Comparing Means and Standard Deviations of Scores in One School to National Norms

Principal Evans, of Central High School, knew that the tenth graders in his school had scored above the national average on a nationally normed achievement test. But, he wondered, was the difference large enough to be considered educationally significant? The average for the Central students was 105, while the national average was 100. The standard deviation for the nation was 15. Fifty Central students had taken the test.

The results when Principal Evans entered this information into the EIC are shown below.  (Note that he only needed to know the standard deviation for the larger group, not his school.) The findings reinforce Principal Evan’s pride in his students. The effect size of .33 is well beyond the level traditionally used to indicate educational significance, and the probability that the result would occur by chance is only two out of 100. The improvement index of 13 indicates that that the average student at Central High had a score that was 13 percentile ranks higher than the average student in the nation.

Data for Your Group
a) Average score of students in your group 105
b) Number of students tested 50
Data for the Larger Group
a) Average score of students in the larger group 100
b) Standard deviation of scores in the larger group 15
Results  
Effect Size 0.33
Improvement Index 13.1
Probability this effect would occur by chance 0.02

To enter your own data Click Here