Lesson 6 - Statistical Visualizations: Scatterplots & Bubble Charts

Welcome back! In the previous Lesson, you dove into your first statistical visualizations in the form of histograms and box plots—both types of visualizations that can help you locate trends within your data sets. In this Lesson, you’ll expand your repertoire of statistical visualizations by learning how to create two more: scatterplots and bubble charts. Scatterplots are an excellent type of chart for visualizing correlations—or relationships—between variables. These relationships are visible through patterns; in other words, data that follows a clear spatial trend. By adding a third variable (and even a fourth variable!) to your scatterplots, you can turn them into bubble charts, allowing you to look for correlations between even larger groups of variables.

 

Let’s take a look at some ways you might use both of these charts within your analyses before walking through how to create them in Tableau. One, two, three—scatter!

Saving Your Workbook
Throughout this Lesson, we will be walking through how to create certain charts in Tableau using a sample data set about different types of candy and their popularity. We encourage you to follow the instructions in this Lesson yourself to practice visualizing data in Tableau before using it to visualize your project data in the task.

We’ll be using the visuals created in this Lesson from the candy data again in Lesson 9: Storytelling with Data Presentations, so be sure to save and publish your Tableau workbook for this Lesson before you move on to the task.

Use a descriptive title to indicate that the workbook contains the sample project for this Lesson. With your workbook for this Lesson saved, you’ll be able to easily retrieve what you’ve done and continue to work on it as needed later on in the Achievement.

 

1. Scatterplots & Correlations

When you explored the history of data visualization back in Lesson 1: Intro to Data Visualization, you learned about the Cartesian plane. Since then, you’ve experimented with a number of different charts that use an x- and y-axis. Bar charts and histograms, for example, are graphed along an x-axis and display frequency (or count) along a y-axis. A scatterplot, on the other hand, is a chart that graphs two variables: one along the x-axis and one along the y-axis. Because of this, scatterplots don’t show aggregations (counts), rather, individual data points.

 

By graphing data points on a two-dimensional reference frame (the x- and y-axes), scatterplots allow you to visualize relationships between variables. The variables must be quantitative (as you’re examining the relationship between numbers); however, the two axes may or may not use the same scale. Let’s look at an example.

 

The following chart plots a group of people in terms of their height and weight. As the variable along the x-axis (height) increases, or moves to the right, the variable along the y-axis (weight) also increases, or moves upward. By displaying the direction of each variable together, the chart makes it obvious that a relationship exists between those variables:

Figure 1. Taller people weigh more—who’d have thought!

 

This relationship can also be described as a trend. This next example from the NYTimes shows the relationship between life expectancy and median household income for all counties in the United States. The trend shows that as household income increases, so does life expectancy:

Figure 2. Source: NYTimes

 

In this way, scatterplots are a great way to visualize correlation—a quantified measure of the relationship between two variables.

 

2. Correlation in Visual Form

The correlation coefficient takes a value between -1 and +1 and provides information about the strength and direction of the relationship between the two variables in question. The closer the absolute value of the coefficient is to 1, the stronger the relationship—if one variable increases, the other also increases. On the opposite end of the spectrum, the same holds true, only in reverse. The closer the coefficient is to -1, the stronger the relationship but in the opposite direction. This means that if one variable increases, the other decreases.

 

Correlation can also be examined visually by way of scatterplots and trend lines. A trend line runs across the entire length of a chart at the minimum distance from every point in the plot. When the data has a strong correlation, or relationship, the trend line reflects this. Let’s take a look at a few examples.

Terminology Tip!
A trend line may also be referred to as a line of best fit.

Figure 3

In the leftmost chart in Figure 3, above, the trend line is more or less horizontal. This means that there’s no correlation between the variables (or an extremely minimal correlation). The correlation coefficient is close to zero, and the two variables are unrelated. A good example for this might be if you were plotting height and hair length for adults—no prediction can be made about a person’s hair length by knowing their height. As such, the two variables, hair length and height, have no correlation.

 

In the middle chart, the trend line travels upwards diagonally from left to right. This shows a positive correlation between the variables. The slope of the line tells you the direction (positive) of the correlation but not the strength—or magnitude—of the correlation coefficient. A trend line for the example given earlier about height and weight would look something like this.

 

Finally, the rightmost chart shows a trend line sloping downwards from left to right. This demonstrates a negative relationship, or correlation, between the variables. A chart visualizing age and flexibility would likely result in a trend line like this—most people become less flexible as they age, leading to a negative correlation between age and flexibility.

Figure 4. Unless they continue to stretch their joints, most people naturally become less flexible as they age.

 

The strength, or magnitude, of a relationship between two variables can be inferred from how close the data points are to the trend line. Take the following two examples in Figure 5: they both display similar data, they both have positive correlations, and they both have similar trend lines; however, the data points in the example on the right are located much closer to the trend line. This chart shows a perfect correlation of +1. Conversely, the data points in the example on the left are scattered all around the trend line, representing a weaker correlation:

Figure 5. Data points closer to the trend line signify a stronger correlation between the two variables in question. 

 

When comparing two charts, it’s generally easy to see which one has a stronger correlation (unless there isn’t much difference between the two). It’s harder, however, to determine the exact magnitude of the correlation coefficient for a given scenario—you can only get a gist of whether the correlation is strong or weak. The exception to this is if the correlation is a perfect +1 or -1, as this means that every data point is located directly on the trend line.

 

Another advantage to scatterplots is that they can quickly show you whether a correlation coefficient is impacted by all the data points in a set relatively equally or only by a few outliers. Take a look at the two scatterplots in Figure 6, below. The correlation coefficients of both sets are roughly equivalent; however, the data points in the left chart are scattered about the trend line, while the data points in the right chart are all located near the trend line—except for one outlier. Without this single outlier, the correlation coefficient would have a greater magnitude, and the trend line would fit the data points more closely. You can’t, however, say the same for the chart on the left. Removing one single data point in this set would have negligible impact:

Figure 6. Only one point in the right-hand chart differs greatly from the other points in the set. The same can’t be said for the left-hand chart. 

 

In this way, scatterplots make it a relatively quick and easy task to determine the reason for a weak correlation: overall scattered data or a few extreme (outlier) values.

 

Consider this simple example of x-and-y data that includes two different sets for the y values: y1 and y2.

Figure 7

The y1 values are all two times the x values. This holds true for every value in the set, from x=1 to x=25. This means there’s a perfect, positive relationship between the x and y values. As the value of x increases, the value of y increases by a set amount (y=2*x).

 

The scatterplot below visualizes the points for x and y1. You can see that the trend line travels through each individual point perfectly. This means the correlation coefficient is 1—a perfect correlation:

Figure 8

 

The y2 values in the table above are also each two times the x values—except for the point at x=8, where y2=6. This means that a single equation (y=2*x) can no longer be used to describe every data point within the table. It’s no longer a perfect relationship.

 

See how the scatterplot in Figure 9, below, differs from the scatterplot in Figure 8. The change of one value, at x=8, drags the entire trend line down and decreases the correlation coefficient to 0.99:

Figure 9

 

While you may have noticed this trend by simply looking at the values in the original table, it’s much easier to understand by way of a visualization. This is especially true for tables with hundreds of records, where a small difference like in the example above would be even harder to spot in table form. A visualization is an efficient way to determine the direction of the correlation, its relative strength (when compared to other data sets), and the degree to which the trend holds true (whether all the points fall along the line with only a few outliers or are similarly scattered about the trend line).

 

2.1. Creating Scatterplots in Tableau

Scatterplots and their corresponding trend lines are quite simple to create in Tableau. In this section, you’ll walk through a simple example to create your own, using the candy data set you first played around with in Lessson 2.

• Download the candy data set again here if you no longer have it.

 

The first thing you’ll need to do is connect to your data set in Tableau and create a sheet for your visualization (named something like “Correlations”). As you should be fairly familiar with the process by this point, we won’t go through each individual step again. You’ve got this!

 

Next, ensure your variables are appropriately categorized as dimensions and measures. If you’ll remember from Lesson 2: Visual Design Basics & Tableau, there were a number of variables that Tableau categorized as measures that were actually dimensions (even though their values were 0s and 1s, these numbers represented “no” and “yes” rather than numerical values). To recap, your final lists should look like this:

Figure 10

 

And, in Tableau:

Figure 11

 

Remember—scatterplots look at the relationships between numeric variables. In this data set, then, you’ll want to examine whether the price (the Pricescale variable) is related to the amount of sugar (the Sugarpercent variable) in each candy. To do so, drag the Pricescale variable to the Rows shelf and Sugarpercent to the Columns shelf:

Figure 12

By default, Tableau aggregates these variables, showing the sum of each one as a single point on the chart. While helpful in some instances, this isn’t what you want for your scatterplot, as it won’t allow you to track the data points and visualize a potential relationship. As such, you need to disaggregate it. Tell Tableau to remove the aggregation by going to the Analysis menu and deselecting the Aggregate Measures option:

Figure 13

Your chart should change quite readily—now boasting a whole assortment of points:

Figure 14

 

Tableau defaulted to this scatterplot view because scatterplots are one of the few chart types that require zero dimensions and at least two measures. Remember—you can check the requirements for each type of chart in the Show Me menu by hovering over the image for a chart.

Figure 15. Scatterplots need two to four measures but don’t require any dimensions.

It’s time to play around with a feature you haven’t used before—Shape! The Shape box on your Marks card allows you to change the marker shape for each data point. Let’s change the hollow circle option currently on display in your chart to something a little less busy; for instance, a filled-circle option. While you’re at it, go ahead and change the color of your points via the Color option. A dark gray would look nice!

Figure 16

From simply looking at the chart, the data seems pretty random. Drawing a single trend line through this data would be a bit difficult, to say the least. No single line would come close to meeting all of those randomly scattered points! As such, you can make an initial guess that there’s no correlation (or at least a very weak correlation) between these two variables. To be absolutely sure, however, let’s graph the trend line and calculate the correlation coefficient.

 

On the upper left-hand side of your Tableau view, you’ll notice two tabs: a Data tab and an Analytics tab. You’re currently in the Data tab, which displays your data source, dimensions, and measures. Now, you need to switch to the Analytics tab, as this is where you’ll create your trend line. This will bring up a new list of options, one of which is Trend Line. Click that now to add a line of best fit to your chart:

Figure 17 

Your new trend line has an upward, or positive, slope, which means that as the Sugarpercent variable increases, so does the Pricescale variable. But how strong is this relationship? Fortunately, Tableau can do the calculation for you!

 

Hover over the trend line itself to see the strength of the relationship in terms of the r-squared coefficient. The r-squared value is actually the Pearson’s correlation. You need to find the square root of this number before you can interpret it.

The strength or weakness of the Pearson’s correlation coefficient is defined by the following value ranges:

• 0: no relationship
• 0.1–0.3: weak relationship
• 0.3–0.5: moderate relationship
• 0.5–1.0: strong relationship

 

If you hover over your trend line, you should get an r-squared value of 0.105681. To get the correlation coefficient, simply calculate the square root of this number, which is 0.325086. This indicates a moderate relationship:

Figure 18

 

While you could have calculated the correlation coefficient without plotting the data, you wouldn’t have been able to visualize the scattered nature of the data points without the help of a chart. This supports the notion that the moderate correlation between your variables comes from all the data—not from a few extreme values. In this way, scatterplots help provide additional explanation, or context, to a correlation.

TIP!
Don’t forget to give your chart a title! Before finishing up, add a descriptive title to your chart, for instance, “The Relationship between Sugar and Price in Halloween Candy.”

 

3. Bubble Charts

Bubble charts are similar to scatterplots, with the only difference being the addition of a third (and possibly fourth) dimension. As you know by now, size and color are some of the most common ways to add additional variables, or dimensions, to a chart, and bubble charts do exactly this. Let’s take a look into how a bubble chart can add even more context to a scatterplot.

 

A bubble chart looks at the relationship between two variables, graphing one each on the x- and y-axes (just like a scatterplot). The size of each dot on the chart is determined by a third variable. Take a look at the example in Figure 19, below, where you can see one of Hans Rosling’s famous bubble charts in action:

Figure 19. If you’ll remember from Lesson 1, Hans Rosling is famous for these bubble charts, using them to present data in novel and innovative ways.

The base of the chart is a scatterplot looking at the relationship between average years in school and literacy rates for women. A trend line would have a positive slope, signifying that as the number of years in school increases, so does the literacy rate. Income is represented as a third dimension—the size of the circles. The larger circles, clustered in the top-right corner of the chart, designate greater income, signifying that more schooling and higher literacy rates are related to higher income. A fourth variable could be added to the chart in the form of color.

 

3.1. Creating Bubble Charts in Tableau

You already know how to make scatterplots in Tableau, and bubble charts won’t be much different. After all, bubble charts are scatterplots—just with an additional size dimension! Let’s continue using the same candy data you’ve already been working with, this time, seeing if your Pricescale and Sugarpercent variables impact a third variable, Winpercent. If you’ll remember, this data set is, itself, the result of hundreds of polls asking participants to choose their favorite between one of two candies. The Winpercent variable is what summarizes how often each piece of candy won in these matchups. Let’s use a bubble chart to see if the price and amount of sugar had any impact on how often each type of candy won.

 

You can start by duplicating the scatterplot you just created, as you’ll simply be adding to it for your bubble chart. To do so, right-click the sheet tab (which you named “Correlations”) and select Duplicate:

Figure 20

 

A copy of your chart will be created in a new sheet called “Correlations (2).” Go ahead and rename this to “Bubble Chart.” Next, let’s remove the trend line, as it won’t be particularly useful for the bubble chart you’re about to make. To do so, open the Analysis and choose Trend Line, upon which you’ll be given an option to deselect the Show Trend Lines option:

Figure 21

 

You want to see whether sugar and price affect the win rate of candy, so you’ll need to add the Winpercent variable to your visualization. Drag it onto the Size card on your Marks card:

Figure 22 

Did you see your dots change in size? Congrats! You’ve just turned your scatterplot into a bubble chart! The size of each circle is now determined by the relative win percentage—in other words, how frequently that candy won in matchups against other types of candy. The bigger the dot, the more times that type of candy won.

 

While the variable you just used to size your points was a measure, you can also use dimensions (the only time you can use a dimension in a scatterplot!). Let’s try this now by dragging Winpercent from the Marks card back to the Measures list and replacing it with the Manufacturer variable. Tableau will automatically update your bubble chart; however, the results may not be what you expect. As the manufacturers in this data set have no numerical value, they’ve simply been assigned different sizes of points, which you can see if you look at the legend to the right of your screen. There’s no inherent order to these sizes, so using sizes to portray them on your bubble chart doesn’t make much sense. (Why, for example, is Wonka Candy Company bigger than Werther’s?) This is a good example of how you should only use a dimension to represent size if there’s some inherent order to its values.:

Figure 23

A better solution might be to use color to portray this variable. Let’s revert back to using Winpercent for the size of your data points. Then, drag the Manufacturer variable onto the Color box on your Marks card. If a menu appears, select the first option to Add all members. This tells Tableau to give each individual value within the variable a unique color rather than grouping some together.

Once finished, you’ll have a bubble chart where the size is determined by the Winpercent and the color is determined by the Manufacturer—pretty cool!

Figure 24 

The color scheme Tableau assigned to your chart is quite varied; however, you know from basic design principles that more than five colors is too many to distinguish well in a chart. A better solution would be to only show the top manufacturers. Let’s set up a filter for this!

 

Drag the Manufacturer variable onto the Filters card (above your Marks card) and select only the top manufacturers: Hershey’s, Mars, and Tootsie Roll (the only three that have more than 10 candies). You could also do this more dynamically, for instance, by having Tableau find the manufacturers with more than 10 candies on its own, but that’s a bit more complicated, so you won’t be covering that until a future Lesson. For now, manually selecting these three manufacturers will work fine.

Figure 25 

Note that the colors in your chart may differ depending on your color settings.

TIP!
Don’t forget to give your new chart a descriptive title and some labels! Something like “The Relationship between Sugar, Price, and Popularity for Top Halloween Candy Manufacturers” would work well for the title. More-descriptive axis titles, a more intuitive color scheme, and different size categories can also help to enhance your chart.

 

The bubble chart now shows the relationship between the Sugarpercent and Pricescale variables—a relationship that’s weak at best. The data points aren’t clustered around a clear trend line path, meaning that the amount of sugar doesn’t have a strong impact on the price of the candy. The chart also shows information about the Winpercent and Manufacturer. The largest win percentages are dispersed throughout the chart, as are the manufacturers. There aren’t any clusters of only dark purple or only high win percentages (big circles).

 

Just because this chart is telling you that there isn’t a relationship between these variables, that doesn’t mean this chart (or the information it’s giving you) isn’t useful. It’s simply telling you that the underlying data is random—the variables you’re analyzing don’t explain why some candies are preferable, why some are more expensive, which type of candy Hershey’s makes, or the impact of sugar content.

 

If, instead, all the large bubbles were near the top-right corner of the graph, this would mean that only the expensive, high-sugar candies won in the various candy matchups. Because of this graph, however, you know this isn’t the case. People enjoy inexpensive, lower-sugar candies just as much as the expensive, higher-sugar candies!

 

In this way, bubble charts are a great way to show a lot of information at the same time. Think of them as a way to add even more dimensions to an already useful scatterplot!

Enhancing Hans Rosling’s Bubble Charts
In the bubble chart shared at the top of this section, color hasn’t been used to add a fourth dimension to the chart; however, a fourth variable could be added in the format of color. Hans Rosling’s online tool, Gapminder, allows you to interact with and enhance their visualizations on your own. Give it a try by adding a fourth variable or adjusting the other three variables to create a chart you find interesting.