First Steps in R

Basic calculations

You can use R for basic computations you would perform in a calculator

# Addition
2-3

[1] -1

# Division
2/3

[1] 0.6666667

# Exponentiation
2^3 

[1] 8

# Square root
sqrt(2)

[1] 1.414214

# Logarithms
log(2)

[1] 0.6931472

Cool lines of code, so let us now run a similar chunk of code

log(10)

[1] 2.302585

Well, I thought that log(10) was equal to one. What if we are actually calculating log based e(2.72)

log(2.72)

[1] 1.000632

Let us compute now some log expressions

log10(10)

[1] 1

Often you will want to test whether something is less than, greater than or equal to something.

3 == 8

[1] FALSE

3 != 8

[1] TRUE

3 <= 8

[1] TRUE

1==0

[1] FALSE

2==5

[1] FALSE

1==1

[1] TRUE

The logical operators are & for logical AND, | for logical OR, and ! for NOT. These are some examples:

# Logical Disjunction (or)
FALSE | FALSE

[1] FALSE

# Logical Conjunction (and)
TRUE & FALSE

[1] FALSE

# Negation
! FALSE

[1] TRUE

# Combination of statements
2 < 3 | 1 == 5

[1] TRUE

Assigning Values to Variables

In R, you create a variable and assign it a value using <- as follows

foo <- 2 + 2
foo*3

[1] 12

#Let us now multiply foo by 5
foo*5

[1] 20

fii<-3+4

To see the variables that are currently defined, use ls (as in “list”)

ls()

[1] "fii" "foo"

To delete a variable, use rm (as in “remove”)

rm(fii)

ls()

character(0)

Either <- or = can be used to assign a value to a variable, but I prefer <- because is less likely to be confused with the logical operator ==

Vectors

The basic type of object in R is a vector, which is an ordered list of values of the same type. You can create a vector using the c() function (as in “concatenate”).

bar <- c(2, 5, 10, 2, 1) 
bar

[1]  2  5 10  2  1

baz <- c(2, 2, 3, 3, 3)
baz

[1] 2 2 3 3 3

There are also some functions that will create vectors with regular patterns, like repeated elements.

# replicate function
rep(2, 5)

[1] 2 2 2 2 2

# consecutive numbers
1:5

[1] 1 2 3 4 5

# sequence from 1 to 10 with a step of 2
seq(1, 10, by=2)

[1] 1 3 5 7 9

seq(1,20,by=3)

[1]  1  4  7 10 13 16 19

rep(1,3)

[1] 1 1 1

Many functions and operators like + or - will work on all elements of the vector.

# add vectors
bar + baz

[1]  4  7 13  5  4

# compare vectors
bar == baz

[1]  TRUE FALSE FALSE FALSE FALSE

# find length of vector
length(bar)

[1] 5

# find minimum value in vector
min(bar)

[1] 1

# find average value in vector
mean(bar)

[1] 4

You can access parts of a vector by using [. Recall what the value is of the vector bar.

bar

[1]  2  5 10  2  1

# If you want to get the first element:
bar[1]

[1] 2

If you want to get the last element of bar without explicitly typing the number of elements of bar, make use of the length function, which calculates the length of a vector:

bar[length(bar)]

[1] 1

You can also extract multiple values from a vector. For instance to get the 2nd through 4th values use

bar[c(2, 3, 4)]

Vectors can also be strings or logical values

quxx <- c("a", "b", "cde", "fg")

quxx

[1] "a"   "b"   "cde" "fg" 

Data Frames

In statistical applications, data is often stored as a data frame, which is like a spreadsheet, with rows as observations and columns as variables.

To manually create a data frame, use the data.frame() function.

data.frame(foo = c(1, 2, 3), 
           bar = c("a", "b", "c"), 
           baz = c(1.5, 2.5, 3)) 

NA

Most often you will be using data frames loaded from a file. For example, load the results of a class survey. The function load or read.table can be used for this.

How to Make a Random Sample

To randomly select a sample use the function sample(). The following code selects 5 numbers between 1 and 10 at random (without duplication)

sample(1:10, size=5)

[1] 4 8 7 2 9

• The first argument gives the vector of data to select elements from.
• The second argument (size=) gives the size of the sample to select.

Taking a simple random sample from a data frame is only slightly more complicated, having two steps:

1. Use sample() to select a sample of size n from a vector of the row numbers of the data frame.
2. Use the index operator [ to select those rows from the data frame.

Consider the following example with fake data. First, make up a data frame with two columns. (LETTERS is a character vector of length 26 with capital letters “A” to “Z”; LETTERS is automatically defined and pre-loaded in R)

bar <- data.frame(var1 = LETTERS[1:10], var2 = 1:10)
# Check data frame
bar

Suppose you want to select a random sample of size 5. First, define a variable n with the size of the sample, i.e. 5

n <- 5

Now, select a sample of size 5 from the vector with 1 to 10 (the number of rows in bar). Use the function nrow() to find the number of rows in bar instead of manually entering that number.

Use : to create a vector with all the integers between 1 and the number of rows in bar.

samplerows <- sample(1:nrow(bar), size=n) 
# print sample rows
samplerows

The variable samplerows contains the rows of bar which make a random sample from all the rows in bar. Extract those rows from bar with

# extract rows
barsample <- bar[samplerows, ]
# print sample
print(barsample)

The code above creates a new data frame called barsample with a random sample of rows from bar.

In a single line of code:

bar[sample(1:nrow(bar), n), ]

Using Tables

The table() command allows us to look at tables. Its simplest usage looks like table(x) where x is a categorical variable.

For example, a survey asks people if they smoke or not. The data is

Yes, No, No, Yes, Yes

We can enter this into R with the c() command, and summarize with the table() command as follows

x <- c("Yes","No","No","Yes","Yes") 
table(x)

x
 No Yes 
  2   3 

y<-c("Yes","No","Yes","Yes")
y

[1] "Yes" "No"  "Yes" "Yes"

table(y)

y
 No Yes 
  1   3 

Numeric measures of center and spread

Suppose, CEO yearly compensations are sampled and the following are found (in millions)

12 .4 5 2 50 8 3 1 4 0.25

sals <- c(12, .4, 5, 2, 50, 8, 3, 1, 4, 0.25)
# the average
mean(sals) 

[1] 8.565

# the variance
var(sals)

[1] 225.5145

# the standard deviation
sd(sals)

[1] 15.01714

# the median
median(sals)

[1] 3.5

# Tukey's five number summary, usefull for boxplots
# five numbers: min, lower hinge, median, upper hinge, max
fivenum(sals)

[1]  0.25  1.00  3.50  8.00 50.00

# summary statistics
summary(sals)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.250   1.250   3.500   8.565   7.250  50.000 

How about the mode?

In R we can write our own functions, and a first example of a function is shown below in order to compute the mode of a vector of observations x

# Function to find the mode, i.e. most frequent value
getMode <- function(x) {
     ux <- unique(x)
     ux[which.max(tabulate(match(x, ux)))]
 }

As an example, we can use the function defined above to find the most frequent value in te vector baz

# Most frequent value in baz
baz

[1] 2 2 3 3 3

getMode(baz)

[1] 3

bar

[1]  2  5 10  2  1

getMode(bar)

[1] 2