Psychometrics

Communicate with percentile ranks…but think and reason with standard scores

Every once in a while, I run into a college student who calculates very basic math facts (e.g., 8 + 5 = 13) by counting on his or her fingers. This method, of course, works perfectly well. Unfortunately, the student who relies upon it is doomed never to master algebra. The act of counting uses up most of the storage space in working memory, often causing miscalculations and attentional lapses (e.g., forgetting where one is in the problem-solving process).

Something similar happens with some professionals who perform psychological assessments. Using percentile ranks is a perfectly reasonable way to communicate where someone’s score falls in a distribution. However, if you think and reason about test scores in terms of percentiles, you will never master the finer points of test interpretation.

The problem is this: No one understands our units of measurement! Therefore we much convert our scores to percentile ranks, which are much easier to understand. This is partly our own fault. Maybe the public would, in time, come to understand our numbers if we used just one kind of measurement unit instead of our usual awful mixture of z-scores, stanines, stens, scaled scores, T-scores, index scores, and normal curve equivalents. Elsewhere I have defended the practice of using different units of measurement. From the ivory tower, the Tower of Babel looks magnificent! From the ground, it looks like a big mess!

Unfortunately, standard scores are just as unfamiliar to new graduate students as they are to the public. A certain percentage of them will persist in using percentile ranks as they reason with test scores. This will work reasonably well in most cases but at the extremes (where precision matters most), it can cause interpretative errors.

Percentiles are not easily compared. When we look at scores that differ considerably within a profile, percentiles can make large differences look small and small differences look large. Consider how much space the there is in the normal distribution between the 1st and 2nd percentile and how little there is between the 50th and 51st percentile. The meaning of percentiles is similarly inconsistent with other distributions (other than the uniform distribution).

Percentiles and z-scores in a normal distribution

Percentiles in a standard normal distribution

Comparing scores is just the beginning of the problem with percentile ranks. Almost every kind of calculation (e.g., to predict performance) must be done with standard scores, not with percentile ranks. Many calculations are done rapidly (and approximately) in our heads. Mastering the art of rapid and fluent test interpretation requires the ability to think in terms of standard scores. If you think about scores in terms of percentile ranks, you are counting on your fingers.

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