[HN Gopher] How to create an unfair coin and prove it with math ...
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       How to create an unfair coin and prove it with math (2011)
        
       Author : homarp
       Score  : 33 points
       Date   : 2021-06-27 11:15 UTC (11 hours ago)
        
 (HTM) web link (izbicki.me)
 (TXT) w3m dump (izbicki.me)
        
       | Danieru wrote:
       | > Amazingly, it takes some pretty big bends to make a biased
       | coin. It's not until coin 3, which has an almost 90 degree bend
       | that we can say with any confidence that the coin is biased at
       | all.
       | 
       | Is this a parody of statistical driven thinking?
       | 
       | The coins are clearly biased from the first bent coin on. It just
       | takes a more extreme bias for the statistics to "prove" the bias
       | assuming no other information using only 100 flips.
       | 
       | But we have other information: you know you bent the coins...
       | 
       | The statistics are not useful for confirming the bias. Rather
       | they are useful for finding "how much cheating" you can push
       | before the statistics alone are enough to get you beat up.
        
         | boublepop wrote:
         | Ironically your being biased when you think that just because
         | you can see a coin it bent that it must then be based. It's
         | perfectly possible that a coin even with an extremely visible
         | bend is still unbiased, and the only way to prove it's biased
         | is to conduct the experiment.
        
         | throwawaybern wrote:
         | Seems unintended parody, the best kind of parody.
         | 
         | Because 3rd coin flipped 41 out of 100, at level 0.95 the
         | confidence interval still contains 0.50
        
         | [deleted]
        
         | BobbyJo wrote:
         | They implicitly mean 'practical' or 'observable' bias. A coin
         | with a .0001 bias isn't very interesting.
        
         | Out_of_Characte wrote:
         | Just because you can easely see the bias in the example doesn't
         | mean you can in other area's. There are magicians that can
         | reliably flip coins.
         | 
         | I mean, what were you expecting? He flipped a coin 600 times.
         | his findings aren't going to be groundbreaking if he did it
         | 6.000 times.
        
           | fighterpilot wrote:
           | The point is that stats isn't useful for demonstrating the
           | existence of bias since we know already the bias exists given
           | the deliberate introduction of bias. We know the population
           | function is biased and sample data from that function isn't
           | going to change that.
           | 
           | The stats in the post is mostly a commentary on the
           | phenomenon of statistical power. It _may_ also be a
           | commentary on how the angle of the bend is non-linearly
           | related to coin flip bias. I did find that bit to be
           | unexpected. Although given the wide sampling distribution due
           | to the low N, this could easily be variance.
        
       | [deleted]
        
       | ac42 wrote:
       | Lol, I thought this was going to be about crypto currency. Lovely
       | article!
        
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       (page generated 2021-06-27 23:01 UTC)