Univariate Data

• manipulate named vectors
• summarize univariate data using statistics and graphics

Announcements:

• I appreciate Irene asking “What is boilerplate?” Please ask when I use words like these without defining them!

live notes

Named vectors

A vector is an ordered sequence of data values. A named vector has names for every element.

Setup:

I want a named vector with some made up data for us to work with. Recall runif creates random data from a Uniform(0, 1) distribution. That’s r for random, unif for uniform. The names will be the letters from a to z, which R provides in the variable letters. There are 26 letters in the English alphabet, so I need 26 random data points. Let’s verify there are 26 letters:

length(letters)

Q: Which is the best way to create this data, and why?

x = runif(26)

# OR

x = runif(length(letters))

It might not be obvious, but x = runif(length(letters)) is much better, because it can easily adapt to new situations without requiring us to change it. For example, if we were using a non English alphabet that has a different number of letters, then x = runif(length(letters)) will still work. Another reason this choice is better is it prevents a whole class of possible typos and errors.

set.seed(128)
x = runif(length(letters))
names(x) = letters

After you call set.seed, R will produce the same sequence of random numbers. This should let us all have the same set of numbers, which implies that the numbers aren’t random at all. 🤣

Helpful functions for homework

Demo all of these, ask students to describe what they do.

names, sort, head, tail, hist, %in%, x["a"]

Try some predictions:

"a" %in% letters
"b" %in% letters
"abcd" %in% letters

Summary statistics

Next n students in the queue, take 2 minutes to call the following functions on x, and report to the class what they do. Everyone else: pick one of these and study it, so that you can help your fellow students if they get stuck.

Measures of center:

mean(x)
median(x)
mean(x, trim = 0.05)

Measures of spread:

sd(x)
quantile(x)
range(x)
summary(x)

Let’s see which measures of center are robust to outliers! We’ll create a data set y that’s just like x, but has an outlier.

y = c(x, 10)

Exponent notation

Print out data, introduce exponent notation.

0.03956565 = 3.956565e-02 = 3.956565 * 10^-2

Watch out for numbers very close to 0!

1d graphics

These should look familiar from stats courses:

x = rnorm(100)
par(mfrow = c(1, 3))
hist(x, main = "histogram")
boxplot(x, main = "boxplot")
d = density(x)
plot(d, main = "kernel density estimate")

More exotic are the kernel density estimators:

Plot all three together:

d = density(x)

plot(d)

The idea of density estimators is to infer the probability density function (PDF) that generated the data, assuming that the data are independent and identically distributed (IID) observations from a particular distribution.

preview filtering by condition

Compare with trimmed means.