries. install.packages() is the function that will install a package for you if you know it's name.

Loading required package: gapminder

library("gapminder") #After installing the package, we need to tell R to load it into our current environment with this function.
head(gapminder) #The package gapminder contains a dataset called gapminder. We can use the "head" function to print out the first 6 rows of this dataset.

# A tibble: 6 x 6
  country     continent  year lifeExp      pop gdpPercap
  <fct>       <fct>     <int>   <dbl>    <int>     <dbl>
1 Afghanistan Asia       1952    28.8  8425333      779.
2 Afghanistan Asia       1957    30.3  9240934      821.
3 Afghanistan Asia       1962    32.0 10267083      853.
4 Afghanistan Asia       1967    34.0 11537966      836.
5 Afghanistan Asia       1972    36.1 13079460      740.
6 Afghanistan Asia       1977    38.4 14880372      786.

?gapminder #the ? operator lauches a help page to describe a particular function, including the arguments it takes. Whenever using a new function, it is good practice to first explore it through ?.

Loops

Oftentimes, we may want to perform the same operation or function many many times. Rather than having to explicitly write out each individual operation, we can make use of loops. For example, let’s say that we want to raise the number 2 to the power of each integer from 0 to 20. We could either write out 2^0, 2^1, 2^2 …, or make use of a for loop to condense our code while getting the same result.

2^0

[1] 1

2^1

[1] 2

2^2

[1] 4

2^3

[1] 8

# ...

#This is a for loop. in the parentheses after the for function, we specify over what range of values we want to loop over, and assign a dummy variable name to take on each of those values in sequence. Within the curly braces, we state what operation we want to perform over all the values taken on by the dummy variable.
for(i in 0:20){
  print(2^i)
}

[1] 1
[1] 2
[1] 4
[1] 8
[1] 16
[1] 32
[1] 64
[1] 128
[1] 256
[1] 512
[1] 1024
[1] 2048
[1] 4096
[1] 8192
[1] 16384
[1] 32768
[1] 65536
[1] 131072
[1] 262144
[1] 524288
[1] 1048576

User-defined Functions (UDF)

Another way to avoid writing out or copy-pasting the same exact thing over and over again when working with data is to write a function to contain a certain combination of operations you find yourself running mutliple times. For example, you may find yourself needing to calculate the Hardy-Weinberg Equillibrium genotype frequencies of a population given the allele frequencies. We can wrap up all the code that you would need to calculate this in a function that we can call upon again and again.

calc_HWE_geno <- function(p = 0.5){ 
  q <- 1-p
  
  pp <- p^2
  pq <- 2*p*q
  qq <- q^2
  
  return(c(pp, pq, qq))
}

calc_HWE_geno(p = 0.1)

[1] 0.01 0.18 0.81

#note that in our UDF we assigned a default value to p (p = 0.5). This means that if we do not specify a value for our argument of p, it will default to using that value.

calc_HWE_geno()

[1] 0.25 0.50 0.25

Plots

In addition to mathematical operations, R can help with data visualization. Base R has a few useful plotting functions, but popular packages such as ggplot2 give more customization and control to the user.

hist(gapminder$lifeExp)

Past versions of Plotting-1.png

boxplot(lifeExp ~ continent, data = gapminder) #box plot for the life expectancies of all years per continent

Past versions of Plotting-2.png

Setting a random seed

R has many functions that use a random number generator to generate an output. For example, the r____ functions (e.g. rbinom, runif) pull numbers from a probability distribution of your choice. In order to create reproducible analyses, it is often advantageous to be able to reliably obtain the same “random” number after running the same function over again. In order to do so, we can set a seed for the random number generator.

runif(1,0,1) #runif pulls a number from the uniform distribution with a set of given parameters

[1] 0.1944457

runif(1,0,1) #we can see that running runif twice gives you differnt results

[1] 0.205278

set.seed(1234) #setting a seed allows us to obtain reproducible results from functions that use the random number generator
runif(1,0,1)

[1] 0.1137034

set.seed(1234)
runif(1,0,1)

[1] 0.1137034

Reading and writing data in R

Finally, let us address probably one of the most important points when working with statistics in science: how to get the data you have collected into your R environment. For this part of the lesson, we will be working with the bandersnatch.csv file (created by Katie Long) located here: https://raw.githubusercontent.com/anthonyhung/MSTPsummerstatistics/master/data/bandersnatch.csv. If you would like to have your own copy of this dataset, you can open up a terminal window and run the commands.

cd ~/Desktop
mkdir data
cd data
wget https://raw.githubusercontent.com/anthonyhung/MSTPsummerstatistics/master/data/bandersnatch.csv

mkdir: data: File exists
--2019-05-27 21:07:24--  https://raw.githubusercontent.com/anthonyhung/MSTPsummerstatistics/master/data/bandersnatch.csv
Resolving raw.githubusercontent.com... 151.101.184.133
Connecting to raw.githubusercontent.com|151.101.184.133|:443... connected.
HTTP request sent, awaiting response... 200 OK
Length: 13511471 (13M) [text/plain]
Saving to: ‘bandersnatch.csv.7’

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  7900K .......... .......... .......... .......... .......... 60% 2.64M 1s
  7950K .......... .......... .......... .......... .......... 60% 4.18M 1s
  8000K .......... .......... .......... .......... .......... 61% 3.45M 1s
  8050K .......... .......... .......... .......... .......... 61% 3.60M 1s
  8100K .......... .......... .......... .......... .......... 61% 3.65M 1s
  8150K .......... .......... .......... .......... .......... 62% 3.26M 1s
  8200K .......... .......... .......... .......... .......... 62% 3.63M 1s
  8250K .......... .......... .......... .......... .......... 62% 3.26M 1s
  8300K .......... .......... .......... .......... .......... 63% 2.47M 1s
  8350K .......... .......... .......... .......... .......... 63% 3.47M 1s
  8400K .......... .......... .......... .......... .......... 64% 3.85M 1s
  8450K .......... .......... .......... .......... .......... 64% 3.67M 1s
  8500K .......... .......... .......... .......... .......... 64% 3.22M 1s
  8550K .......... .......... .......... .......... .......... 65% 4.12M 1s
  8600K .......... .......... .......... .......... .......... 65% 3.49M 1s
  8650K .......... .......... .......... .......... .......... 65% 3.72M 1s
  8700K .......... .......... .......... .......... .......... 66% 2.68M 1s
  8750K .......... .......... .......... .......... .......... 66% 4.16M 1s
  8800K .......... .......... .......... .......... .......... 67% 3.59M 1s
  8850K .......... .......... .......... .......... .......... 67% 3.49M 1s
  8900K .......... .......... .......... .......... .......... 67% 3.89M 1s
  8950K .......... .......... .......... .......... .......... 68% 3.22M 1s
  9000K .......... .......... .......... .......... .......... 68% 3.86M 1s
  9050K .......... .......... .......... .......... .......... 68% 3.47M 1s
  9100K .......... .......... .......... .......... .......... 69% 2.27M 1s
  9150K .......... .......... .......... .......... .......... 69% 3.06M 1s
  9200K .......... .......... .......... .......... .......... 70% 3.75M 1s
  9250K .......... .......... .......... .......... .......... 70% 3.92M 1s
  9300K .......... .......... .......... .......... .......... 70% 3.29M 1s
  9350K .......... .......... .......... .......... .......... 71% 3.63M 1s
  9400K .......... .......... .......... .......... .......... 71% 3.42M 1s
  9450K .......... .......... .......... .......... .......... 71% 4.30M 1s
  9500K .......... .......... .......... .......... .......... 72% 2.72M 1s
  9550K .......... .......... .......... .......... .......... 72% 3.47M 1s
  9600K .......... .......... .......... .......... .......... 73% 3.58M 1s
  9650K .......... .......... .......... .......... .......... 73% 3.97M 1s
  9700K .......... .......... .......... .......... .......... 73% 3.62M 1s
  9750K .......... .......... .......... .......... .......... 74% 3.55M 1s
  9800K .......... .......... .......... .......... .......... 74% 3.69M 1s
  9850K .......... .......... .......... .......... .......... 75% 3.61M 1s
  9900K .......... .......... .......... .......... .......... 75% 2.80M 1s
  9950K .......... .......... .......... .......... .......... 75% 3.39M 1s
 10000K .......... .......... .......... .......... .......... 76% 3.32M 1s
 10050K .......... .......... .......... .......... .......... 76% 3.20M 1s
 10100K .......... .......... .......... .......... .......... 76% 3.03M 1s
 10150K .......... .......... .......... .......... .......... 77% 3.74M 1s
 10200K .......... .......... .......... .......... .......... 77% 3.86M 1s
 10250K .......... .......... .......... .......... .......... 78% 3.74M 1s
 10300K .......... .......... .......... .......... .......... 78% 2.46M 1s
 10350K .......... .......... .......... .......... .......... 78% 3.96M 1s
 10400K .......... .......... .......... .......... .......... 79% 3.41M 1s
 10450K .......... .......... .......... .......... .......... 79% 4.08M 1s
 10500K .......... .......... .......... .......... .......... 79% 3.51M 1s
 10550K .......... .......... .......... .......... .......... 80% 3.60M 1s
 10600K .......... .......... .......... .......... .......... 80% 3.56M 1s
 10650K .......... .......... .......... .......... .......... 81% 3.71M 1s
 10700K .......... .......... .......... .......... .......... 81% 2.73M 1s
 10750K .......... .......... .......... .......... .......... 81% 3.61M 1s
 10800K .......... .......... .......... .......... .......... 82% 3.71M 1s
 10850K .......... .......... .......... .......... .......... 82% 3.77M 1s
 10900K .......... .......... .......... .......... .......... 82% 3.59M 1s
 10950K .......... .......... .......... .......... .......... 83% 3.19M 1s
 11000K .......... .......... .......... .......... .......... 83% 3.27M 1s
 11050K .......... .......... .......... .......... .......... 84% 3.13M 1s
 11100K .......... .......... .......... .......... .......... 84% 2.70M 1s
 11150K .......... .......... .......... .......... .......... 84% 3.50M 1s
 11200K .......... .......... .......... .......... .......... 85% 3.66M 1s
 11250K .......... .......... .......... .......... .......... 85% 3.51M 1s
 11300K .......... .......... .......... .......... .......... 86% 4.06M 1s
 11350K .......... .......... .......... .......... .......... 86% 3.38M 1s
 11400K .......... .......... .......... .......... .......... 86% 3.60M 0s
 11450K .......... .......... .......... .......... .......... 87% 3.84M 0s
 11500K .......... .......... .......... .......... .......... 87% 2.69M 0s
 11550K .......... .......... .......... .......... .......... 87% 3.61M 0s
 11600K .......... .......... .......... .......... .......... 88% 3.39M 0s
 11650K .......... .......... .......... .......... .......... 88% 3.97M 0s
 11700K .......... .......... .......... .......... .......... 89% 3.57M 0s
 11750K .......... .......... .......... .......... .......... 89% 3.62M 0s
 11800K .......... .......... .......... .......... .......... 89% 3.59M 0s
 11850K .......... .......... .......... .......... .......... 90% 3.74M 0s
 11900K .......... .......... .......... .......... .......... 90% 2.66M 0s
 11950K .......... .......... .......... .......... .......... 90% 3.29M 0s
 12000K .......... .......... .......... .......... .......... 91% 3.61M 0s
 12050K .......... .......... .......... .......... .......... 91% 3.34M 0s
 12100K .......... .......... .......... .......... .......... 92% 3.64M 0s
 12150K .......... .......... .......... .......... .......... 92% 3.05M 0s
 12200K .......... .......... .......... .......... .......... 92% 3.65M 0s
 12250K .......... .......... .......... .......... .......... 93% 3.50M 0s
 12300K .......... .......... .......... .......... .......... 93% 2.85M 0s
 12350K .......... .......... .......... .......... .......... 93% 3.32M 0s
 12400K .......... .......... .......... .......... .......... 94% 4.01M 0s
 12450K .......... .......... .......... .......... .......... 94% 2.42M 0s
 12500K .......... .......... .......... .......... .......... 95% 7.39M 0s
 12550K .......... .......... .......... .......... .......... 95% 3.39M 0s
 12600K .......... .......... .......... .......... .......... 95% 3.59M 0s
 12650K .......... .......... .......... .......... .......... 96% 3.76M 0s
 12700K .......... .......... .......... .......... .......... 96% 2.92M 0s
 12750K .......... .......... .......... .......... .......... 97% 3.51M 0s
 12800K .......... .......... .......... .......... .......... 97% 3.78M 0s
 12850K .......... .......... .......... .......... .......... 97% 3.55M 0s
 12900K .......... .......... .......... .......... .......... 98% 3.56M 0s
 12950K .......... .......... .......... .......... .......... 98% 3.77M 0s
 13000K .......... .......... .......... .......... .......... 98% 3.65M 0s
 13050K .......... .......... .......... .......... .......... 99% 3.24M 0s
 13100K .......... .......... .......... .......... .......... 99% 2.70M 0s
 13150K .......... .......... .......... .......... ....      100% 5.09M=3.7s

2019-05-27 21:07:29 (3.44 MB/s) - ‘bandersnatch.csv.7’ saved [13511471/13511471]

Now that we have a copy of the data in a data directory on our desktop, we can load it into R using a relative or absolute directory path and the read.csv function.

data <- read.csv("~/Desktop/data/bandersnatch.csv")
#let's take a look at the dataset we've just loaded
head(data)

  Color  Fur Baseline.Frumiosity Post.Frumiosity
1   Red Nude            4.477127        11.46590
2   Red Nude            4.113727        11.09354
3   Red Nude            4.806221        11.81268
4   Red Nude            5.357348        12.36704
5   Red Nude            5.951754        12.96135
6   Red Nude            3.593995        10.62375

summary(data)

  Color           Fur         Baseline.Frumiosity Post.Frumiosity 
 Blue:200000   Furry:200000   Min.   :-1.108      Min.   : 1.887  
 Red :200000   Nude :200000   1st Qu.: 4.001      1st Qu.: 4.044  
                              Median : 6.980      Median : 8.976  
                              Mean   : 6.001      Mean   : 9.001  
                              3rd Qu.: 8.961      3rd Qu.:13.956  
                              Max.   : 9.174      Max.   :16.192  

#what is the difference between these two function calls?
head(read.csv("~/Desktop/data/bandersnatch.csv", header = T))

  Color  Fur Baseline.Frumiosity Post.Frumiosity
1   Red Nude            4.477127        11.46590
2   Red Nude            4.113727        11.09354
3   Red Nude            4.806221        11.81268
4   Red Nude            5.357348        12.36704
5   Red Nude            5.951754        12.96135
6   Red Nude            3.593995        10.62375

head(read.csv("~/Desktop/data/bandersnatch.csv", header = F))

     V1   V2                  V3              V4
1 Color  Fur Baseline Frumiosity Post-Frumiosity
2   Red Nude         4.477127244     11.46590322
3   Red Nude         4.113726932     11.09353649
4   Red Nude         4.806220524     11.81268077
5   Red Nude         5.357347878     12.36703951
6   Red Nude         5.951754455     12.96134984

#let's look at the structure of the data
class(data)

[1] "data.frame"

class(data$Color)

[1] "factor"

class(data$Baseline.Frumiosity)

[1] "numeric"

#let's make some plots with the data
hist(data$Baseline.Frumiosity)

Past versions of read write-1.png

hist(data$Post.Frumiosity)

Past versions of read write-2.png

plot(data$Baseline.Frumiosity, data$Post.Frumiosity)

Past versions of read write-3.png

#we can also write data files and export them using R
data$Size <- rnorm(nrow(data))
write.csv(data, "~/Desktop/data/new_bandersnatch.csv")