In this Case Study, you will refresh your memory of STOR 155 while you learn some basic commands and tools for analyzing data with R. We’ll be looking at some data from college basketball games last year.
Run the following R code to load the data into your RStudio and take a look at it.
# Load dataset
bball = read.csv("http://kbodwin.web.unc.edu/files/2016/06/basketball.csv")
# Look at dataset
head(bball)
summary(bball)The command read.csv( ) will read a dataset into R from your computer or from online. “csv” stands for “comma separated value”, a common file type where the data is listed in a text file, with variables separated by commas. For now, you don’t need to worry about the details of read.csv( ). Once you have loaded the data, the command summary( ) will tell you about the variables in the dataset and their values. Another useful function is head( ), which shows you the first 6 rows of the dataset.
Look at the outputs of summary(bball) and head(bball), and describe the variables using vocabulary from STOR 155.
If head( ) shows the first 6 rows of the dataset, what command do you think might show the last 6 rows? Try out your proposed function and see what happens
Try the commands ncol( ) and nrow( ). What do these do? How could you get the same information from head( ), summary( ), and/or the command you figured out in part (b)?
Sometimes, we will want to look at individual entries, rows, or columns of our data matrix. We can do this using brackets [ ] after our dataset. We can also look at a variables (columns) by name using the $ symbol. Try the following examples.
# Look at a single row
bball[123, ]
# Look at a single column
bball[ , 4]
bball$Team.Score
# Look at a single entry
bball[123, 4]
bball$Team.Score[123]
# Calculate mean, median, variance, and standard deviation
mean(bball$Team.Score)
median(bball$Team.Score)
var(bball$Team.Score)
sd(bball$Team.Score)What is the difference between mean(bball$Team.Score) and mean(bball[,4])? Why might it be useful to have two ways to get access the variable Team.Score?
In plain English, what were the events of the game represented by the first row of the dataset?
(Note: If you don’t know much about basketball - for example, if you don’t know what it means to play a game “Home” versus “Away” - ask people around you.)
All these commands we have been using, like summary( ) and mean( ) are called functions. A function can take all different kinds of input depending on what you are trying to do: datasets, vectors such as bball$Team.Score, etc. An important skill in R is figuring out for yourself how functions work.
For example, type ?boxplot into your R console. A help page will pop up telling you about this function. Notice that under Usage, it says boxplot(x, ...). This tells you that you need to supply something called x to the function, and the rest of the input is optional. But what is x? Ah-ha! There is a section called Arguments, which tells us that x is the vector of values you want to put in a boxplot.
Run the code below to make a boxplot of the team scores of college basketball games.
# make boxplot of team scores
boxplot(bball$Team.Score)?hist, a function for making histograms. Below is basic code to make a histogram of Team.Scores, and also code for the same histogram but with a lot of the optional input changed. Mess around with these inputs until you understand what each is doing.# Boring histogram
hist(bball$Team.Score)
# Fancy histogram
hist(bball$Team.Score, breaks = 5, main = "I am a title", xlab = "I am an x-axis label", col = "grey", freq = FALSE)Explain in your own words what breaks and freq change about the histogram.
main, xlab, ylab, and col are common to most plotting functions. Use what you learned in (a) to make a boxplot of Team.Scores with proper axis labels and title.# make boxplot of team scores
boxplot(bball$Team.Score, YOUR CODE HERE)# Boring histogram
hist(bball$Team.Score, freq = FALSE)
# overlay Normal Curve
curve(dnorm(x, mean=120, sd=20),
add = TRUE, col = "blue", lwd = 2)Explain what the role is of the functions curve( ) and dnorm( ). Why did we put add = TRUE in the inputs?
# overlay smoothed curve
lines(density(bball$Team.Score),
col = "red", lwd = 2, lty = 2)What is the difference between lines( ) and curve( )? When might we want to use density( ), and when would it be better to overlay a Normal curve on a histogram?
YOUR CODE HEREOne of the most powerful qualities of R is the ability to select a subset of a dataset. Suppose we want to look only at games involving UNC or Duke. We would need to figure out which rows of bball involve one of those teams, and then make a new dataset out of only those rows.
For this, we will use booleans, which are variables with the value TRUE or FALSE. Play around with the following code until you feel comfortable with ==, >, <, and %in% as well as & (and) and | (or).
# booleans practice
1 == 1
1 == 2
1 < 2
1 == 1 | 1 > 2
1 == 1 & 1 > 2You can make up your own vector using the function c( ), which stands for “concatenate”. This is like making a new variable - the variable can contain anything you want, such as numbers, strings, booleans. Try the example below to make a vector and subset it. Note that we can use either <- or = to store information in a variable.
vec <- c("cat", "dog", "horned toad", "Her Majesty Queen Elizabeth", "dog")
vec
# Some more booleans
vec == "dog"
"dog" == vec
vec %in% c("dog", "cat")
c("dog", "cat") %in% vec
# Finding indices
which(vec == "dog")
which(vec %in% c("dog", "cat"))
which(c("dog", "cat") %in% vec)
# Subsetting
new = vec[vec %in% c("dog", "cat")]
newvec = c(1, 2, 3, "4")
vec + 2vec = c(TRUE, FALSE, FALSE, TRUE)
vec + 2bball.Try running each of the following lines of code. None of them will make the datset we want. What was the problem with each one?
# Make new dataset with only UNC or Duke games
#A
my_subset = bball[Team == "North Carolina" | Team == "Duke", ]
#B
my_subset = bball[bball$Team == "North Carolina", bball$Team == "Duke"]
#C
my_subset = bball[bball$Team = "North Carolina" | bball$Team = "Duke", ]
#D
my_subset = bball[bball$Team == "North Carolina" & bball$Team == "Duke", ]
#E
unc_games = which(bball$Team == "North Carolina")
my_subset = bball[unc_games | bball$Team == "Duke", ]
#F
my_subset = bball[bball$Team == "North Carolina" | bball$Team == "Duke"]YOUR CODE HEREAlright, enough of that data wrangling. Time to do some statistics.
Check out ?Normal. These are some functions that will help us calculate probabilities about the Normal distribution. (No more using Table A!) The most important ones are pnorm and qnorm.
pnorm(q) will tell you the probability of a standard Normal being below the value q
qnorm(p) will tell you the z-score that has area p below it on a standard Normal curve
pnorm and qnorm.# practice with Normal densities in R
#i
pnorm(0)
qnorm(0)
#ii
pnorm(100)
qnorm(100)
#iii
qnorm(pnorm(0))
qnorm(pnorm(7))
#iv
pnorm(qnorm(0))
pnorm(qnorm(0.5))
#v
pnorm(0, sd = 10)
pnorm(0, mean = 1, sd = 10)
#vi
qnorm(0.05)
qnorm(0.05, sd = 10)
qnorm(0.05, mean = 1, sd = 10)Why did you get an error in part (ii)?
Now use this code to make a new variable for the total score of a game:
# Make new variable
bball$Total.Score = bball$Team.Score + bball$Opponent.ScoreWe will use z-scores and t-scores to think about whether a game is unusually high scoring.
bball actually displays each game twice: once for each team. Make a new dataset with each game listed only once by subsetting bball.YOUR CODE HERETeam.Score are actually the population mean and standard deviation.)YOUR CODE HEREsum( ) and length( ) will help you answer this question.YOUR CODE HEREWhat is the difference between what we did in (b) and (c)? Do you think the Normal approximation is reasonable for this data? Why or why not?
Recall that t-scores are used instead of z-scores when the population standard deviation is unknown. The functions pt and qt work almost same way as pnorm and qnorm, but for the t-distribution instead of the Normal. However, be careful, and read ?pt for help! These functions don’t let you enter the mean and standard deviation as input - you need to figure out what do about that!
Use all your new R skills to answer this question: Was the Feb 17th game between UNC and Duke particularly high scoring for a UNC game?
YOUR CODE HEREYou now have all the R knowledge you need to make some confidence intervals! You may wish to go over your lecture notes for this section, especially to remind yourself how to deal with proportions.
YOUR CODE HEREYOUR CODE HEREYou have now had lots of practice learning to use a function by reading the documentation. Part of the point of this course is for you to become familiar enough with R to learn new commands and functions without being shown how to use them. This will make you a skillful (and hireable!) programmer in the future.
Check out ?t.test and ?prop.test. Figure out what these functions do, what input they take, etc. Then answer the following questions.
YOUR CODE HEREYOUR CODE HEREYOUR CODE HERENow it’s your turn to think like a Statistician.
Many sports fans believe that teams tend to play better when they are in their home arena, perhaps because they are more comfortable there or because they are energized by their fans. This idea is called “Home Court Advantage”.
Based on the bball data, do you think there is any evidence of Home Court Advantage? Be creative - think about different ways you might measure if a team is playing “better” at home.
Explain and justify your answer.