Recommendation to the Superintendent
The Sun Beach school system conducted a comparative educational experiment. A random sample of 200 third grade students was randomly selected from the district. The students were then randomly assigned to one of two groups. Each group received a different type of supplemental help designed to prepare them for the end of grade reading test. A pretest was given to all students in the study at the beginning of the third grade year. It is now the end of the school year and you have been assigned the task of analyzing the data. Just as you begin to examine the data using some basic descriptive statistics, the Superintendent calls and demands a fast answer on the spot about which treatment did better in the study.
Using your best diplomacy, you explain that you are planning to run additional descriptive statistics, and inferential tests to determine if there are statistically significant differences between the groups. You patiently explain that you plan on testing the difference between the two groups to examine two types of potential differences: 1.) the proportion of students who made gains from pretest to posttest, and 2.) the mean gain score from pretest to posttest. Not to be deterred, the Superintendent pushes you to make a judgment about which method is better because a decision has to be made immediately about which program to expand for next year.
The only analysis you have completed at the time of the call consists of displaying the gain scores for each group in the form of boxplots. The table below summarizes the information contained in the boxplots. Note that positive values indicate the student made a gain from pre to post, and negative values indicate that the student did worse on the posttest than on the pretest.