3 ms·

You throw a dice 3 times. It always show 6. How do you know the dice is loaded, and that it wasn't a fluke? Repeat the experiment, and see if it starts looking

You throw a dice 3 times. It always show 6. How do you know the dice is loaded, and that it wasn't a fluke? Repeat the experiment, and see if it starts looking random (pattern disappears) or if the pattern is strengthened (always saying 6).

nonbel 10y ago
For a rational person, it depends who gave you the dice. It sounds like you just put a low prior on dice being loaded since you are so used to getting well made dice from neutral parties...
nonbel 10y ago
Also, I couldn't get the original documents at the time, but you reminded me of this: >'The simplest assumption about dice as random-number generators is that each face is equally likely, and therefore the event “five or six” will occur with probability 1/3 and the number of successes out of 12 will be distributed according to the binomial distribution. When the data are compared to this “fair binomial” hypothesis using Pearson’s 2 test without any binning, Pearson found a p-value of 0.000016, or “the odds are 62,499 to 1 against such a system of deviations on a random selection.”' https://galton.uchicago.edu/about/docs/2009/2009_dice_zac_labby.pdf https://galton.uchicago.edu/about/docs/2009/2009_dice_zac_la... The point is you will always find deviations (with extremely low p-values) if you look hard enough. It is about collecting data as carefully as possible, and determining which model fits best, not which fits perfectly.
- GFK_of_xmaspast 10y ago
  > The point is you will always find deviations (with extremely low p-values) if you look hard enough I don't know how you can get that point from the article instead of 'an 1894-era die is biased but you need a lot of statistical power in order to see that'.
  - nonbel 10y ago
    I think the lesson is clear... the more messed up your methods the easier to see the deviation (ie the historical vs modern experiment). Also, where do you get this: >"you need a lot of statistical power in order to see that"

nonbel 10y ago

For a rational person, it depends who gave you the dice. It sounds like you just put a low prior on dice being loaded since you are so used to getting well made dice from neutral parties...

nonbel 10y ago

Also, I couldn't get the original documents at the time, but you reminded me of this: >'The simplest assumption about dice as random-number generators is that each face is equally likely, and therefore the event “five or six” will occur with probability 1/3 and the number of successes out of 12 will be distributed according to the binomial distribution. When the data are compared to this “fair binomial” hypothesis using Pearson’s 2 test without any binning, Pearson found a p-value of 0.000016, or “the odds are 62,499 to 1 against such a system of deviations on a random selection.”' https://galton.uchicago.edu/about/docs/2009/2009_dice_zac_labby.pdf https://galton.uchicago.edu/about/docs/2009/2009_dice_zac_la... The point is you will always find deviations (with extremely low p-values) if you look hard enough. It is about collecting data as carefully as possible, and determining which model fits best, not which fits perfectly.

GFK_of_xmaspast 10y ago
> The point is you will always find deviations (with extremely low p-values) if you look hard enough I don't know how you can get that point from the article instead of 'an 1894-era die is biased but you need a lot of statistical power in order to see that'.
- nonbel 10y ago
  I think the lesson is clear... the more messed up your methods the easier to see the deviation (ie the historical vs modern experiment). Also, where do you get this: >"you need a lot of statistical power in order to see that"