Measuring Up: What Educational Testing Really Tells Us

by Daniel Koretz

If standardized scales are so handy, why are they never used to present test scores to the public? Because most lay people cannot abide fractional and, worse, negative scores. Imagine a parent receiving a report from her child’s school that said, “Your daughter received a score of 0.50, which put her well above average.” A standardized score of 0.50 is well above average—if scores follow the bell curve exactly, it represents a percentile rank of 69—but it certainly does not seem like it. It is easy to envision a worried parent responding that she does not quite understand how her child obtained a score of one-half and nonetheless ended up above average. Did half the class get no questions right? Or worse, imagine a report that said, “Your son’s score on our math test was –.25.” Less than zero? I’d hate to be that child at the dinner table the night that report went home. So in a great many cases, psychometricians start with a standardized scale—it is produced automatically by many current scaling methods—and then convert it to some other scale that they think will be more palatable, one with a larger standard deviation to avoid fractional scores and a high enough mean that no one gets a negative score.