Comparing
the Percentile Rank of the Average Student in a District to the Percentile Rank
of the Average Student in the State
Superintendent Jensen had recently accepted a position in Seacoast district. She knew that the district had a history of achievement problems, but wanted to understand the issue in greater detail. She was especially interested in knowing if the achievement of Seacoast's students was significantly lower than the achievement of other students in the state. In the previous year the average Seacoast third grader scored at the 35th percentile on the state assessment, while the average student in the state scored (by definition) at the 50th percentile. One hundred fifty Seacoast third graders had been tested.
The results that appeared when Superintendent Jensen entered these data into the EIC are shown below. The effect size of -.39 would be considered educationally significant. The probability value of 0.000 reflects less than one out of 1000 (<.001) and indicates that an effect size of this magnitude would occur very rarely. The improvement index of -.15 shows that the average Seacoast third grader scored 15 percentile points below the average student in the state. Superintendent Jensen would no doubt conclude that there were indeed serious achievement problems in Seacoast District.
| Data for Your Group | |
| a) Percentile rank of average score | 35 |
| b) Number of students tested | 150 |
| Data for the Larger Group | |
| a) Percentile rank of average score | 50 |
| Results | |
| Effect Size | -0.39 |
| Improvement Index | -15.0 |
| Probability this effect would occur by chance | 0.000 |
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