Goals:

• Understand what correlation means and how it is used and presented in research

Activity Guide:

Which label goes on the X axis and which on the Y? Think about what titles and labels you would put on the X and Y axes in each of these cases:

 

Student absences are negatively correlated with grades (as absences increase, grades go down)
ANSWER (mouse over to see)

As students exercise more, their weight and body fat are less, so negatively correlated
ANSWER (mouse over to see)

On a snow day, the more it snows, the fewer drivers are on the roads
ANSWER (mouse over to see)

Typically if one of the variables is manipulated in the study (an experimental variable) then by convention that variable is placed on the X axis. Similarly, if both variables were free to vary, then the one that is suggested as controlling the other is the one placed on the X axis.  For example, consider the literacy rate and mortality rate by country. Higher literacy is correlated with lower mortality rates (a strong negative correlation). So if we thought that higher literacy lead to lower mortality, we would place the literacy rate on the X axis. But literacy rate is also related to GDP and wealth. And literacy is also related to compliance with medical treatments. So is ability to read really the cause, or is it some 3rd factor?

OK.. Time to try one yourself.

Using a free online correlation calculator let’s compute a correlation between any 2 grades for 10 of your students.

1. Select 10 of your students and get 2 of the grades for each student from your grade book (or use my list if you prefer– but it would work best with real data from your gradebook).
   1. student 95 92
   2. student 88 84
   3. student 76 91
   4. student 87 88
   5. student 76 88
   6. student 98 50
   7. student  84 89
   8. student 91 95
   9. student 84 72
   10. student 94 87
2. Enter the first set of grades for all 10 students into X column of the calculator tool.
   1. 95 88 76 87 76 98 84 91 84 94
3. Enter the second set of grades for all 10 students into the Y column
   1. 92 84 91 88 88 50 89 95 72 87
4. Scroll down to see the correlation(s) computed for you automatically. For my scores these are
   1. Pearson r= .4976 (a strong positive correlation)
   2. Spearman rho = .3456 (a positive correlation)
   3. Kendall tau = .3219 (a positive correlation)
5. Report your results and reflections in the HuskyCT discussion forum for this module.
6. This resource may provide some further detail on correlation: Correlation Coefficient