### Hands-on introduction to R

R is a powerful, comprehensive, open-source software framework for doing statistics. It is possible to download and install the software on computers, or to use it through a website-interface without downloading anything.

We will use R through a website-interface in the form of Sage worksheets. In fact, what you are reading here is a Sage worsheet that will guide you through the first steps of getting familiar with R.

Let us begin by learning how to input (small) datasets into R.

#### How to input simple datasets by hand

Prelude: To use R through Sage worksheets (and Sage cells), the first line in each new cell must always be "%r" (without the quotes).

Another alternative is to choose "R" from the modes menu at the top of the worksheet.

R allows setting up your data through keyboard input, or by reading the data through an input file. It is extremely useful to know how to do keyboard input for simple and small datasets.

Example: Find the mean, standard deviation and 5-number summary for the set of values: 1, 2, 3, 4, 8

The commands below show how to do this.
Note that all the information following any "#" sign is just to explain what is going on. R ignores anything that follows a "#" sign.
%r
# Example showing calculations done in the simplest way for
# a dataset consisting of the 5 numbers: 1, 2, 3, 4, 8
a = c(1, 2, 3, 4, 8)  # define your dataset and give it some name, say, a
mean(a)               # find its mean
sd(a)                 # find its standard deviation
var(a)                # find its variance
summary(a)            # find its 5-number summary & mean

3.62.701851217221267.3
Min. 1st Qu. Median Mean 3rd Qu. Max. 1.0 2.0 3.0 3.6 4.0 8.0
Now, let's define a 2nd variable that is categorical.

For example, suppose it contains the 5 values: Yes, No, Yes, Yes, Maybe
%r
# A dataset consisting of the 5 values: Yes, No, Yes, Yes, Maybe
acat = c("Yes", "No", "Yes", "Yes", "Maybe")
# notice that you must use quotes to enclose categorical values
table(acat)           # make a frequency table


acat Maybe No Yes 1 1 3
Exercise 1: Create an R variable for each of the following datasets
1.   $P=\{$blue, pink, blue, green, green, blue, pink, blue$\}$
2.   $Q=\{3.9, 0, -4.6, -3.3, 2.2, 3.6, -2.9, -0.4, 0.9, 1.5\}$
3.   $R=\{0, 1, 2, 3, a, b, c\}$

Compute summary stats for each quantitative variable, and make a frequency table for each categorical variable.

A very useful thing to know about R is how to access the builtin help utility that is available for every function: simply type the "?" symbol, followed by the command-name or function for which you want help.

For example: ?table
?var
?sd

#### How to input a spreadsheet of data

A spreadsheet or table of raw data can be created manually via keyboard input, or by reading in data files written in various standard formats. The structure used in R to represent such tables is called a "dataframe."

Consider, for example, the following dataset

 Age Sex Class year SAT score Financial aid? 18 F 1 1014 N 20 F 3 1222 Y 17 M 1 1141 Y 17 F 1 1082 N 19 M 2 1261 Y 18 F 2 1288 N 20 F 1 1002 N 21 M 3 1078 N

We will input each column of data as a separate variable first, after which we will organize them into a dataframe. The dataframe can be given any convenient name, e.g., "mydata"
%r
# First create each column as a separate variable: I'll use the names
# "age", "sex", etc., for the names of my variables
age = c(18, 20, 17, 17, 19, 18, 20, 21)
sex = c("f", "f", "m", "f", "m", "f", "f", "m")
year = c(1, 3, 1, 1, 2, 2, 1, 3)
sat_score = c(1014, 1222, 1141, 1082, 1261, 1288, 1002, 1078)
f_aid = c("n", "y", "y", "n", "y", "n", "n", "n")

# Next, I'll combine the variables into a dataframe that
# I will call "mydata"
mydata = data.frame(age, sex, year, sat_score, f_aid)

# Let's print out the dataframe and see if it is what I expect
mydata

# Now we can compute summary stats, make histograms, boxplots,
# piecharts, etc.

agesexyearsat_scoref_aid
18 f 1 1014n
20 f 3 1222y
17 m 1 1141y
17 f 1 1082n
19 m 2 1261y
18 f 2 1288n
20 f 1 1002n
21 m 3 1078n
Once a dataframe is created, it is easy to make various displays, and to compute summary statistics for variables in the dataframe. The following examples show how to do this for variables in the dataframe created above.
%r
table(mydata["f_aid"])   # creates frequency table using "f_aid" from "mydata"
pie(table(mydata["f_aid"]))      # pie chart of "f_aid"
barplot(table(mydata["f_aid"]))  # bar graph of "f_aid"
summary(mydata["sat_score"])     # 5-number summary & mean of "sat_score"
hist(mydata[ , "sat_score"])     # plot histogram; NOTE the comma inside []
boxplot(mydata[ , "sat_score"])

# A simple way to set the histogram scale is to specify
# the number of bars to use, like this
hist(mydata[ , "sat_score"], breaks=6)  # histogram with 6 equal-width bars

# It is also easy to customize the plot title, axes labels, etc., like this
hist(mydata[ , "sat_score"], breaks=6, xlab="SAT scores", main="A title test")

# Try the "?hist" command to see more features of R's histogram function.

n y 5 3
sat_score Min. :1002 1st Qu.:1062 Median :1112 Mean :1136 3rd Qu.:1232 Max. :1288
Exercise 2.1: The following table contains data on the employment status of a sample of college students

Age Major Employment Work hours
19 English Part time 30