Superintendent Paul Johnson had data on student achievement on a standardized achievement test for students in his district and in a nearby district with similar demographic characteristics. The average (mean) score of his students was 110 with a standard deviation of 15. The average in the other district was 107, with a standard deviation of 14. One hundred fifty students had been tested in both districts. Clearly Superintendent Johnson’s students scored higher than those in the other district. But was this difference large enough to be considered educationally significant? Could it have just appeared by chance?

To answer this question Superintendent Johnson could enter the data into the EIC, as shown below. Note that for this comparison Superintendent Johnson needed to know the mean and standard deviation for each group.  The results are shown in the bottom panel.  The effect size of .21 is close to the level typically deemed educationally significant and corresponds to a difference of 8 percentile ranks between average students in the two districts. The probability that differences this large would occur by chance is only 7 out of 100. Many would suggest that, based on these results, Superintendent Johnson was entitled to be quite proud of the accomplishments of his students relative to those in the nearby district.

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