Comparing Changes over Time in Percentile Rank of the Average Student in Two Classrooms

Another example describes Principal White’s comparison of scores of students in two classrooms. Students had been randomly assigned at the beginning of the year, but at the end of the year those in Classroom A had markedly lower scores, a difference that was large enough to be seen as educationally significant. Given those results Principal White worked with the teacher in Classroom A to help her improve her skills. At the end of the following year, Principal White was gratified to find that the average student in Classroom A was now doing much better than in the previous year, with a percentile rank of 75. The average student in Classroom B scored just slightly higher than the average student in the previous cohort, with a percentile rank of 79.

Principal White could use the EIC to examine the gains made in Classroom A relative to the gains made in Classroom B. The  data that she would enter and the results are shown below. Both Principal White and the teacher in Classroom A would no doubt feel gratified by the findings. The effect size of .23 shows that the improvement in Classroom A from the previous year was almost a quarter of a standard deviation greater than the change in Classroom B. This difference corresponds to a difference of nine percentile ranks. Thus, while the students in Classroom A were still not scoring at equivalent levels to those in Classroom B, differences for the current cohort were much smaller than for the previous cohort. (The results of the probability line of the EIC no doubt reflect the relatively small samples involved.)