Scatter Plots

Students create scatter plots, which are visualizations that show the relationship between two quantitative variables. They learn how to construct scatter plots by hand, and in Pyret.

Pie and Bar charts help us see the frequency of values in a categorical column. There are other displays, like histograms and box plots, that help us explore the distribution of values in a quantitative column.

But what we really want is a display that will help us search for a relationship between two quantitative columns, and that’s exactly what scatter plots do.

Before we can draw a scatter plot, we have to make an important decision: which variable is explanatory and which is the response? In this case, are we suspecting that an animal’s weight can explain how long it takes to be adopted, or that how long it takes to be adopted can explain how much an animal weighs? The first one makes sense, and reflects our suspicion that age plays a role in adoption time.

It’s customary to use the horizontal axis for our explanatory variable and the vertical axis for the response variable. Each row in the dataset will be a point on the scatter plot with age for x and weeks for y.

We will produce our scatter plot by graphing each animal’s age and weeks values as a point on the x and y axes.

When you created the scatter plot by hand, you started with a Table. Then you plotted a series of dots, using one column for your x’s, one column for your y’s, and the name column to provide a label for each dot.

The scatter-plot function works exactly the same way: it starts with a table, and then needs to know which columns to use for labels, xs, and ys. Here’s the contract:

scatter-plot :: (t::Table, ls::String, xs::String, ys::String)

Have students report back on their findings from the starter file and on Creating a Scatter Plot.

Scatter plots show us a collection of points, arranged along two axes. If there’s a relationship between these axes, we’ll see clumps and clouds of points in the graph.

🖼Show image Think back to our discussion of random sampling and statistical inference. In this case, the null hypothesis is that there is no relationship between these two columns. The image on the right shows a collection of points, with no pattern.

Students apply what they’ve learned about scatter plots to the Data Cycle, using it to answer questions about relationships in the animals dataset.

Have students discuss.

Many apartment buildings do not allow large breeds of dogs, and have a limit on how heavy a tenant’s dog can be. Bigger dogs are not welcome in many apartments. Perhaps the weight of an animal influences the adoption time!

Let’s use the Data Cycle to explore whether there’s a connection between weight and adoption time.

Discuss as a class:

We’ve got a lot of tools in our toolkit that help us think about an entire column of a dataset:

Now we also have a tool that lets us think about two columns at the same time!

Students are asked to identify patterns in their scatter plots. This activity builds towards the idea of linear associations, but does not go into depth (as as a later lesson on correlations does).

Shown below is a scatter plot of the relationships between the animals' pounds and the number of weeks it takes to be adopted.

🖼Show image

A straight-line pattern in the cloud of points suggests a linear relationship between two columns. If we can find a line around which the points cluster (as we’ll do in a future lesson), it would be useful for making predictions. For example, our line might predict how many weeks a new dog would wait to be adopted, if it weighs 68 pounds.

Do any data points seem unusually far away from the main cloud of points? Which animals are those? These points are called unusual observations. Unusual observations in a scatter plot are like outliers in a histogram, but more complicated because it’s the combination of x and y values that makes them stand apart from the rest of the cloud.

These numbers and scatter plot both come from the same datasets (you’ll learn more about those numbers in later lessons!). The patterns in the scatter plot vary wildly, but the numbers that summarize the dataset barely change at all!

🖼Show image

Data Scientists and Statisticians use their eyes all the time. Sometimes there’s a pattern hiding in the data, which can’t be seen just by focusing on numbers and measures. Until we really look at the shape of the data, we aren’t seeing the whole picture. (Optional: this animation is from Autodesk, which has an amazing page showing off how similar numbers can be generated from radically different scatterplots. If time allows, have students explore some of the visualizations on the Autodesk website (Autodesk)!)

Debrief, showing the plots on the board. Make sure students see plots for which there is no relationship!

It might be tempting to go straight into making a scatter plot to explore how weeks to adoption may be affected by age. But different animals have very different lifespans! A 5-year-old tarantula is still really young, while a 5-year-old rabbit is fully grown. With differences like this, it doesn’t make sense to put them all on the same scatter plot. By mixing them together, we may be hiding a real relationship, or creating the illusion of a relationship that isn’t really there!

It would be nice if the dots in our scatter plot were different colors or shapes, depending on the species. That would give us a much better picture of what’s really going on in the data. But making a special image for every single row in the table would take a very long time! If only there was a function with a contract like:

species-dot :: (r :: Row) -> Image

This function could take in a row from the animals table, and draw a special dot depending on the species. Unfortunately, no such function exists…​yet! Later lessons will teach you to define functions of your own, and extend Pyret to deepen your analysis, create more useful and engaging charts, and dig further into our data.

Students apply what they’ve learned to their own dataset.

The Animals Dataset contains a number of sub-groups that we might want to compare to one another. For example: maybe we’d like to compare the average adoption time for dogs v. cats!