Thursday, October 7, 2010

I Don't Think That Word Means What You Think It Means

Danger Room:
Recruits also passed their military-capability exams, known as the Armed Forces Qualification Test, in greater numbers. In 2009, 66 percent scored at or above average, while 62 percent did the previous year.

Uh, last time FLG checked only 50% can be at or above average. It's kind of a rule, actually. Well, FLG guesses that if your testing sample is drawn from a population that omits the lowest scores in advance, then you could have more than 50% above average, but it's squirrelly.

7 comments:

Andrew Stevens said...

Another possible explanation is that your distribution is such that the median does not equal the mean. Much less than 50% of people have greater than average income, for example. I imagine the AFQT is a normal Gaussian distribution, so I doubt that applies here.

What does apply is that the testing population is above average on average. This is easily done because the norming test which sets the scoring scale is done on a different population than the people who are actually taking the test to be admitted. That norming population is a random sample of all people, not just military recruits.

FLG said...

That second paragraph was what I was trying to get at in the last sentence.

Andrew Stevens said...

Yes, I knew that. I was confirming that it was actually the case and I don't consider it particularly squirrely.

FLG said...

Oh, it's squirrelly.

Andrew Stevens said...

I'll file that along with your opinions on Harry Potter characters.

FLG said...

Hey!

RP Johnson said...

Andrew's response is phrased so gently. When I taught statistics I would have said something like, "You bonehead! The mean and the median are NOT the same statistic"

But at that time I was young and arrogant (and talked like a pirate).

RP Johnson

 
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