Comparing Changes in the Average Scores of Students in One Group with Changes in a Larger Group

Principal Greene, of East High school, was concerned that seniors in recent years seemed to have lower Scholastic Achievement Test scores than those in previous years. He wanted to compare the change from 2010 to 2015 for East seniors to those for the nation as a whole. In 2010 the average score of the 150 students tested was 685. In 2015 170 students were tested, and their average score was 650, reflecting a decline of 35 points in the average. One hundred fifty East students were tested in each year. For the nation, the average in 2015 was 585 and the average in 2010 was 590, a decline of 5 points. In both years the standard deviation for the national data was 150. Principal Greene could use the EIC to examine the extent to which the decline in East students’ scores was greater than the decline among all students in the nation. Was this difference educationally significant?

The data entered and the results are shown below. Note that, to obtain information regarding the probability of the results occurring by chance, Principal Greene did not need to know how many students were in the national testing. He only needed to know the number of students in his school in each year. Also note that it is only necessary to know the standard deviation for the larger group.

The effect size of -.20 is close to the .25 threshold of educational importance, and the associated probability level of .08 indicates that an effect of this size would occur less than eight times out of a hundred. From 2010 to 2015 the decline in the SAT scores of the average East student, relative to the decline among students in the nation as a whole, was almost eight percentile ranks. Given this information it would seem logical for Principal Greene to be concerned about his students’ performance on the SAT.

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