Scatterplots

Basic Scatterplot Creation

In the simplest most common case, scatterplots are made by plotting the (x, y) coordinates of two variables in a data set. The example in Figure 1 uses school district data to show the relationship between the percent proficient in Grade 3 on a standardized achievement test and the percentage of students eligible for free or reduced price lunch (FRL). Each point in the figure is plotted at its (x, y) coordinates and represents a unique school district. For example, the point farthest to the right has (x, y) coordinates of approximately (100, 60) indicating that this school district has 100% of their students eligible for FRL and that approximately 60% of their students were proficient in grade three. Similar statements could be made from every point shown in the scatterplot in Figure 1.

Traditional scatterplots are two dimensional; however, three-dimensional scatterplots can be made that plot points using the (x, y, z) coordinates of three variables. Three-dimensional scatterplots can become difficult to view, particularly in print form; therefore, it is much more common to create two-dimensional scatterplots. An alternative to include additional variables, especially qualitative variables, is to change the shape of the points or facet the plot into separate panels. An example of faceting is shown in Figure 2 where [Page 1458]two scatterplots are created, one representing small school districts and a second representing large school districts. These types of figures as shown in Figure 2 are helpful to explore if the relationship changes, or is moderated, as a function of a third variable.

Figure 1 Grade 3 percent proficient by the percentage of students eligible for a free or reduced price lunch for school districts

Figure 2 Grade 3 percent proficient by the percentage of students eligible for a free or reduced price lunch and school district size

Data used in the first two figures explore the relationship between two quantitative variables. Data do not need to be quantitative to be plotted in a scatterplot. Instead, data on the x-axis could be qualitative, categorical, or ordinal. Figure 3 provides an example of such a plot where the population density of the counties are plotted for various states. Each point in the plot represents a unique county in each state. The primary difficulty in this approach is issues of overplotting. This is discussed in more detail in the limitations section later in this entry.

Uses for Scatterplots

There are many uses for scatterplots in educational research including estimating correlations, exploring the form of bivariate relationships (i.e., linear or nonlinear), creating interaction plots, detecting outliers, and assessing model assumptions. As an example, from Figure 1, one can easily see the negative bivariate relationship between the percentage proficient at Grade 3 and the percentage of students eligible for FRL. Also from Figure 1, the correlation between the two variables could be estimated to be close to −0.5, a moderate to large correlation.

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