To perform group analysis, one must first define the groups under study (J. Park & Park, 2016). From the problem statement above, it appears that neither the school, individual teachers, nor the students in classrooms define the groups. Rather, the groups would be defined by the independent variable, which is the average number of days per week each math teacher spends in a collaborative setting. However, there are complicating factors associated with using the same teacher’s average as the independent variable in a bivariate pair with the dependent variable the difference between the post-test and pre-test scores for multiple students. For example, for teacher A who has an average of 4 days per week, this teacher will have multiple students so the bivariate data would create ordered pairs of the form (4, difference of student 1), (4, difference of student 2) and so on for each student in the teacher’s class. Thus, correlation would not be the preferred method for exploring a relationship.

If I were analyzing this data, I would transform the independent variable into ranges of time. For example, if the letter t represents the average time per week, the first category would be 0=t