*Yeah, yeah. Greek, Latin, who cares?

Tuesday, December 21, 2010

Percentiles

Just a quick whine, while I'm busy prepping for next term:

The AP has an article today worrying that the American education system is failing to prepare students for military service. Now, I strongly suspect that's true...after all, I see how poorly prepared many students are for college.

What I'm annoyed by, though, is the apparent ill-preparedness of the journalist who wrote the damn article. The headline is that 23% of students taking the ASVAB (Armed Services Vocational Aptitude Battery) are scoring too low to be allowed to enlist. The article itself, however, later states that

Recruits must score at least in the 31st percentile on the first stage of the three-hour test to get into the Army or the Marines. Air Force, Navy and Coast Guard recruits must have higher scores.
Does anyone else see the problem here? If you have to beat out 31% (or more) of the other people taking the test, then it literally cannot be possible for less than 31% of the takers to fail the test! The percentage who fail just has to be more-or-less constant (and at least 31%)*.

Now, I'll admit I haven't taken the time to read the study on which the AP article is based, so I'm not casting aspersions on those who carried out the study, or even on those who've expressed concern over its results. But for the love of all that's mathematically possible, can we get journalists who know more about math than my 4-year-old?

*More-or-less constant because the pool of scores from which the percentile-score equivalences are derived is probably multi-year, so the percent who score at or below that value can fluctuate from year to year. At least 31% must fail because that cutoff is described as applying to the first section--if it's possible to fail on the other sections, then some who pass the first may fail overall.