Freakonomics

by Steven D Levitt and Stephen Dubner. A local bestseller that attempts to find the hidden answers from (not necessarily economic) data. The answers presented are controversial to say the least, but yet not quite far fetched. That’s I guess the main selling point of the book.

The following passage is from the book. It has nothing much to do with the theme/thesis proposed by the authors. But when I read it, I began thinking whether or not it was mathematically consistent.

The ECLS project surveyed roughly one thousand schools, taking samples of twenty children from each. In 35 percent of those schools, not a single black child was included in the sample. The typical white child in the ECLs study attends a school that is only 6 percent black; the typical black child, meanwhile, attends a school that is about 60 percent black.

Another completely unrelated thing. Simpson’s paradox. A google search will reveal several good write-ups.

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2 Responses to Freakonomics

  1. Vivero says:

    I think it’s compatible. I don’t know if it’s possible in practice, for I’m writing from Spain, and have no idea of the ethnic composition of schools there. But if you mix a) 617 schools with 3% of its children black, b) 310 with 12% of its children black and c) 73 with 100% black, and the size of all schools is similar (let’s say, 100 children per school)… you will get aprox. 35% of the 20-sized-samples without black children (it’s a Bernouilli experiment, with 0 successes; you will probably get full-white samples either from a and b type schools). It’s easy to check that the average white child has 6% black companions, and the average black child has 60% black companions

    Thank you for the amusement, you have been very helpful for a man that can’t sleep.
    and greetings from Madrid!

  2. tpc says:

    Hi,

    Thanks for visiting. I’m glad that the problem at least is interesting enough to make another person do some calculations. I did not even consider sampling in my own calculations.

    I guess it should be an exciting year to be in Madrid, with the ICM. Hope you have a great time!

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