New analysis of achievement gap: ½ x ½ = 1½
My guest is David Berliner, Regents’ professor emeritus at Arizona State University who is a prominent researcher and educational psychologist.
By David Berliner
The numbers referred to in the title are standard deviation units. I want people to understand a special set of circumstances in which two sociological variables, each producing approximately a one-half standard deviation difference in the achievement test scores of students, end up producing jointly a one and one-half standard deviation difference in the scores of those same students ( ½ x ½ = 1½ ).
For those who are not familiar with standard deviation units, just think of them as a convenient way to break up the normal curve that is so commonly found when we measure many human characteristics.
If IQ or the height of 16 year-olds are distributed normally, as they usually are, then the bell-shaped normal curve occurs. Whether the mean (average) score is in IQ units, inches, or millimeters, that score would be at the 50th percentile in the distribution of IQ scores or height.
A score about one half standard deviation above that average would be at about the 70th percentile, while a score about a half a standard deviation below the mean score would be at about the 30th percentile. That is, a score half of a standard deviation greater or lesser than that of another individual or group, represents a rather large difference between those individuals or groups. If a student or group of students were to be 1 ½ standard deviation units above or below the mean score of another individual or group, the difference between them would be considered huge, not just large.