Guess the Correlation

[sue_frantz]

After introducing students to the concept of correlations, it may help students to see a scatterplot to understand what the correlation coefficient means.

Give students an example of correlation. For example, Cornell, et.al. (2013) found a correlation of .32 between the number of dropouts from 289 Virginia high schools and student perceptions of teasing and bullying. At this website, enter .32 in the “r” box and enter 200 in the “n” box (289 of course would be better, but the site limits the number of data points to 200.  Press enter. In pairs or small groups, ask students to describe the graph, and then ask a volunteer to share their description. (Students may explain that the number of dropouts is plotted along the x axis and the student perceptions of teasing and bullying are plotted along the y axis. As perceptions increase, so do number of dropouts.)

Explain that Cornell, et.al. (2013) also found a correlation of .46 between the percent of students who qualify for free and reduced price meals and academic failure rate. Ask students to predict what will happen to the points on the scatterplot when you enter .46 into the “r” box. Again, ask students to explain what the scatterplot means to a partner, and then ask for a volunteer to share their description.

Give one last example from Cornell, et.al. (2013). They found a correlation of -.42 between the percent of students who qualify for free and reduced price meals and the size of the high school. Ask students to predict what will happen to the points on the scatterplot when you enter -.42 into the “r” box. Again, ask students to explain what the scatterplot means to a partner, and then ask for a volunteer to share their description.   

Finally, ask students to predict what will happen to the data points when you enter 1 in the “r” box.

Now that students have a handle on what is happening in scatterplots, invite students (perhaps as an assignment), to visit http://guessthecorrelation.com. Here, players try to guess the correlation based on the scatterplot. You get three lives. If your guess is off by more than .1, you lose a life. If your guesses are good, you earn lives and coins. The data collected are used for research; you can read about that on the “About” page. Unfortunately, the site only gives scatterplots for positive correlations.

Cornell, D., Gregory, A., Huang, F., & Fan, X. (2013). Perceived prevalence of teasing and bullying predicts high school dropout rates. Journal of Educational Psychology, 105(1), 138-149. doi:10.1037/a0030416