Wednesday, May 02, 2007

Comments, Links

(Below is a copy of the e-mail I just sent out to the AP Stats students I teach this year. The AP test is coming up next Tuesday. 加油!)

The baby is taking a nap so I thought I would spam your e-mail inbox with some stats examples I saw in the wild over this past week:

1) There is an article in the current New York Times called "Study of N.B.A. Sees Racial Bias in Calling Fouls". This is what the article has to say about the study's conclusion:

A coming paper by a University of Pennsylvania professor and a Cornell University graduate student says that, during the 13 seasons from 1991 through 2004, white referees called fouls at a greater rate against black players than against white players.

Justin Wolfers, an assistant professor of business and public policy at the Wharton School, and Joseph Price, a Cornell graduate student in economics, found a corresponding bias in which black officials called fouls more frequently against white players, though that tendency was not as strong. They went on to claim that the different rates at which fouls are called “is large enough that the probability of a team winning is noticeably affected by the racial composition of the refereeing crew assigned to the game.”

Does that language sound like something we've done before in class? The study in the article used a statistical technique called multivariable regression analysis, which is basically regression (y = a + bx) extended to multiple explanatory variables and a single response variable (y = a + b1x1 + b2x2 + b3x3 + ... We might spend some time on multiple regression after the AP test.). If they were to do a hypothesis test instead, what would be H0 and Ha, and which test would they use? I can think of a couple different ways.

2) I'm reading a book called "The New Father: A Dad's Guide to the First Year" to learn about Charlotte's development and how to be a better dad. On exposing babies to music, I ran across this quote:

According to [education researcher Edwin] Gordon, every child is born with at least some musical aptitude: 68 perent have perfectly average aptitude; 16 percent well above; and 16 percent well below. "Just as there are no children without intelligence," he says, "there are no children without musical aptitude."

Hmm, that number sounds suspiciously familiar. Where have you seen 68% many times before? What do you think the distribution of musical aptitudes in babies looks like?

3) Well, it turns out that Jodi's baby was a girl. This was somewhat of a surprise because pretty much everybody had a guess based on the shape of her tummy, the stretch marks, the foods she like to eat, etc, and most of the guesses were for a boy.

Jodi's mom based her prediction (boy) on the experience she had with three of her friends when they were pregnant. Jodi's mom was the only one out of the four who did not develop stretch marks, where as the other three did. Then, Jodi's mom was the only one who had a girl; the other three mothers had boys. So Jodi's mom believed -- alternate hypothesis! -- that wrinkles were a good predictor of the baby being a boy. Does the evidence from her and her friends allow us to reject the prevailing belief that there is no relationship -- null hypothesis! -- between stretch marks and the baby's sex? Do you see any problems with this test (hint: check the conditions).

OK, that's it. You guys are lucky that I'm not writing a test for Chapter 13, or those questions might have ended up on it! Maybe next year...


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