A hack is a "down and dirty" and usually very clever solution or workaround to a problem. The central problem in Statistics Hacks is a monumental one--coming to terms with the randomness that surrounds us. The author suggests that, to get a handle on the confusing unpredictability, we turn to what he calls the heart and soul of statistics--probability. The journey is quirky.
What does random look like? Go to Hack #63, Sense the Real Randomness of Life. Here, Frey reminds us that "looking random and being random are not the same things." For instance, if you toss a quarter, what do you think is the most likely outcome of five flips: (a) heads, tails, heads, heads, tails; (b) tails, tails, tails, tails, tails; (c) heads, heads, tails, tails, tails; or (d) heads, heads, heads, heads, tails? Most people choose (a) just because it looks more random. Actually, it isn't because the probability for every combination is the same: 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/32 = .03125. The coin doesn't know that it has just turned up heads three times in a row, so the next toss is still fifty-fifty; each toss is independent. This misperception of randomness is responsible for what Frey calls the "gambler's fallacy." It accounts for the wrong notion that slot machines are due to pay out after a number of consecutive losses and that seven consecutive reds almost force us to lay our money on black the next turn.
There are a number of hacks that will improve your card and Monopoly play, but let's skip to the really big payoff--improving your odds of winning the Powerball lottery, Hack #41. Okay, so Frey has worked out the odds (1 in 146,107,962) and says he doesn't play because of that. But if you can't help yourself, here are a few pointers. "For Powerball and its number of balls and their range of values, $146,107,962 is the magic number." Not that your chance of winning is any better, but when the stakes reach that number, "the payoff amount has increased to a level where playing is worthwhile." Let the computer pick because random numbers have less meaning for others. Then, if you win, you're less likely to have to share the prize. Don't pick numbers that could be dates for the same reason--avoid numbers lower than 32. Stay away from well-known numbers. But at the end of his list of strategies, Frey does reminds us that lotto is Italian for destiny.
When should a coach go for the two-point conversion after a touchdown? (There's a chart for when you're ahead or behind, college and NFL.) How can you use matchboxes and the laws of probability to build a Tic-Tac-Toe machine that learns how to never lose? How not to misread coincidences? It's all in the book in short chapters that have a much lower probability to induce narcolepsy than the standard statistics text. www.oreilly.com
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|Title Annotation:||Statistics Hacks by Bruce Frey|
|Date:||Jul 1, 2006|
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