Comparing Changes in Average Scores of Students in Two Districts

Another example describes how Superintendent Johnson compared standardized achievement test scores for students in his district to those in another district. A few years later Superintendent Johnson found that the scores in his district had fallen, from an average of 110 to 105. Scores in the comparison district had also fallen, but only by one point (from an average of 107 to 106). (One hundred fifty students were tested in each district in each year.) Was this difference large enough to be seen as educationally significant or statistically significant?

The data that Superintendent Johnson could enter in the EIC to answer this question are shown below along with the results. Data for the user’s group are entered first, followed by data for the comparison group, and for each group data for the more recent year are entered first. The results indicate that Superintendent Johnson would be wise to worry about the results. Relative to the other district, his students’ achievement had declined by .28 of a standard deviation, a decline that is equivalent, for the average student, to 11 percentile ranks. The probability value indicates that these results would be very unlikely to have occurred by chance (only once out of 1,000).

Enter the data for your group  
a) Mean (Average) for the more recent year 105
b) Standard deviation for the more recent year 16
c) Number of students tested for the more recent year 150
d) Mean (Average) for the comparison year 110
e) Standard deviation for the comparison year 15
f) Number of students tested for the comparison year 150
Enter the data for the other group
a) Mean (Average) for the more recent year 106
b) Standard deviation for the more recent year 13
c) Number of students tested for the more recent year 150
d) Mean (Average) for the comparison year 107
e) Standard deviation for the comparison year 14
f) Number of students tested for the comparison year 150
Results
Effect Size -0.28
Improvement Index -10.9
Probability this effect would occur by chance 0.001

To enter your own data, Click Here