Samstag, 14. März 2015

Rolling Dice & Regression to the Mean:

"Imagine we’ve thrown 3,600 [dice]. Purely by chance we’d expect about 600 of them to show a 1, about 600 a 2, and so on up to about 600 showing a 6. Now let’s pick all those showing a 6, ignoring the others. Since each of these shows a 6, the average value they show is obviously also a 6. We then throw all these again. By chance again, we’d expect about 100 of them to show a 1, about 100 a 2, and so on up to about 100 of them showing a 6. The overall average of the numbers showing on the dice on this second set of throws will be about 3.5 (it’s just [100 × 1 + 100 × 2 + … + 100 × 6] ÷ 600). Now the average has decreased from 6 the first time we threw these particular 600 dice to 3.5 the second time we threw them."

[According to Cochran, the "final" IQ that an individual will get is not only influenced by genes, but also influenced by chance. Probably some day it will be possible to predict the range in which an individual's adult IQ will fall with high accuracy at the moment of birth (the individual's intelligence genes will be known at birth or even earlier, but it will be unknown what "chance events" the indidviual will encounter during its life-time). In other words, at the moment when egg and sperm cell fuse it becomes determined what numbers there are on "an individual's IQ-dice". But the result of the dice roll (the adult's IQ-score) won't be known until the dice "stop rolling" (the adult IQ-score will be measured) in adulthood.]

Source of the quote:
The Improbability Principle (2014) by David J. Hand

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