Getting Started with R

a. Start R.

b. Verify that the computations above worked as advertised. Note that for the longer expressions, you may want to copy and paste from the online version of this lab.

As you may recall, Activity 2-6 reports on two sections of Introductory Statistics, one that they term a “Regular Section” and one that the term a “Sports section”. In the Regular section, 16 students got good scores, 11 students got fair scores, and 2 students got poor scores. In the Sports section, 7 students got good scores, 15 students got fair scores, and 6 students got poor scores.

a. Write R expressions that assign names to those six values.

b. Write an R expression that computes the total number of students in the Regular section and assigns that value to RegularStudents.

c. Write an R expression that computes the proportion of students who passed the Regular section (good and fair grades are passing grades; poor grades are not).

d. Repeat the previous two steps using the grades of the Sports section.

Strings are pieces of text that you might use in your analysis. They can be values associated with variables (e.g., the name of a state) or they can be titles you use in your diagrams (e.g., the title of an axis or of the whole diagram). In R, you surround each string with quotation marks, typically double quotation marks. For example, "Connecticut", "Usage Percentage", and " February High Temperature" are all strings.

As you've noted, we often gather a large number of values in response to a single question. For example, in our study of states that students visited, we had over 100 values spread across the four sections of introductory statistics that participated. Clearly, it would not be sensible to name each of those values separately. R supports vectors for sequences of values.

The easiest way to create a vector is with the c(v1,v2,...,vn) command. Here's a short vector giving a few counts of states visited.

> StatesVisited = c(20,37,15,20,20,15,4,18,25,4,4,4)
> StatesVisited
[1] 20 37 15 20 20 15  4 18 25  4  4  4

Similarly, here are two vectors, one of which contains the ratios of performances in the regular section and one of which contains strings that describe those ratios.

> RegularGood = 16
> RegularFair = 11
> RegularPoor = 2
> RegularTotal = RegularGood + RegularFair + RegularPoor
> RegularProportions = c(RegularGood/RegularTotal, RegularFair/RegularTotal, RegularPoor/RegularTotal)
> RegularLabels = c("Good Grades", "Fair Grades", "Poor Grades")

You will use vectors in a variety of ways. For example, you can use the two vectors we've just created to create a simple bar graph. (We'll return to the details of bar graphs a little bit later.)

> barplot(RegularProportions, names.arg=RegularLabels, main="Grades in Regular Section")

Similarly, you can use the vector of states visited to create a dot plot. (You may find the first command a little confusing. We'll return to the details of dot plots a little later.)

> library(BHH2, lib="/home/rebelsky/Stats115/Packages")
> dotPlot(StatesVisited,main="States Visited by Stats Students")

More importantly, you can also compute summary statistics for a vector of values. (Don't worry if you don't understand all of the things we compute in the next examples ... they are intended for demonstration purposes only.) In particular, we can find the length (number of entries), max (maximum value), min (minimum value), mean (average value), median (middle value), and sum (total of values) of a vector.

> length(StatesVisited)
[1] 12
> max(StatesVisited)
[1] 37
> min(StatesVisited)
[1] 4
> mean(StatesVisited)
[1] 15.5
> median(StatesVisited)
[1] 16.5
> sum(StatesVisited)
[1] 186

We can even produce a table that summarizes the values in the vector.

> table(StatesVisited)
StatesVisited
 4 15 18 20 25 37 
 4  2  1  3  1  1 

At times, you will need vectors with regularly-spaced values. For example, you might want to create the vector (0,5,10,15,20,25,30,35,40,45,50) as labels for a diagram or as boundaries for ranges. To create vectors of regularly-spaced values, you use the seq(from=val, to=val,by=val) command.

> seq(from=0,to=50,by=5)
[1]  0  5 10 15 20 25 30 35 40 45 50
> seq(from=10,to=20,by=1.2)
[1] 10.0 11.2 12.4 13.6 14.8 16.0 17.2 18.4 19.6
> seq(from=10,to=1,by=-1)
[1] 10  9  8  7  6  5  4  3  2  1

a. Try the example above in which we created vectors for the regular section of introductory statistics and then created a bar graph from them. We've repeated those commands here:

> RegularGood = 16
> RegularFair = 11
> RegularPoor = 2
> RegularTotal = RegularGood + RegularFair + RegularPoor
> RegularProportions = c(RegularGood/RegularTotal, RegularFair/RegularTotal, RegularPoor/RegularTotal)
> RegularLabels = c("Good Grades", "Fair Grades", "Poor Grades")
> barplot(RegularProportions, names.arg=RegularLabels, main="Grades in Regular Section")

b. Create a similar graph for the sports section of the class.

c. Create a similar graph for both sections. (Hint: You'll need to build bigger vectors.)

The data in the previous exercise were already tabulated for us. What if the data are not already tabulated? As we've just seen, the table command will tabulate for you. You can even tell R to graph that table.

a. Verify that R tabulates the simulated states visited data.

> StatesVisited = c(20,37,15,20,20,15,4,18,25,4,4,4)
> table(StatesVisited)

b. Build a bar graph from the data by first tabulating it and then building a bar graph from the table.

> barplot(table(StatesVisited), main="States Visited by Intro Stats Students")

Here's a vector of strings that represent the grades that students got in a class.

> LetterGrades = c("C","A","B","A","A","B","C","C","B","A","C","C")

a. Build that vector.

b. Using table, build a tabular summary of the grades.

c. We can use barplot to plot that table. In particular, try the following and see what happens.

> barplot(table(LetterGrades))

d. Create a similar vector, table, and plot of the genders of the ten or so students nearest you.

Interestingly (or perhaps not so interestingly), R lets you include vectors in computations. In this exercise, you'll explore those computations a bit.

a. Create the vector 95,85,90,78,70,90,95,100,92 and name it Grades. This vector is intended to represent a group of sample grades.

b. Create the vector 50,20,33,90,60 and name it Answers. This vector intended to represent how many students selected answers a, b, c, d, and e on a multiple-choice problem.

c. What do you expect the result of the following command to be? (Don't enter it yet: Describe what you think should happen.)

> Grades + 10

d. Check your answer experimentally. (That is, type in the command and see what the result is.)

e. What do you expect the result of the following command to be? (Once again, don't enter it yet: Describe what you think should happen, now that you have a little more experience.)

> 2 * Answers

f. Check your answer experimentally.

g. Of course, neither of those computations makes sense. Here's one that might. What do you expect the result of the following computation to be?

> Grades - mean(Grades)

h. Check your answer experimentally.

i. Why might someone want to do that computation?

j. Create a bar graph from those modified data.

> students = c("Adam","Beth","Charles","Dani","Eric","Fiona","Greg","Hanna","Iggy")
> barplot(Grades - mean(Grades), names.arg=students)

k. What do you expect the output of the following command to be?

l. Check your answer experimentally.

m. Why might someone want to do that computation?

n. Create a bar graph for those scaled counts.

> Letters = c("A","B","C","D","E")
> barplot(Answers/sum(Answers), names.arg=Letters, main="Responses to Question 3")

Vectors are a great way to accumulate all the values associated with a single variable (as we did for grades and states visited) or to gather data for a bar graph (as we did for numbers of students getting certain categories of grades in different statistics sections ). However, most of the time we're analyzing data, we work with more than one variable per observational unit. For example, in Activity 2-4, each OU had three variables: The state name, the kind of law, and the percentage of usage.

When you deal with data with more than one variable, R prefers to organize those data into what R calls a data frame. (In fact, there are times when you're dealing with only one variable that R still prefers to organize those data into a data frame.) A frame is a table-like object (in fact, R often refers to it as a table) in which each column represents a variable and each row an observational unit.

We can build data frames at the command line, using the data.frame procedure, and creating a vector for each column. For example, here's a data frame for the start of the seatbelt data.

> SeatbeltUsage = data.frame(State=c("Alabama","Alaska","Arizona","Arkansas"), 
+   Law=c("Primary","Secondary","Secondary","Secondary"), 
+   Compliance=c(81.8,78.4,94.2,68.3))
> SeatbeltUsage
     State       Law Compliance
1  Alabama   Primary       81.8
2   Alaska Secondary       78.4
3  Arizona Secondary       94.2
4 Arkansas Secondary       68.3

Of course, that mechanism for building frames is both inconvenient and awkward (since, for example, you enter different variables for the same OU at different places), and almost no one every uses it except for quick tests. Instead, we either read pre-existing data from a file or build the data using a data editor.

To use the data editor, you write

> TableName = edit(data.frame())

The specifics of the data editor vary from system to system. On our Linux boxes, it's a bit clumsy, but gets the job done.

Once you've built a data frame and want to update it, you use the command fix(TableName). This command brings up the same editor, but on an existing frame. Many R users find it convenient to build a small table at the command line and then update it using fix.

A lot of the time, you'll simply want to read data from a file. The read.table("filename", header=TRUE) command is the most typical command for reading from a file. If the data are in CSV (comma-separated values) format, as they often are for this class, you use read.csv instead of read.table.

> SeatbeltUsage = read.csv("/home/rebelsky/Stats115/Data/SeatBeltUsage05.csv")

So, once you have a frame (that you've created at the command line, that you've built in the data editor, or that you've read from a file), what can you do with it? You can look at the first few lines with head(table).. You can look at the whole thing (not usually advisable) by entering the name of the table. Early on, you are likely to want to extract particular columns from the table to use as vectors. For example, you might do that to analyze them individually. You can extract a column by writing Table$ColName. For example, we might get the Law column from the SeatbeltUsage frame with SeatbeltUsage$Law.

R also contains a wealth of techniques for extracting particular rows from a frame. You can, for example, follow the name of a frame with square brackets and, within those square brackets, give a vector of rows and then a comma. We get rows 1, 2, and 4 of SeatbeltUsage with

> SeatbeltUsage[c(1,2,4),]
     State       Law Compliance
1  Alabama   Primary       81.8
2   Alaska Secondary       78.4
4 Arkansas Secondary       68.3

As importantly, instead of the vector, we can substitute a predicate (test) based on some column of the table. For example, the following selects all the rows of the SeatbeltUsage table for which the law is Primary. (We use == rather than = because = is used for assigning names to values, and we don't want R to be confused.)

> SeatbeltUsage[SeatbeltUsage$Law == "Primary",]
            State     Law Compliance
1         Alabama Primary       81.8
5      California Primary       92.5
7     Connecticut Primary       81.6
8        Delaware Primary       83.8
..

We can also use inequality tests to get states with above or below a certain compliance.

> SeatbeltUsage[SeatbeltUsage$Compliance < 70,]
              State       Law Compliance
4          Arkansas Secondary       68.3
16           Kansas Secondary       69.0
17         Kentucky Secondary       66.7
21    Massachusetts Secondary       64.8
24      Mississippi Secondary       60.8
NA             <NA>      <NA>         NA
40   South Carolina Secondary       69.7
41     South Dakota Secondary       68.8
NA.1           <NA>      <NA>         NA

The two NA rows are for the states for which there was no compliance data. (It's a strange quirk of R that the whole row gets turned to NA.) For most of the data we use, we won't have that problem.

Finally, if you've created (or modified) a table in R, you may want to save it for later use. You do so with the write.table("filename") command. You can also use the write.csv("filename") command.

a. Using the data.frame(Name=c(...),...) construct, create the following data frame, named GradeBook.

   Name      Year Grade
1 Adams Sophomore     90
2 Brown    Junior     80
3 Davis Sophomore     90
4   Doe Freshling     85
5 Jones    Senior     70
6 Smith    Senior    100

b. Create a vector, Years, that contains just the years from that frame.

c. Create a summary table from Years. (Remember, you use table(...) to create a summary table.)

d. Can you find a way to create a summary table of student years directly from GradeBook?

e. Edit GradeBook using fix(GradeBook) and add a few more rows.

f. Repeat steps c and d.

g. Edit GradeBook using fix(GradeBook) and add another column entitled Major. You may choose whatever major you want for our observational units.

h. Build a summary table of majors from the modified GradeBook.

i. Write GradeBook to a text file and a CSV file using

> write.table(GradeBook, "~/Desktop/GradeBook.txt")
> write.csv(GradeBook, "~/Desktop/GradeBook.csv", row.names=FALSE)

j. Read each of those files back into variables called, respectively GB1 and GB2.

k. Two files should have appeared on the desktop, corresponding to the names that you gave above (GradeBook.txt and GradeBook.csv). Double click on each to open it in some editor. What differences do you see between the ways in which you edit the files?

l. Add a few more rows to each file, save it, and then redo step j. Note that when you're editing the CSV file (in Gnumeric on our Linux systems), you'll need to remind it to save the file as CSV.

The file /home/rebelsky/Stats115/Data/survey-a.csv contains five of the variables from the introductory statistics survey:

a. Read in that table and store it in a data frame named Survey.

> Survey = read.csv("/home/rebelsky/Stats115/Data/survey-a.csv", header=TRUE)

b. Look at the first few lines of that frame with head(Survey).

c. Write a command to extract rows 5, 10, 15, 20, ... 100. (Hint: Think about ways to construct the vector 5, 10, 15, ..., 100.)

d. Write a command to build a bar graph of responses to the question of whether to retain or abolish the penny.

e. Write a command to determine the mean number of states respondents to the survey have visited.

f. Write a command to extract the rows of the table in which the goal variable has the value "Olympic gold medal".

g. Write a command to assign the name GoldMedalists to the result of the previous computation.

h. Find the mean number of states that respondents who selected "Olympic gold medal" have visited.

a. Create a bar plot of the goals of introductory statistics students with the following commands.

> Survey = read.csv("/home/rebelsky/Stats115/Data/survey-a.csv", header=TRUE)
> barplot(table(Survey$Goal), main="Goals of Intro Stats Students")

b. Save that bar plot to your desktop with the following commands.

> dev.copy(jpeg, filename="~/Desktop/goals.jpg", width=600, height=400)
> dev.off()

c. On your desktop, you should now see a file called goals.jpg. Double-click on it.

a. Repeat the previous set of commands to verify that the plots are created as described. Note that you will need to run the library command first. Note also that you will need to have the Survey frame defined. See earlier in the lab for how to read in the survey.

b. Create a dot plot for the StatsValue column of the Survey frame.

c. Create a bar graph for the StatsValue column of the Survey frame.

d. What are the relative advantages and disadvantages of these two ways of displaying the responses to the value of statistics question?

e. Create a bar graph for the States column of the Survey frame.

f. What problems, if any, do you think one would have reading the bar graph rather than the dot plot for the number of states visited data?