To measure the effectiveness of a new teaching method for math in elementary school, each student in a class getting the new instructional method is matched with a student in a separate class on IQ, family income, math ability level the previous year, reading level, and all demographic characteristics. At the end of the year, math ability levels are measured again.

A data collection method is described to investigate a difference in means. In each case, determine which data analysis method is more appropriate: paired data difference in means or difference in means with two separate groups.