Comparing the Percentage of Students at Benchmark in Two Schools

Principal Mary Brown wanted to compare the achievement of students in her school with the achievement of students in a nearby school. Fifty percent of the students in fifth grade at her school were rated as proficient on the state assessment, while 65 percent of the fifth graders in the nearby school were rated as proficient. One hundred students were tested at Principal Brown’s school and 120 students were tested at the nearby school. Clearly the students at Principal Brown’s school did not do as well as those at the other school, but was this difference large enough to be considered educationally significant? Would it be considered statistically significant?

The table below shows how the data were entered into the EIC and the results that were produced. The effect size of -.31 is beyond the level of .25 generally seen as educationally significant. The improvement index, which translates the effect size into percentile terms, indicates that the average student in Principal Brown’s school scored 12 percentile ranks lower than the average student in the comparison school. The value of .02 in the final line of results indicates that a difference as large as that between Principal Brown’s school and the other school would occur by chance only 2 times out of 100. In other words, it is quite unlikely that the results were a fluke. Taken together, these results suggest that Principal Brown would be wise to be concerned about her students’ achievement and consider corrective action.