Phil Sauer
United States Willow Street Pennsylvania

I know enough statistics in CERTAIN areas to be functional, but there are other areas that baffle me... hence my question, which really isn't a hard one to answer, if you have the understanding I lack:
I suspect a die of being biased. Let's assume, for simplicity, that it is a sixsided  standard  die.
How many rolls of this die do I need to make (and record) to conclude with some measure of certainty (say, 95%) that it does indeed possess a bias (or not)?
Thanks!

Ken Shogren
United States Rochester Michigan

It depends on if you are a roleplayer or a boardgamer.
If you are a boardgamer  you'll need a good number of rolls, but if you are a roleplayer I suspect that one bad roll is all it'll take.

Matthew M
United States New Haven Connecticut
8/8 FREE, PROTECTED
513ers Assemble!

It depends on how biased the die is. If it heavily favors one side over another then it would take fewer observations to arrive at that conclusion with 95% confidence than if it is a small bias.
MMM



Wouldn't it be easier to just through the die away and get a good pro set of well balanced dice than worrying about it?
BOb

Pieter
Netherlands Maastricht
Good intentions are no substitute for a good education.
I take my fun very seriously.

Octavian wrote: It depends on how biased the die is. If it heavily favors one side over another then it would take fewer observations to arrive at that conclusion with 95% confidence than if it is a small bias. This.
You can calculate exactly how many rolls you need to conclude with 95% certainty that, for instance, a 6 is rolled 0.1% more often than any of the other sides. But to conclude whether the 6 is rolled 0.095% more often than the other sides needs more rolls.

David Molnar
United States Ridgewood New Jersey

I'm sorry, despite the answers so far to this question... there is no answer to this question. Any statistical inference depends not only on the size of the random sample, but also the actual results. Without knowing the results ahead of time, how can we know what conclusion we will be able to draw from those results?? Even a strongly biased die might, over the next 6000 rolls, produce exactly 1000 of each number 1 through 6, which would allow us to conclude nothing.
Anyway, what you're looking for is the chisquare test.

Ookami Snow
United States Kansas

Octavian wrote: It depends on how biased the die is. If it heavily favors one side over another then it would take fewer observations to arrive at that conclusion with 95% confidence than if it is a small bias.
MMM
For an example, if the die is fair, and we want a 95% chance of detecting the bias, and we have a 5% Type I error rate we would get the following:
"Fair" chance of getting a 6 is onesixth.
Now say we have a very loaded die that rolls a 6 onethird of the time, we could find this after 65 rolls.
But if that die was only slightly off balance and it rolled a 6 onefifth of the time we would have to roll 1421 times to find this.
So the less biased it is the more rolls are needed to detect the bias.

Ookami Snow
United States Kansas

molnar wrote: I'm sorry, despite the answers so far to this question... there is no answer to this question. Any statistical inference depends not only on the size of the random sample, but also the actual results. Without knowing the results ahead of time, how can we know what conclusion we will be able to draw from those results?? Even a strongly biased die might, over the next 6000 rolls, produce exactly 1000 of each number 1 through 6, which would allow us to conclude nothing.
It is true that a die that is highly biased could roll even results for the next 6000 rolls, but the chances for that is very slim. Statistics isn't about "yes or no" answers, but rather "we have evidence that supports yes instead of no."
Essentially conclusions are drawn in statistics when there is so much evidence for the proposed hypothesis that it has a much better chance of being right than wrong.
In your example above the statistical test would have made a Type II error, that being that we failed to conclude that die was biased even though it actually is biased. Every statistical test performed has a very real chance of doing this, but steps are taken (in this case by taking a large sample size) to reduce these errors.


