Teaching an intelligent guy about a basic statistics concept - Page 6

Wyman · #51 07-22-2007, 10:50 AM

If you picked up a coin I had never seen before and flipped 10 heads in a row, I'd be inclined to predict that your next flip will be heads, questioning the fairness of the coin.

If your friend agrees that this is a fair coin, ask him what "fair" means (on each flip, the probability of heads = 0.5). This should end the discussion. If there is a question of whether the coin is fair, the obvious guess is that the coin is biased towards heads. Tails is the least logical thing for him to predict.

chezlaw · #52 07-22-2007, 03:42 PM

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If you picked up a coin I had never seen before and flipped 10 heads in a row, I'd be inclined to predict that your next flip will be heads, questioning the fairness of the coin.

If your friend agrees that this is a fair coin, ask him what "fair" means (on each flip, the probability of heads = 0.5). This should end the discussion. If there is a question of whether the coin is fair, the obvious guess is that the coin is biased towards heads. Tails is the least logical thing for him to predict.

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Its not a fairness issue. The confusion is whether there's some external book-keeping going on.

chez

vhawk01 · #53 07-22-2007, 04:36 PM

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If you picked up a coin I had never seen before and flipped 10 heads in a row, I'd be inclined to predict that your next flip will be heads, questioning the fairness of the coin.

If your friend agrees that this is a fair coin, ask him what "fair" means (on each flip, the probability of heads = 0.5). This should end the discussion. If there is a question of whether the coin is fair, the obvious guess is that the coin is biased towards heads. Tails is the least logical thing for him to predict.

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Its not a fairness issue. The confusion is whether there's some external book-keeping going on.

chez

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Right, he accepts that the coin is fair, he just thinks its hyper-fair.

chezlaw · #54 07-22-2007, 04:53 PM

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If you picked up a coin I had never seen before and flipped 10 heads in a row, I'd be inclined to predict that your next flip will be heads, questioning the fairness of the coin.

If your friend agrees that this is a fair coin, ask him what "fair" means (on each flip, the probability of heads = 0.5). This should end the discussion. If there is a question of whether the coin is fair, the obvious guess is that the coin is biased towards heads. Tails is the least logical thing for him to predict.

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Its not a fairness issue. The confusion is whether there's some external book-keeping going on.

chez

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Right, he accepts that the coin is fair, he just thinks its hyper-fair.

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Yes, if we were talking about picking black cards from a deck without replacement then the friend would be correct about hyper-fairness.

Its a very common view, some people can't be persuaded against hyper-fairness even when there's no reason to believe the events are dependent and all the evidence demonstrates independence.

The main point for the op is its not a misunderstanding of statistics so concentrating on statistical principles isn't going to clear up any confusion.

chez

Wyman · #55 07-24-2007, 08:43 PM

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If you picked up a coin I had never seen before and flipped 10 heads in a row, I'd be inclined to predict that your next flip will be heads, questioning the fairness of the coin.

If your friend agrees that this is a fair coin, ask him what "fair" means (on each flip, the probability of heads = 0.5). This should end the discussion. If there is a question of whether the coin is fair, the obvious guess is that the coin is biased towards heads. Tails is the least logical thing for him to predict.

[/ QUOTE ]
Its not a fairness issue. The confusion is whether there's some external book-keeping going on.

chez

[/ QUOTE ]

Right, he accepts that the coin is fair, he just thinks its hyper-fair.

[/ QUOTE ]
Yes, if we were talking about picking black cards from a deck without replacement then the friend would be correct about hyper-fairness.

Its a very common view, some people can't be persuaded against hyper-fairness even when there's no reason to believe the events are dependent and all the evidence demonstrates independence.

The main point for the op is its not a misunderstanding of statistics so concentrating on statistical principles isn't going to clear up any confusion.

chez

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Right, I suppose I was suggesting pressing OP's friend about the definition of fair. My thoughts were that there was no good definition of fair that would avoid the idea of each flip being 50/50, but after some thought that's not clear. I guess I would, as others, joke that the coin doesn't remember what happened last time.

Or, now that the coin has been flipped 10 times, ask him to start the experiment over (surely that doesn't require a new coin!!). What's the probability of flip 1 being heads?

tarheeljks · #56 07-25-2007, 02:53 AM

we are talking about the laws of independence, i think this is most certainly an issue of misunderstanding statistics.

chezlaw · #57 07-25-2007, 08:29 AM

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we are talking about the laws of independence, i think this is most certainly an issue of misunderstanding statistics.

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That's not the op. The friend believes the results of the first 10 flips influences the 11th - that's a belief that the flips aren't independent.

Clear that up and the problem will evaporate. Either he will agree they are independent and therefore the 11th flip doesn't depend on the early ones or he will continue believing they are dependent. (or he will fall into a holy trinity type hole).

chez

tarheeljks · #58 07-25-2007, 07:11 PM

i know it's not the original point, i was just pointing it out

Wyman · #59 07-25-2007, 09:21 PM

Does your friend believe the same phenomenon occurs if 10 _different_ coins are flipped and each comes heads? Does he believe that an eleventh coin is more likely to come up tails?

You might try to convince him that the "in the long run, flips should be 50/50" concept should hold across all fair coins, not just for any given coin (this is true). Given this, his logic dictates that flipping one coin influences the flip of another. He may agree that this is silly, or you may now have convinced him that coins influence each other.

This is a very interesting question.