@DoyleB - I think (unfortunately) we’re pretty much in agreement.
Are we misinterpreting the data? Did CB make one (or more) mistakes?
[Note - I ramble on quite a bit. If anyone wants to skim, I actually think my final paragraph might be somewhat interesting…]
The fact that the concordance table and the SI table don’t agree leads me to believe that those tables were generated with different techniques. (If they just generated the concordance table directly from the percentile table, then obviously they would agree.)
Even though they define their concordance table to essentially match up percentiles, a logical way to try to generate it (especially for a new test) is to have their research group take both the new PSAT and an old one (or whatever they’re trying to concord it to).
I guess one explanation would be the following. Say people in their research group who got a 214 on the new psat tended to also get a 214 on the old (I’m assuming that’s what the concordance table says) - but only 0.5% got >= 214 on the new (while 1% got >= 214 on the old when it was given for real). They then have a discrepancy. The concordance table would say that 214 → 214 - but the percentile table would say that 214 was 99.5% (instead of 99%). Maybe the research group just didn’t have the correct fraction of smart(est) kids? Would that just imply that the percentiles are wrong, and concordance is right? Not sure why they wouldn’t adjust for that. Maybe seems too simple minded to me.
Another high-level possibility. The research group prepared for the old PSAT, but not the new one. This means that current students (who presumably prepared for it) would find the test easier than the research group. But this should affect both concordance and percentiles - not sure why that would make concordance accurate but percentiles wrong.
Also - maybe they wanted the scores to be directly comparable to old PSAT scores. I actually think this is a stated goal of theirs (at least PSAT should match what you would get on the SAT). Maybe they started with that goal, and so set up the raw score translation table such that final scores would somewhat match previous PSAT scores. And then maybe they used some other technique to try to estimate the percentiles (and just failed)?
Obviously the anecdotes make us think that the concordance tables are correct (and the percentiles are not). The biggest problem that us percentilers
have is that getting accurate percentiles seems SO EASY!!! Some people say that they know the accurate percentiles, and just don’t want to release them, because DRAMA. I don’t buy that. Could it be possible that the scores are distributed across data centers, and so they actually can’t put them all together and sort them? That seems mind-bogglingly stoooopid to me - but I work at Google. Maybe they’re a bunch of statisticians and educators - and their IT stuff isn’t up to snuff.
I guess a final possibility (I should stop writing already) is that they do know the accurate percentiles for each year, but prefer to compare to the previous year, because they feel it’s more accurate / helpful somehow. If the population of test takers changes dramatically from year to year - maybe it’s more helpful to say how you did compared to the population last year?
OK, one last thought - I promise - that could explain both the concordance tables and the percentile tables being correct (though not the anecdotes). Maybe the kids taking the test this year are actually not as smart (no offense
) as either predicted and/or last year. I mean, if I understand things properly, I think that’s exactly what the concordance table and percentile table are saying. That the top 1% of kids last year would get a 214 on this test (and also the old test) - but only the top 0.5% of kids this year got a 214… (Put another way, maybe CB predicted that from studying specifically for the new PSAT, scores would go up a lot, and maybe they overcompensated.)