# Thread: is the dice average?- theory discussion

1. ## is the dice average?- theory discussion

i throw a dice 300times. attahced picture is the result.
the question is whether the dice is average?
if i do not use any tool, the 5points face is 66 times,much higher than 41 times of 6 ponts. i will say the dice is not average. is that right thought?

2. ## Re: is the dice average?- theory discussion

You may try to use the Pearson's chi square test to test goodness of fit against the uniform categorical distribution.

3. ## Re: is the dice average?- theory discussion

it's not good to automatically use tool, we need to ask why.do we really find the best method to solve problem?
Originally Posted by BGM
You may try to use the Pearson's chi square test to test goodness of fit against the uniform categorical distribution.

4. ## Re: is the dice average?- theory discussion

Originally Posted by nicegirl
it's not good to automatically use tool, we need to ask why.do we really find the best method to solve problem?
Are you saying you object to the suggestion to use a chi-square goodness of fit test here? It seems to be the natural thing to do in this situation...

5. ## Re: is the dice average?- theory discussion

you regard this as natural thing...but
if you throw dice as the above data, do you think your dice is average?i think most people will chose another dice.
which means chi squre method is not useful in this situation, even give me bad suggestion. do you think so?
i ask again, why do we use a bad method as natual thing??
Originally Posted by Dason
Are you saying you object to the suggestion to use a chi-square goodness of fit test here? It seems to be the natural thing to do in this situation...

6. ## Re: is the dice average?- theory discussion

Do you know what the chi-square test of goodness of fit is? Why would you think it's a bad suggestion. It basically will test exactly what you're looking to test. The question it would answer in this situation basically is "does this data seem like it could have come from a fair die" which is exactly what it seems like you're asking to me.

So maybe instead of dismissing the suggestion you can either explain why this wouldn't work for your data or maybe do some research because it sounds like you don't really understand (or misunderstood) the test we were suggesting.

7. ## Re: is the dice average?- theory discussion

the asymp.sig is .111,then people think the dice is average.is that your suggestion?
if i give you another dice, the result is 50 times for each face, which one do you think is average？
the chi square method is not a exactly method. and i don't think it's a natural thing to use this method in non normal situation.
what's the true thing?the 5points face is 66 times,much higher than 41 times of 6 ponts. it means the dice is not average.do you think so?

8. ## Re: is the dice average?- theory discussion

With 300 samples the asymptotics are fairly decent at that point. Do I think that seeing a 66 and a 41 is enough evidence to convince me that the die isn't normal? No - it's not enough evidence because the test wasn't significant. This isn't to say that the die is fair - just that we don't have enough evidence to say that it isn't fair (sort of a 'assume innocent until proven guilty' type thing).

If that doesn't convince you and you still think that 25 is too large of a difference between the highest and lowest counts then you might be interested in this...

I simulated 1000 trials of 300 tosses of a fair die and then calculated the difference between the highest and lowest groups (in your case this would be the 66-41=25). The histogram is the result. Looking at that it doesn't appear to be particularly extreme to observe a difference of 25 even when the die is fair. Is it slightly higher than one might expect? Sure but not enough to convince me that we are definitely dealing with a biased die.

9. ## The Following User Says Thank You to Dason For This Useful Post:

spunky (09-28-2014)

10. ## Re: is the dice average?- theory discussion

Originally Posted by nicegirl
it's not good to automatically use tool, we need to ask why.do we really find the best method to solve problem?
I am in sympathy with your ambition. It is good the try to find the "best" method.

But what do we mean by "best" method?

One way could be to say that a method that has the highest test power in detecting a deviation from a null hypothesis would be optimal, and thus "best". So a dice that deviates from being a "fair" dice, should be discovered with high power in the used test. Right now I can't remember any proof for that the chi-squared test should be optimal. But I am quite sure that it would be good (in the sense of having high power).

the chi square method is not a exactly method. and i don't think it's a natural thing to use this method in non normal situation.
But maybe Nicegirl can suggest a better method. That would be really nice!

11. ## Re: is the dice average?- theory discussion

the die has 2 possiblity:normal or not.that's we are need to research. if a methond cannot give me the answer, the method is not a good method.
300 tosses is enough to test. it means the answer is also included in the test.
so, we should use a method to tell us which possiblity is close to test result. which means we have >50% confidence to make the conclusion.
if the die get the above result(66,41), i have more confidence to say the die is not normal than the die is normal.
am i right?

12. ## Re: is the dice average?- theory discussion

Originally Posted by nicegirl
if the die get the above result(66,41), i have more confidence to say the die is not normal than the die is normal.
am i right?
I think Dason gave you an answer to this in post #8 above.

13. ## Re: is the dice average?- theory discussion

the die has 2 possiblity:normal or not.that's we are need to research. if a methond cannot give me the answer, the method is not a good method.
The very basic understanding is that you have a non-zero probability of committing errors when you make a decision. No statistical tests can guarantee you a 100% answer to this question. As said above, you can evaluate the test - to see whether it is the most powerful test or not for example. Although the Chi Square test is an asymptotic test, I think it is good enough to answer your question and the method itself is very popular.

14. ## Re: is the dice average?- theory discussion

let's make the question simple:
1.is the dice normal?
2.if you don't know the answer of above question, how to evaluate a test is the most powerful test?
Originally Posted by BGM
The very basic understanding is that you have a non-zero probability of committing errors when you make a decision. No statistical tests can guarantee you a 100% answer to this question. As said above, you can evaluate the test - to see whether it is the most powerful test or not for example. Although the Chi Square test is an asymptotic test, I think it is good enough to answer your question and the method itself is very popular.

15. ## Re: is the dice average?- theory discussion

Originally Posted by nicegirl
how to evaluate a test is the most powerful test?
well you could prove its an uniformly most powerful test using the Neyman-Pearson lemma

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