Scatterplots

Interpreting the Data

Scatterplots illustrate the relationship between two variables, such as performance and growth. Specifically, scatterplots enable you to visually examine the relationship between the variables and answer the question, "As variable A changes, what happens to variable B?" In the case of performance and growth, you might ask, "As the average performance of students in a building increases, does the average growth also increase?" In other words, is there a relationship between performance and growth?

When data points on a scatterplot are distributed somewhat symmetrically along a horizontal or vertical line, there is little to no relationship between the selected variables.

No Relationship

Additionally, a more diagonal pattern indicates that the variables are related. The closer the pattern is to a diagonal line, the stronger the relationship.

Variables are positively correlated if one variable increases or decreases as the other variable increases or decreases. A good example of positive relationship is that of temperature and the sale of ice cream. As the temperature rises, ice cream sales rise with it.

Positive Relationship

Variables are negatively correlated if they move in opposition to each other. In other words, when one increases, the other decreases. For example, as the temperature goes up, sales of hot chocolate go down.

Negative Relationship

When interpreting the relationship between two variables on a scatterplot, it's important to remember that correlation does not prove causation. If variable B increases as variable A increases, that does not necessarily mean that changes in variable A caused the changes in variable B. Also, if the graph contains only a small number of data points, a correlation might be suggested that does not exist in a larger set of data.

For example, if we were to create a scatterplot of performance vs. growth in fifth-grade Math and we included only a few buildings, the relative performance and growth of those buildings would determine the correlation that is suggested in the graph. We might mistakenly conclude that performance and growth are positively correlated if the selected buildings that serve a lower-achieving population of students haven't had great success in helping those students make growth, and the other buildings serve a higher-achieving population of students and have had great success with student growth. In other words, we might believe that buildings serving lower-achieving students cannot achieve high growth.

However, comparing only a few buildings might not offer a fair representation of the true relationship between performance and growth. If we added all the buildings in the state to the scatterplot, we would see little to no relationship between the two variables. With that in mind, it's important to be careful when drawing conclusions from small amounts of data on a scatterplot.