Is there a reason to report standardized test scores on crazy ranges?

Question

The SAT comprises two sections, each scored on the range 200-800 (in 10-point increments, so it's really 20-80), so the final score is on the range 400-1600. It used to have three such sections, for a total range of 600-2400.

The GRE, on the other hand, comprises three sections, two of which are scored on the range 130-170, in 1-point increments, and the third is scored 2-8, in 1-point increments.

This makes scores hard to interpret from a lay perspective, even though you can easily look up percentile conversion tables (SAT, GRE^[pdf]).

Is there any legitimate reason to make scores more difficult to interpret than necessary? Why not report percentiles? Or even just score on 0-100?

Answer 1

There is indeed no statistical reason to use these unusual ranges - zero to one hundred would do the job just as well. So why don't they just use that scale?

The main reason is that most standardized tests need to use some kind of difficulty scaled scoring system, to allow having different editions of the tests etc. One easy way to stop people from mixing up the scaled score and say a raw percentage score is to use a different range for the scaled scores. See e.g. Why Do Standardized Testing Programs Report Scaled Scores? written by two ETS psychometricians (Xuan Tan and Rochelle Michel) in 2011. Relevant quote:

If two test takers taking Forms A and B respectively got the same scaled score of 194 (corresponding to raw scores of 95 on Form A and 96 on Form B), we know these two test takers exhibited the same level of performance on this test. One might ask: Why not report the adjusted scores for Form B instead of the scaled scores? This is because the adjusted scores would be on the same scale as the raw scores and could be easily misinterpreted as the raw scores. Thus, the scaled scores are used and are commonly set to a range of values different from the raw score values.

The same is true for percentile scores, which are easily misinterpreted for the percent of correctly answered questions. The test takers can probably figure out the right interpretation either way, but with this approach e.g. parents less conversant with SAT scoring or percentiles are more likely to go "oh, 1500, is that good?" rather than "only 52%?!".

Next, the test designer has to pick an actual range. As far as I understand it, this is somewhat arbitrary. It involves picking an increment (e.g. 1 or 10),

For example, the scaled score can be reported in various increments (1-point increments, 5-point increments, 10-point increments, etc.). Usually, we want each additional correct answer to make a difference in the test takers’ scaled score, but not such a large difference that people exaggerate its importance. The selection of a score scale, with appropriate increments, aids in the usefulness of the reported scaled scores to the test-score users.

Then you naturally have an interval of scaled scores, which can be offset to whatever minimum you prefer. See e.g. the answers to Why do some tests have a (nonzero) minimum score? for more details.

Answer 2

It prevents confusion by people without a solid foundation in mathematics.

Both tests have an offset. The score range for SAT is really 0-60 for each section, a total of 120.

Similarly the GRE is 2 × [0,40] + [1,6] for a total of 86. A majority of those scores would be in the high multiple tens - which would make them look a lot like a percentage score already. Add in percentile and that's begging for confusion.

The offset in each case prevents this problem. A score minimum of 400 couldn't possibly be confused with a percentage mark or a percentile ranking (and the associated increment allows for granularity in the event of changes to the test format) while a score minimum of 262 has similar benefits even if only one section's score was viewed (although with increment of 1, this is the extent of the gain).