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A statistical icon falls to modern science ...

by Bill Osler / February 24, 2004 7:04 AM PST

One of the classic physical examples of an unbiased random physical process is the coin toss. Tossing a coin is perceived as such an unbiased process that we even use it for 'important' things like deciding the beginning of sports games. We even say that something unpredictable is a 'toss up'

It turns out that coin flipping may be random, but it is not unbiased. The side of the coin that starts out on top is slightly more likely to finish on top. Hear about it at NPR : All Things Considered for Tuesday, February 24, 2004 (scroll down to The Not So Random Coin Toss (the audio link is not active yet, but should be later this evening). There is some text information at NPR : The Not So Random Coin Toss and there should be an audio link there later on.

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Re:A statistical icon falls to modern science ...
by Roger NC / February 24, 2004 7:52 AM PST

Of course, there is the complications of different wearing on different coins affecting their balence, air currents, if the coin and hands were dry, wet, oily, etc.

Chuckling, interesting but when you think about it, not surprising that identical flipping motions would tend to produce the same results in a lab experiment. With identical initial forces, the flight and rotation should be classical physics, or almost.

But outside the lab, all the other stuff that get thrown in.

And don't forget the possibility (ok, slight) of parapsychic (telekenisis for obvious one) influences. Wink

Looks like a great weekend in the future in eastern NC, hope is the same your way. And coincides with my long weekend (every fourth week) of shift rotation. I don't do much outside, but still like nice weather.


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I ignored the mechanical issue in my post ...
by Bill Osler / February 24, 2004 8:03 AM PST

As I understand it, the claim of the researchers is that when humans flip the coin the result is biased, but still random. When a well designed machine flips the coin it is possible to make the flip non-random. The result with the machine is not really surprising, although it was not foregone. Some physical processes are 'complex' and subject to apparent randomness due to the possibility that immeasurably small forces can disrupt the result (think chaos theory - does a butterfly in Africa really affect the course of an Atlantic hurricane?) and I don't think anybody could really have said whether machine-flipped coins represent a complex process or not up until now. I guess this result proves that machine-flipped coins do not represent a complex process.

I'm willing to risk the non-randomness from para-normal phenomena. In fact, IIRC, in ancient societies there was a presumption that non-physical forces could and sometimes did intervene when decisions were made using apparently random processes like 'casting lots'.

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This reminds me of something - Any word from Louis Marchal?
by Bill Osler / February 24, 2004 8:04 AM PST

He had some interest in statistical type stuff. I don't remember seeing any posts in a while. Last I heard he was having some problems with health.

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That's the problem with random sampling ...
by Mosonnow / February 24, 2004 8:08 AM PST

You have to take a big enough sample to get the projected average to come out correctly and thus prove the theory (i.e. 100 tosses of the coin never works therefore "the sample must be too small"). The only way I can think of to do this, is to take an infinite sample - and then stop. Scratches head in thought at this point.


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That's the nature of sampling ...
by Mark Leiker / February 24, 2004 9:40 AM PST

it is designed to represent a population of interest, but sampling margin is always a factor. It's just that we accept very small sampling errors when our sample is large enough, randomly drawn, etc.

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Oh Oh - trouble again ....
by Mosonnow / February 24, 2004 10:02 AM PST

Dear Mark

I can be very abstruse on occasion (Note to self: must try harder). I do understand the nature of random sampling - i.e. that one does not sample ad infinitum to prove a theory, rather that the sample suggests a representation of the whole. I posted this because the flipping of coins has erstwhile been one of life's mysteries - it rarely works out as they say it should, and Bill's post at last throws some light as to why this might be.

I would love to have posted a sensible technical philosphy, but - erm. I'm just grateful that Bill posted this new insight.


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NT - Understood :)
by Mark Leiker / February 24, 2004 10:46 AM PST


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Re:A statistical icon falls to modern science ...
by C1ay / February 24, 2004 10:45 AM PST
Tossing a coin is perceived as such an unbiased process that we even use it for 'important' things like deciding the beginning of sports games.

There is a difference of methods though with this example. The researchers claim that the toss favors heads when you start with the coin heads up on your thumb, flip it and catch it in your hand. In the case of many sporting events, if not all, the flipped coin is not caught but allowed instead to hit the ground.

I personally tried 50 tosses as the researchers described and in my small sample tails won, 23 to 22. Throughout the test neither heads or tails took the lead by more than four. Carrying this on for long by one's self would get monotonous quickly. I wonder how the researcher's performed their tests.
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NT 23-22? What happened to the other 5 tosses? ;)
by Mark Leiker / February 24, 2004 10:48 AM PST


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Re:NT 23-22? What happened to the other 5 tosses? ;)
by C1ay / February 24, 2004 11:02 AM PST

5 more tosses to bring the total to 50 yeilded 4 more tails and 1 head for a grand total of 27 tails to 23 heads.

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