Lecture 8: Summarizing Data Part 2: Plots

Recap

• Summary statistics are ways of describing the distribution of a variable
• Examples include mean, percentiles, SD, and specific percentiles of interest (median, min, max)
• Another, very good way to describe a variable is by actually showing that distribution with a graph
• I showed you plenty of graphs last time, this time I’m going to show you how to make them yourself!

Note about ggplot

• As I mentioned before, we’re going straightforward, doing our plotting with base R
• In the case of plotting, it’s going to be easier to use base R, but also not look as good as the alternative, ggplot2, which is also in the tidyverse package.
• ggplot2 code for plots will be available in the slides. Just search for ‘ggplot’
• And have also been for most previous slides - I’ve been making most graphs with it!
• Don’t forget extra credit opportunity for learning ggplot2

Plot types we will cover:

• Density plots (for continuous)
• Histograms (for continuous)
• Box plots (for continuous)
• Bar plots (for categorical)
• Plus:
  • Adding plots together
  • Putting lines on plots
  • Makin ’em look good!

Plots we won’t:

• Lots and lots and lots of plot options
• Mosaics, Sankey plots, pie graphs
• Some aren’t common in Econ but could be!
• Others are just too tricky (like maps)
• See The R Graph Gallery

Density plots and histograms

• Density plots and histograms will show you the full distribution of the variable
• Values along the x-axis, and how often those values show up on y
• The difference - density plots will present a smooth line by averaging nearby values
• A histogram will create “bins” and tell you how many observations fall into each
• (don’t forget we can save plots using Export in the Plots pane)

Density plots

• To make a density plot, we take our variable and make a density() object out of it, then plot() that thing!
• Let’s play around with data from the Ecdat package

install.packages('Ecdat')
library(Ecdat)
data(MCAS)
plot(density(MCAS$totsc4))

Titles and labels

• Readability is super important in graphs
• Add labels and titles! Titles with ‘main’ and axis labels with ‘xlab’ and ‘ylab’

plot(density(MCAS$totsc4),main='Massachusetts Test Scores',
     xlab='Fourth Grade Test Scores')

Histograms

• Histograms require a little less typing - just hist()

hist(MCAS$totsc4)

Histograms

• These need labels too! Other important options:
• Do proportions with freq=FALSE, or change how many bins there are, or where they are, with breaks

hist(MCAS$totsc4,xlab="Fourth Grade Test Scores",
     main="Test Score Histogram",freq=FALSE,breaks=50)

Box plots

• Less common in economics, but a good way to look at your data
• And check for outliers!
• Basically a summary table in graph form
• Shows the 25%, 50%, 75% percentiles
• Plus lines that represent 1.5 IQR (75th minus 25th)
• And dots for anything otuside that range

Box plots

• Simple!
• Note the negative outliers - not necessarily a problem but good to know!

boxplot(MCAS$totsc4,main="Box Plot of 4th Grade Scores")

Box plots

• Easy to look at multiple variables at once, too

boxplot(select(MCAS,totsc4,totsc8),main="Box Plot of 4th Grade Scores")

Bar plots

• Last time we talked about the table() command, which shows us the whole distribution of a categorical variable
• Still a great command! Let’s look at majors of students taking advanced micro from a mid-1980s sample in the Ecdat package

data(Mathlevel)
table(Mathlevel$major)

## 
## other   eco   oss    ns   hum 
##   130   209   103   126    41

Bar plots

• Bar plots, express this table, graphically
• Stick that table in there!

barplot(table(Mathlevel$major),main="Majors of Students in Advanced Microeconomics Class")

Bar plots

• And, just like before, we can make it a proportion instead of a count by wrapping that table() in prop.table()

barplot(prop.table(table(Mathlevel$major)),main="Majors of Students in Advanced Microeconomics Class")

Adding Lines

• It’s pretty common for us to want to add some explanatory lines to our graphs
• For example, adding mean/median/etc. to a density
• Or showing where 0 is
• We can do this with abline() which adds a line with a given intercept (a) and slope (b), after we make our plot.

Adding Lines

• After creating the plot, THEN add the abline(intercept,slope), or abline(h=horizontal), abline(v=vertical) for horizontal or vertical numbers

hist(MCAS$totsc4)
passingscore <- 705
abline(0,1)
abline(v=passingscore,col='red')
abline(h=50)

Adding Lines

hist(MCAS$totsc4)
passingscore <- 705
abline(v=passingscore,col='red')

Adding Lines

• A common use of adding lines is to show where the mean or median of the distribution is, as I did in the last lecture

plot(density(MCAS$totsc4))
abline(v=mean(MCAS$totsc4),col='red')
abline(v=median(MCAS$totsc4),col='blue')

Overlaying Densities

• Sometimes it’s nice to be able to compare two distributions
• Because density plots are so simple, we can do this by overlaying them
• The lines() function will, like abline(), add a line to your graph
• But it can do this with a density! Be sure to set colors so you can tell them apart

Overlaying Densities

plot(density(filter(MCAS,tchratio < median(tchratio))$totsc4),
     col='red',main="Mass. Fourth-Grade Test Scores by Teacher Ratio")
lines(density(filter(MCAS,tchratio >= median(tchratio))$totsc4),col='blue')

Practice

• Install Ecdata, load it, and get the MCAS data
• Make a density plot for totsc4, and add a vertical green dashed (tough!) line at the median
• Create a bar plot showing the proportion of observations that have nonzero values of bilingua
• Create a box plot for totday, and add a horizontal line at the mean
• Go back and add appropriate titles and/or axis labels to all graphs

Practice answers

install.packages('Ecdata')
library(Ecdata)
data(MCAS)
plot(density(MCAS$totsc4),xlab="4th Grade Test Score")
abline(v=median(MCAS$totsc4),col='green',lty='dashed')

MCAS <- MCAS %>% mutate(nonzerobi = bilingua > 0)
barplot(prop.table(table(MCAS$nonzerobi)),main="Nonzero Spending Per Bilingual Student")

boxplot(MCAS$totday,main="Spending Per Pupil")
abline(h=mean(MCAS$totday))