Traditionally, statisticians use 5% as the probability cutoff for correlation. If there's less than a 5% chance something would happen randomly, they assume it's a non-random process. The chances that my fashion choices would correctly predict 4 games in a row is just 1/16, or about 6.3%. That's not statistically significant, but it's close. If my jersey gets one more game right however, the odds move to 3.1%, a level that actually is significant. I won't be wearing the jersey for game 5 (go Mavs!) so a Dallas win will be more than just an important finals game, it'll be validation for all who ever believed that their particular scrap of cloth influences their team's play.
*Okay, clearly my shirt doesn't influence the game. What's wrong with this analysis?
First, I set the null hypothesis halfway through. Flip a coin 5 times, then hypothesize those results happen, and your test will be significant. If I say my jersey is a predictor one way or another, it could predict a Dallas win or loss, so 6 games is the level of significance, not 5.
Second, correlation does not imply causation, so it's possible some non-random third party is influencing both. Maybe I put the jersey on only when Dallas is losing (subconsciously). Or maybe Dirk watches what clothes I wear and then plays accordingly just to mess with my head.
Finally, even if something happens only 3.1% of the time from random chance, a random distribution will still give that answer 3.1% of the time. If you have 32 octopi picking 5 games, one of them is probably going to pick all 5 right. Then you can name him Paul and get the whole world to watch him.
Nonetheless, even though it's not true, I still kind of believe in this stuff. The truth is, I won't be wearing the Nowitzki jersey for game 5 because I want Dallas to win. But I won't be placing bets on it.
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