Problem Set 02: Data Visualization

Relevant reading for this problem set: ModernDive Chapter 2: Data Visualization.

In this problem set we will use the ggplot2 package to generate graphics. The “The Grammar of Graphics,” is the theoretical basis for the ggplot2 package. Much like how we construct sentences in any language by using a linguistic grammar (nouns, verbs, etc.), the grammar of graphics allows us to specify the components of a statistical graphic.

In short, the grammar tells us that:

A statistical graphic is a mapping of data variables to aesthetic attributes of geometric objects.

We can break a graphic into the following three essential components:

• data: the data-set comprised of variables that we plot
• geom: this refers to our type of geometric objects we see in our plot (points, lines, bars, etc.)
• aes: aesthetic attributes of the geometric object that we can perceive on a graphic. For example, x/y position, color, shape, and size. Each assigned aesthetic attribute can be mapped to a variable in our data-set.

Getting Set up

Go ahead and launch the R Studio Server, and open a new R Markdown file. Recall, to do this:

• click on the little green plus on the upper left hand of the window
• select R Markdown, as in the image below.

Once you have opened the document:

• change the title at the top to “Data Visualization”. Be sure to keep the quotation marks.
• add an author line, following the example below. You need quotation marks!
• delete any extra code

Finally, save your new document:

• File > Save As
• Browse to your introstatsR folder
• set the file name as ps02_lastname_firstname

You will hand in a knitted html file as your problem set. It is OK if your lab report includes the example code from the lab, as well as your Exercises. Just be sure to make a header to label each Exercise. Please type your code to answer the questions in a code chunk (gray part), under the exercise headers and type (BRIEF) answers to any interpretation questions in the white part under the headers.

R Packages

R Packages are like apps on your cell phone - they are tools for accomplishing common tasks. R is an open-source programming language, meaning that people can contribute packages that make our lives easier, and we can use them for free. For this problem set we will use the following R packages:

• dplyr: for data wrangling
• ggplot2: for data visualization
• readr: for reading in data

These packages are already installed for you on Smith’s R Studio Server. Every time you open a new R session you need to load (open) any packages you want to use. We do this with the library function. Copy, paste and run the following in a code chunk (see the figure above if you forget how to insert a code chunk).

library(dplyr)
library(ggplot2)
library(readr)

Remember, “running code means” telling R “do this”. You tell R to do something by passing it through the console. You can run existing code many ways:

• re-typing code out directly in the console (most laborious method)
• copying and pasting existing code into the console and hitting enter (easier method)
• click on the green triangle in the code chunk (easiest method 1)
• highlight the code and hit Control-Enter on PC or Command-Return on a Mac (easiest method 2)

The Data

Today we will practice data visualization using data on births from the state of North Carolina. Copy, paste and run the code below to load the data.

nc <- read_csv("https://docs.google.com/spreadsheets/d/e/2PACX-1vTm2WZwNBoQdZhMgot7urbtu8eG7tzAq-60ZJsQ_nupykCAcW0OXebVpHksPWyR4x8xJTVQ8KAulAFS/pub?gid=202410847&single=true&output=csv")

The data set that shows up in your Environment is a large data frame. Each observation or case is a birth of a single child.

The data command instructs R to load some data built into a package. The workspace area in the upper right hand corner of the R Studio window should now list a data set called nc with 800 observations (rows or cases) and 13 variables (columns).

How to look at data in R

Take a glimpse

You can see the dimensions of this data frame (# of rows and columns), the names of the variables, the variable types, and the first few observations using the glimpse function. Copy, paste, and run the following in a new code chunk.

glimpse(nc)

We can see that there are 1000 observations and 13 variables in this data set. The variable names are fage, mage, mature, etc. This output also tells us that some variables are numbers…some specifically integers <int>, others are numbers with decimals <dbl>. Some of the variables are factors <fct>. It is a good practice to see if R is treating variables as factors <fct>; as numbers <int> or <dbl> (basically numbers with decimals); or as characters (i.e. text) <chr>.

1. What type of variable is R considering the variable habit to be? What variable type is visits? (answer with text)

The data viewer

You can view the data by clicking on the name nc in the Environment pane (upper right window). This will bring up an alternative display of the data set in the Data Viewer (upper left window). R has stored these data in a kind of spreadsheet called a data frame. Each row represents a different birth: the first entry or column in each row is simply the row number, the rest are the different variables that were recorded for each birth. You can close the data viewer by clicking on the x in the upper left hand corner.

It is a good idea to try kitting your document from time to time as you go along! Go ahead, and make sure your document is knitting, and that your html file includes Exercise headers, text, and code. Note that knitting automatically saves your Rmd file too!

Types of Graphs

We will explore three different types of graphs in this problem set.

scatterplots
boxplots
histograms

Scatterplots

Scatterplots allow you to investigate the relationship between two numerical variables. While you may already be familiar with this type of plot, let’s view it through the lens of the Grammar of Graphics. Specifically, we will graphically investigate the relationship between the following two numerical variables in the flights data frame:

• weeks: length of a pregnancy on the horizontal “x” axis and
• weight: birth weight of a baby in pounds on the vertical “y” axis

ggplot(data = nc, aes(x = weeks, y = weight)) + 
  geom_point()

Let’s view this plot through the grammar of graphics. Within the ggplot() function call, we specified:

• The data frame to be nc by setting data = nc
• The aesthetic mapping by setting aes(x = weeks, y = weight)
• The variable weeks maps to the x-position aesthetic
• The variable weight maps to the y-position aesthetic.

We also add a layer to the ggplot() function call using the + sign. The layer in question specifies the geometric object here as points, by specifying geom_point().

Finally, we can also add axis labels and a title to the plot like so. Again we add a new layer, this time a labs or labels layer.

ggplot(data = nc, aes(x = weeks, y = weight)) + 
  geom_point() + 
  labs(x = "Length of pregnancy (in weeks)", y = "Birth weight of baby (lbs)", 
       title = "Relationship between pregnancy duration and newborn weight")

1. Is there a positive or negative relationship between these variables? (text only to answer)

2. Make a graph showing weeks again on the x axis and the variable gained on the y axis (the amount of weight a mother gained during pregnancy). Include axis labels with measurement units, and a title. (code only to answer)

3. Study the code below, and the resulting graphical output. Note that I added a new argument of color = premie inside the aesthetic mapping. The variable premie indicates whether a birth was early (premie) or went full term. Please answer with text:

   A. What did adding the argument color = premie accomplish?

   B. How many variables are now displayed on this plot?

   C. What appears to (roughly) be the pregnancy length cutoff for classifying a newborn as a “premie”” versus a “full term”.

ggplot(data = nc, aes(x = weeks, y = gained, color = premie))+ 
  geom_point() + 
  labs(x = "Pregnancy length (wks)", y = "Maternal weight gain (lbs)") +
  scale_color_brewer(palette = "Dark2")

1. Make a new scatterplot that shows a mothers age on the x axis (variable called mage) and birth weight of newborns on the y axis (weight). Color the points on the plot based on the gender of the resulting baby (variable called gender). Does there appear to be any strong relationship between a mother’s age and the weight of her newborn? (code and text to answer)

Make sure your document is knitting, and that your html file includes Exercise headers, text, and code. Note that knitting automatically saves your Rmd file too!

Histograms

Histograms are useful plots for showing how many elements of a single numerical variable fall in specified bins. This is a very useful way to get a sense of the distribution of your data. Histograms are often one of the first steps in exploring data visually.

For instance, to look at the distribution of pregnancy duration (variable called weeks), copy, paste and run the following in a new code chunk:

ggplot(data = nc, aes(x = weeks))+ 
  geom_histogram()

## `stat_bin()` using `bins = 30`. Pick better value `binwidth`.

A few things to note here:

• There is only one variable being mapped in aes(): the single numerical variable weeks. You don’t need to compute the y-aesthetic: R calculates it automatically.
• We set the geometric object as geom_histogram()
• The warning message encourages us to specify the number of bins on the histogram, as R chose 30 for us.

We can change the binwidth (and thus the number of bins), as well as the colors like so.

ggplot(data = nc, aes(x = weeks))+ 
  geom_histogram(binwidth = 1, color = "white", fill = "steelblue")

Note that none of these arguments went inside the aesthetic mapping argument as they do not specifically represent mappings of variables.

1. Inspect the histogram of the weeks variable. Answer each of the following with text.

   A. The y axis is labeled count. What is specifically being counted in this case? Hint: think about what each case is in this data set.

   B. What appears to be roughly the average length of pregnancies in weeks?

   C. If we changed the binwidth to 100, how many bins would there be? Roughly how many cases would be in each bin?

2. Make a histogram of the birth weight of newborns (which is in lbs), including a title and axis labels. (code only to answer)

Faceting

Faceting is used when we’d like to create small multiples of the same plot over a different categorical variable. By default, all of the small multiples will have the same vertical axis.

For example, suppose we were interested in looking at whether pregnancy length varied by the maturity status of a mother (column name mature). This is what is meant by “the distribution of one variable over another variable”: weeks is one variable and mature is the other variable. In order to look at histograms of weeks for older and more mature mothers, we add a plot layer facet_wrap(~ mature, ncol = 1). The ncol = 1 argument just tells R to stack the two histograms into one column.

ggplot(data = nc, aes(x = weeks)) +
  geom_histogram(binwidth = 1, color = "white", fill = "steelblue") +
  facet_wrap(~ mature, ncol = 1)

1. Make a histogram of newborn birth weight split by gender of the child. Set the binwidth to 0.5. Which gender appears to have a slightly larger average birth weight? (code and text to answer)

Make sure your document is knitting, and that your html file includes Exercise headers, text, and code. Note that knitting automatically saves your Rmd file too!

Boxplots

While histograms can help to show the distribution of data, boxplots have much more flexibility, and can provide even more information in a single graph. The y aesthetic is the numeric variable you want to include in the boxplot, and the x aesthetic is a grouping variable. For instance, below we set gender as the aesthetic mapping for x, and gained as the aesthetic mapping for y. This creates a boxplot of the weight gained for mothers that had male and female newborns. Note that the fill argument is not necessary, but sets a color for the boxplots.

ggplot(data = nc, aes(x = gender, y = gained)) +
  geom_boxplot(fill = "sienna")

For review, these are the different parts of the boxplot: ’

• The bottom of the “box” portion represents the 25th percentile (1st quartile)
• The horizontal line in the “box” shows the median (50th percentile, 2nd quartile)
• The top of the “box” represents the 75th percentile (3rd quartile)
• The height of each “box”, i.e. the value of the 3rd quartile minus the value of the 1st quartile, is called the interquartile range (IQR). It is a measure of spread of the middle 50% of values. Longer boxes indicating more variability.
• The “whiskers” extending out from the bottoms and tops of the boxes represent points less than the 25th percentile and greater than the 75th percentiles respectively. They extend out no more than 1.5 x IQR units away from either end of the boxes. The length of these whiskers show how the data outside the middle 50% of values vary. Longer whiskers indicate more variability.
• The dots represent values falling outside the whiskers or outliers. The definition of an outlier is somewhat arbitrary and not absolute. In this case, they are defined by the length of the whiskers, which are no more than 1.5 x IQR units long.

8. Make a boxplot of the weight gained by moms, split by the maturity status of the mothers (mature). Include axis labels and a title on your plot. Is the median weight gain during pregnancy larger for younger or older moms? (text and code)

9. Make a boxplot of pregnancy duration in weeks by smoking habit. Is the duration of pregnancy more variable for smokers or non-smokers? (i.e. which group has the greater spread for the variable weeks?). (code and text to answer)

Make sure your document is knitting, and that your html file includes Exercise headers, text, and code. Note that knitting automatically saves your Rmd file too!

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Independent Practice

For the following, you need to determine which type of plot to use, make the plot, and answer any questions with text. There is a table at the end of this document that can help you determine which plot to use, given the question/types of variables.

1. Using a data visualization, visually assess: Is the variable for father’s age (fage) symmetrical, or does it have a skew?

2. Using a data visualization, visually assess: (in this sample) is the median birth weight of babies greater for white or non-white mothers (variable called whitemom)?

3. Using a data visualization, visually assess: (in this sample) as a mother’s age (mage) increases, does the duration of pregnancy (weeks) appear to decrease?

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Data visualization table

This table is a great resource for thinking about how to visualize data.

Table 3.5: Summary of the Five Named Graphs (5NG)

Named graph	Shows	Geometric object	Notes
Scatterplot	Relationship between 2 numerical variables	geom_point()
Linegraph	Relationship between 2 numerical variables	geom_line()	Used when there is a sequential order to the x-variable, e.g. time
Histogram	Distribution of 1 numerical variable	geom_histogram()	A faceted histogram shows the distribution of 1 numerical variable split by 1 categorical variable
Boxplot	Distribution of 1 numerical variable split by 1 categorical variable	geom_boxplot()
Barplot	Distribution of 1 categorical variable	geom_bar() when counts are not pre-counted, geom_col() when they are	Stacked and dodged barplots show the distribution of 2 categorical variables

Table 3.5 from Modern Dive http://moderndive.netlify.com/index.html

Turning in your work

Submit your problem set html file on Moodle. This involves downloading the html file from the R Studio Server to your personal computer. The steps to do this are as follows:

• Make sure you knit a final copy with all your changes and work
• Look at your final html file to make sure it contains the work you expect, and is formatted properly (e.g. Exercise headers, each with answers)
• Go to your Files pane
• Click on your introstatsR folder
• Check the little box in front of the html file
• Click the little blue gear labeled More just a little to the upper right
• Click export > Download
• Submit the file to Moodle

If you need more help, there is a video at the top of this page that can help.

Logging out of the Server

• Save all your work.
• Click on the orange button in the far right corner of the screen to quit R
• Click on the icon of your name in the top right to log out
• You are signed out!

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