# 1 Data in R

In this chapter, we give some information about how to use R and common data types. We begin by showing how to do basic arithmetic, assign values to variables.

## 1.1 Arithmetic and Variable Assignment

R can be used as a calculator. Here R a bunch of examples:

1+1
## [1] 2
3*7
## [1] 21
7/3
## [1] 2.333333
exp(2)
## [1] 7.389056
2^3
## [1] 8
log(7)
## [1] 1.94591
log(7, base = 10)
## [1] 0.845098
sqrt(2)
## [1] 1.414214
2^(1/2)
## [1] 1.414214
pi/2
## [1] 1.570796

A couple of things to note are that pi is a variable that contains the value $$\pi$$, and that the default base of log is the natural logarithm.

You can’t get very far without storing results of your computations to variables! The way to do so is with the <- command, as shown below.

height <- 62 #in inches
height <- height + 2
height <- 3*height

Note that Alt + - is the keyboard shortcut for <- when working on the command line. (That means that <- is one keystroke less than =!)

If you want to see what value is stored in a variable, you can

1. type the variable name
height
## [1] 192
1. look in the environment box in the upper right hand corner of RStudio.

2. Use the str command. This command gives other useful information about the variable, in addition to its value.

str(height)
##  num 192

This says that height contains numeric data, and its current value is 192 (which is 3(62 + 2)). Note that there is a big difference between typing height + 2 (which computes the value of height + 2 and displays it on the screen) and typing height <- height + 2, which computes the value of height + 2 and stores the new value back in height.

It is important to choose your variable names wisely. Variables in R cannot start with a number, and they should not start with a period. Do not use c, q, t, C, D, F, I, T as variable names, as they are already defined. It is also a terrible idea (and one of the most frustrating things to debug) to use sum, mean, or other commonly used functions as variable names. T and F are variables with default values TRUE and FALSE, which can be changed. I recommend writing out TRUE and FALSE rather than using the shortcuts T and F for this reason.

If you have a longish variable name in your environment, then you can use the tab key to autocomplete. Many variable names that you run across will contain periods to indicate some hierarchical structure.

## 1.2 Vectors

Data often takes the form of lists of values, rather than single values. We need to be able to store lists of values in order to be able to work with them. For this, we use vectors. A vector is a list of values (usually) of length bigger than one. (Formally, a list is a different data type. Here, I just mean a finite sequence of values of the same type.)

There are many ways to create vectors. Perhaps the easiest is:

c(2,3,5,7,11)
## [1]  2  3  5  7 11

This vector is the list of the first 5 prime numbers. We can store vectors in variables just like we did with numbers:

primes <- c(2,3,5,7,11)

Another way is with the scan() command, which is interactive. Try primes <- scan() and type in a few primes. When you want to be done, just hit return one more time. Using scan() is fine when doing some work on your own, but it is not reproducible, in the sense that you can’t re-run your code and re-create the same output.

You can create a vector of numbers in order using the : operator:

1:10
##  [1]  1  2  3  4  5  6  7  8  9 10

The rep( ) function will create a vector of repeated values of a given times: rep(x, times). For example,

rep(2,3)
## [1] 2 2 2
rep(1:3,4)
##  [1] 1 2 3 1 2 3 1 2 3 1 2 3
rep(c(2,4),5)
##  [1] 2 4 2 4 2 4 2 4 2 4

Most of the operations in R work well with vectors. Suppose you wanted to see what the square roots of the first 5 primes were. You might guess:

primes^(1/2)
## [1] 1.414214 1.732051 2.236068 2.645751 3.316625

and you would be right! Guess what would happen when you type primes + primes, primes * primes and primes & primes. Were you right?

## 1.3 Indexing Vectors

To examine or use a single element in a vector, you need to supply its index. primes[1] is the first element in the list of primes, primes[2] is the second, and so on.

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

You can do many things with indexes:

primes[1:3]
## [1] 2 3 5
primes[-1]
## [1]  3  5  7 11
primes[c(1,5)]
## [1]  2 11
primes[c(T,F,T,F,T)]
## [1]  2  5 11
primes > 6
## [1] FALSE FALSE FALSE  TRUE  TRUE
primes[primes > 6]
## [1]  7 11

R comes with many built-in data sets. For example, the discoveries dataset is a vector containing the number of “great” inventions and scientific discoveries in each year from 1860 to 1959. Try ?discoveries to see more information about the discoveries dataset.

discoveries
## Time Series:
## Start = 1860
## End = 1959
## Frequency = 1
##   [1]  5  3  0  2  0  3  2  3  6  1  2  1  2  1  3  3  3  5  2  4  4  0  2
##  [24]  3  7 12  3 10  9  2  3  7  7  2  3  3  6  2  4  3  5  2  2  4  0  4
##  [47]  2  5  2  3  3  6  5  8  3  6  6  0  5  2  2  2  6  3  4  4  2  2  4
##  [70]  7  5  3  3  0  2  2  2  1  3  4  2  2  1  1  1  2  1  4  4  3  2  1
##  [93]  4  1  1  1  0  0  2  0

For larger data sets, this book will often display only the first few cases, using head:

head(discoveries)
## [1] 5 3 0 2 0 3

Here are a few more things you can do with a vector:

table(discoveries)
## discoveries
##  0  1  2  3  4  5  6  7  8  9 10 12
##  9 12 26 20 12  7  6  4  1  1  1  1
max(discoveries)
## [1] 12
sum(discoveries)
## [1] 310
discoveries[discoveries > 5]
##  [1]  6  7 12 10  9  7  7  6  6  8  6  6  6  7
which(discoveries > 5) + 1859
##  [1] 1868 1884 1885 1887 1888 1891 1892 1896 1911 1913 1915 1916 1922 1929

## 1.4 Data Types

There are several types of data that R understands. Data can be stored as numeric, integer, character, factor and logical data types, among others. There are lots of issues and special cases that come up when dealing with these data types, and we do not plan to go over all of them here.

numeric data is numerical data, including all real numbers. If you type x <- 2, then x will be stored as numeric data. (You can test this by typing str(x).)

integer data is data that is integers! If you type x <- 2L, then x will be stored as an integer. (Why L? I don’t know.) When reading data in from files, R will store data that is all integer as an integer, unlike when you enter data in like x <- 2. Again, str() is your best friend here.

character data is what many languages call strings. It is a vector of characters. If you type x <- "hello", then x is a character variable. Compare str("hello") to str(c(1,2)). Note that if you want to access the e from hello, you cannot use x[2]. If you find yourself in the situation where you need to manipulate strings, I recommend using the stringr package. We will not be doing much with strings in this book.

logical data is TRUE and FALSE.

factor data is common in statistics, but maybe not so commonly implemented and used in other programming languages. factor data can take on values in a predefined set: the variable sex could be set up to allow only entries of Male or Female, for example. Depending on the reason for collecting sex data, you might allow sex to have more values.

NA isn’t a data type, but a value that can take on any data type. It stands for Not Available, and it means that there is no data collected for that value. This is most useful if you think of a big set of data with lots of variables. Maybe you are collecting height, weight, sex and blood pressure. You aren’t able to get all of the data from all of the people, so you record what data you can get, and put NA in the other columns. Missing data is a problem that comes up frequently; see the subsection Missing Values below for a brief introduction on how to deal with missing values.

My experience has been that students underestimate the importance of knowing what type of data they are working with. R works really well when the data types are assigned properly. However, some bizarre things can occur when you try to force R to do something with a data type that is different than what you think it is! My strong suggestion is, whenever you examine a new data set (especially one that you read in from a file!), your first move is to use str() on it, followed by head(). Make sure that the data is stored the way you want before you continue with anything else.

## 1.5 Data Frames

Consider the built-in data set rivers. By typint ?rivers, we learn that this data set gives the lengths (in miles) of 141 major rivers in North America, as compiled by the US Geological Survey. This data set is explored further in the exercises in this chapter. By typing head(rivers), we see that rivers is a vector of values that give the length of the rivers.

Now, it would be very useful if the rivers data set also had the names of the rivers also stored. That is, for each river, we would like to know both the name of the river and the length of the river. This leads us to one of the most common data types in R, data frames. A data frame consists of a number of observations of variables. Some examples would be:

1. The name and length of major rivers.
2. The height, weight and blood pressure of a sample of healthy, adult females.
3. The high and low temperature in St Louis, MO, for each day of 2016.

As a specific example, let’s look at the data set mtcars, which is a predefined data set in R.

Start with str(mtcars). You can see that mtcars consists of 32 observations of 11 variables. The variable names are mpg, cyl, disp and so on. You can also type ?mtcars on the console to see information on the data set. Some data sets have more detailed help pages than others, but it is always a good idea to look at the help page.

You can see that the data is from the 1974(!) Motor Trend magazine. You might wonder why we use such an old data set. In the R community, there are standard data sets that get used as examples when people create new code. The fact that familiar data sets are usually used lets people focus on the new aspect of the code rather than on the data set itself. In this course, we will do a mix of data sets; some will be up-to-date and hopefully interesting. Others will be so that you begin to familiarize yourself with the common data sets that developeRs use.

There are two ways to access the data in mtcars. You can use $notation or [] notation. To examine the weights of the car, for example, we could do mtcars$wt
##  [1] 2.620 2.875 2.320 3.215 3.440 3.460 3.570 3.190 3.150 3.440 3.440
## [12] 4.070 3.730 3.780 5.250 5.424 5.345 2.200 1.615 1.835 2.465 3.520
## [23] 3.435 3.840 3.845 1.935 2.140 1.513 3.170 2.770 3.570 2.780

Or, we could do mtcars[,"wt"] or mtcars[,6]. If we want to see what the third car’s weight is, we could use

mtcars$wt[3] ## [1] 2.32 Or, we could use mtcars[3,6]. If we want to form a new data frame, call it smallmtcars, that only contains the variables mpg, cyl and qsec, we could use smallmtcars <- mtcars[,c(1,2,7)]. If we want to look at only the first 10 observations, we could use mtcars[1:10,]. We can also select observations of the data that satisfies certain properties. For example, if we want to pull out all observations that get more than 25 miles per gallon, then we could use mtcars[mtcars$mpg > 25,].

In order to test equality of two values, you use ==. For example, in order to see which cars have 2 carburetors, we can use mtcars[mtcars$carb == 2,]. Finally, to combine multiple conditions, you can use the vector logical operators & for and and |, for or. As an example, to see which cars either have 2 carburetors or 3 forward gears (or both), we would use mtcars[mtcars$carb == 2 | mtcars$gear == 3,]. There are several exercises below which will allow you to practice manipulating data frames. In Chapter @ref(data_manipulation), we will introduce dplyr tools which we will use to do more advanced manipulations, but it is good to be able to do basic things with [,] and $ as well.

## 1.6 Reading data from files

Loading data into R is one of the most important things to be able to do. If you can’t get R to load your data, then it doesn’t matter what kinds of neat tricks you could have done. It is also one of the most frustrating things - not just in R, but in general. If you are lucky, then the data that you are trying to load into R is saved as a .csv file. The extension .csv stands for “Comma Separated Values” and means that the data is stored in rows with commas separating the variables. For example, it might look like this:

"Gender","Body.Temp","Heart.Rate"
"Male",96.3,70
"Male",96.7,71
"Male",96.9,74
"Female",96.4,69
"Female",96.7,62

This would mean that there are three variables: Gender, Body.Temp and Heart.Rate. There are 5 observations; 3 males and 2 females. The first male had a body temperature of 96.3 and a heart rate of 70.

Now, even though you are lucky that your data is in .csv format, if you are a computer novice, then you will still have some frustration getting the file into R. One way to do it is to store the file on your computer. Now, type getwd() in the Console to see what your current working directory is. Make sure that the file you want to read is stored in the current working directory. How do you know? Well, you can click on the Files tab in the lower-right panel in R Studio, and see whether you see the file. If you do not, then it isn’t in the right directory. You will need to move it into the directory specified by getwd().

Once you have it in the correct directory, you are ready to load the file into R. At this point, you simply type my_variable <- read.csv("file.name"). For example, to load the .csv normtemp.csv, which contains the gender, body temperature and heart rate data mentioned above, I would type temp_data <- read.csv("normtemp.csv"). More advanced users may want to set up a file structure that has data stored in a separate folder, in which case they could either specify the full path or the relative path to the file they want to load. There are also interactive ways to load data, but we do not encourage their use in this book, as the results of an analysis from interactive loading of data will not be reproducible.

In other instances, the csv that you want to read is available as a file hosted on a web page. In this case, it is usually easier to read the file directly from the web page by using read.csv("http://website.csv"). As an example, there is a csv hosted at http://stat.slu.edu/~speegle/_book_data/stlTempData.csv, which you can load by typing stlTemp <- read.csv("http://stat.slu.edu/~speegle/_book_data/stlTempData.csv").

I can’t emphasize enough the importance of looking at your data after you have loaded it. Start by using str() and head() on your variable after reading it in. As often as not, there will be something you will need to change in the data frame.

Finally, you can also write R data frames to a csv file, in order to share with other people. If you have a data frame that you wish to store as a .csv file, you use the write.csv() command. If your row names are not meaningful, then often you will want to add row.names = FALSE. The command write.csv(mtcars, "mtcars_file.csv") writes the variable mtcars to the file mtcars_file.csv, which is again stored in the directory specified by getwd() by default.

## 1.7 Missing Values

Many times, there will be missing values in a data set, which is denoted by NA. If your data contains missing values, then sum and max will return the value NA, rather than any meaningful number. Let’s look at an example. These are daily precip, maximum and minimum temperature readings at the St Louis Science Center for the calendar year 2016, as downloaded from noaa.gov.

stlTempData <- read.csv("http://stat.slu.edu/~speegle/_book_data/stlTempData.csv")

As always, we want to run str(), summary and head on this new data set!

str(stlTempData)
## 'data.frame':    349 obs. of  6 variables:
##  $STATION : Factor w/ 1 level "GHCND:USC00237452": 1 1 1 1 1 1 1 1 1 1 ... ##$ STATION_NAME: Factor w/ 1 level "ST LOUIS SCIENCE CTR MO US": 1 1 1 1 1 1 1 1 1 1 ...
##  $DATE : int 20160101 20160102 20160103 20160104 20160105 20160106 20160107 20160108 20160109 20160110 ... ##$ PRCP        : num  0 0 0 0 0 0 0 0.21 0.22 0.15 ...
##  $TMAX : int 33 42 49 38 37 40 47 48 53 37 ... ##$ TMIN        : int  26 28 29 28 24 28 33 32 37 6 ...
summary(stlTempData)
##               STATION                        STATION_NAME
##  GHCND:USC00237452:349   ST LOUIS SCIENCE CTR MO US:349
##
##
##
##
##
##
##       DATE               PRCP             TMAX            TMIN
##  Min.   :20160101   Min.   :0.0000   Min.   :14.00   Min.   : 2.00
##  1st Qu.:20160404   1st Qu.:0.0000   1st Qu.:55.50   1st Qu.:36.50
##  Median :20160702   Median :0.0000   Median :73.00   Median :55.00
##  Mean   :20160669   Mean   :0.1304   Mean   :69.45   Mean   :51.76
##  3rd Qu.:20160930   3rd Qu.:0.0200   3rd Qu.:87.00   3rd Qu.:69.00
##  Max.   :20161231   Max.   :4.3900   Max.   :99.00   Max.   :82.00
##                     NA's   :1        NA's   :18      NA's   :18
head(stlTempData)
##             STATION               STATION_NAME     DATE PRCP TMAX TMIN
## 1 GHCND:USC00237452 ST LOUIS SCIENCE CTR MO US 20160101    0   33   26
## 2 GHCND:USC00237452 ST LOUIS SCIENCE CTR MO US 20160102    0   42   28
## 3 GHCND:USC00237452 ST LOUIS SCIENCE CTR MO US 20160103    0   49   29
## 4 GHCND:USC00237452 ST LOUIS SCIENCE CTR MO US 20160104    0   38   28
## 5 GHCND:USC00237452 ST LOUIS SCIENCE CTR MO US 20160105    0   37   24
## 6 GHCND:USC00237452 ST LOUIS SCIENCE CTR MO US 20160106    0   40   28

From this, we can see that not all dates are represented, as there are only 349 observations, where there should have been 366. Moreover, we can also see that the max temperature, min temperature and precipitation were not recorded on 18, 18 and 1 day(s) respectively. We can also see that the hottest it got was 99 degrees (huh), and the coldest it got was 2 degrees. The most it rained on any one day was 4.39 inches.

Suppose, however, that we wanted to compute the mean of the maximum temperatures using the mean function, as we did above. We could try

mean(stlTempData$TMAX) ## [1] NA But, this gives us the answer NA. If we want R to compute the mean of the values that are there, we need to add the option na.rm = TRUE. mean(stlTempData$TMAX, na.rm = TRUE)
## [1] 69.45317

Similarly, if we want to compute the max using max or the standard deviation using sd, we would need to do it as follows:

max(stlTempData$TMAX, na.rm = TRUE) ## [1] 99 sd(stlTempData$TMAX, na.rm = TRUE)
## [1] 19.89868

## 1.8 Exercises

1. Let x <- c(1,2,3) and y <- c(6,5,4). Predict what will happen when the following pieces of code are run. Check your answer.
1. x * 2
2. x * y
3. x[1] * y[2]

2. Let x <- c(1,2,3) and y <- c(6,5,4). What is the value of x after each of the following commands? (Assume that each part starts with the values of x and y given above.)
1. x + x
2. x <- x + x
3. y <- x + x
4. x <- x + 1

3. Determine the values of the vector vec after each of the following commands is run.
1. vec <- 1:10
2. vec <- 1:10 * 2
3. vec <- 1:10^2
4. vec <- 1:10 + 1
5. vec <- 1:(10 * 2)

4. Use R to calculate the sum of the squares of all numbers from 1 to 100: $$1^2 + 2^2 + \dotsb + 99^2 + 100^2$$

5. Let x be the vector obtained by running the R command x <- seq(10, 30, 2).
1. What is the length of x? (By length, we mean the number of elements in the vector. This can be obtained using the str function or the length function.)
2. What is x[2]?
3. What is x[1:5]?
4. What is x[1:3*2]?
5. What is x > 25?
6. What is x[x > 25]?
7. What is x[-1]?
8. What is x[-1:-3]?

6. Consider the built-in data frame airquality.
1. How many observations of how many variables are there?
2. What are the names of the variables?
3. What type of data is each variable?
4. Do you agree with the data type that has been given to each variable? What would have been some alternative choices?

7. R has a built-in vector rivers which contains the lengths of major North American rivers.
1. Use ?rivers to learn about the data set.
2. Find the mean and sd of the rivers data.
3. Make a histogram (hist) of the rivers data.
4. Get the five number summary (summary) of rivers data.
5. Find the longest and shortest river in the set.
6. Make a list of all (the lengths of the) rivers longer than 1000 miles.

8. There is a built in data set state, which is really seven separate variables with names such as state.name, state.region, and state.area.
1. What are the possible regions a state can be in? How many states are in each region?
2. Which states have area less than 10000 square miles?
3. Which state’s geographic center is furthest south? (Hint: use which.min)

9. Consider the mtcars data set.
1. Which cars have 4 forward gears?
2. What subset of mtcars does mtcars[mtcars$disp > 150 & mtcars$mpg > 20,] describe?
3. Which cars have 4 forward gears and manual transmission? (Note: manual transmission is 1 and automatic is 0.)
4. Which cars have 4 forward gears or manual transmission?
5. Find the mean mpg of the cars with 2 carburetors.

10. Complete the Introduction to R datacamp tutorial.

11. In the text, we loaded the data at http://stat.slu.edu/~speegle/_book_data/stlTempData.csv by reading it directly from the web site. For large files, this can be time-consuming to do every time, and it also requires you to always have an internet connection when you want to use that data. Load the data set contained here by first downloading it onto your machine, putting it in the correct directory, and using read.csv.

12. Install the package Lahman by clicking on Install under the Packages tab. Type in Lahman. (Or, use the command install.packages("Lahman").) Then, load the library into memory by typing library(Lahman). Consider the data set Batting, which should now be available. It contains batting statistics of all major league players broken down by season since 1871. We will be using this data set extensively in the data wrangling chapter of this book.
1. How many observations of how many variables are there?
2. Use the command head(Batting) to get a look at the first six lines of data.
3. What is the most number of triples (X3B) that have been hit in a single season?
4. What is the playerID(s) of the person(s) who hit the most number of triples in a single season? In what year did it happen?
5. Which player hit the most number of triples in a single season since 1960?