# Thread: Is the dice normal?

1. ## Is the dice normal?

there are 2 dices in a box. one is normal, another is not normal.
i select one, and throw 300 times, get the result as below:

question: is that dice normal?

solution1:
if the dice is normal, the probability of each face is 1/6, then use chi square method to test whether the result match.
spss result:asymp sig .111, which means only 11.1% confidence to say the dice is normal. less than 50%,even less than 25%.
so, i say this dice is not normal.

solution2:
if the dice is normal, will go to any face randomly.
i use spss runs test, asymp sig .000, which means the result is not random, which means the dice is not normal.

2. ## Re: Is the dice normal?

A binomial test may be more appropriate with a 16.67 probability reference level.

Not sure you are totally interpretinng the chi-sq test correctly. If you are comparing your proportion to a uniformed 16.67 then if p-value below your level of significance cut-off then you would say, given the die is fair you would expect to see that extreme of results < 0.001 times.

3. ## Re: Is the dice normal?

Originally Posted by hlsmith
A binomial test may be more appropriate with a 16.67 probability reference level.

Not sure you are totally interpretinng the chi-sq test correctly. If you are comparing your proportion to a uniformed 16.67 then if p-value below your level of significance cut-off then you would say, given the die is fair you would expect to see that extreme of results < 0.001 times.

Where are you getting 16.67 from?

4. ## Re: Is the dice normal?

And it is said the other die is not normal. Do we know the probabilities for each side on the non normal die? If so we could use bayes theorem.

5. ## Re: Is the dice normal?

Originally Posted by Dason
And it is said the other die is not normal. Do we know the probabilities for each side on the non normal die? If so we could use bayes theorem.
we only know the probability of normal dice,1/6 for each face.

6. ## Re: Is the dice normal?

I assumed it was a six-sided fair dice (i.e., 1/6 = 0.1667), then my brain thought 16.67% looked nicer, so I type that on the post leaving the % sign off as an error.

7. ## Re: Is the dice normal?

It isn't binomial though - it's multinomial. Which is pretty much what the chi-square goodness of fit test is for.

8. ## Re: Is the dice normal?

But if you have the computing power why not go exact test.

9. ## Re: Is the dice normal?

You could but it wouldn't be a binomial test. You would need to do the equivalent but for a multinomial.

10. ## Re: Is the dice normal?

is that a hard question or too easy??
no one post the solution and answer.

11. ## Re: Is the dice normal?

If you don't know anything about the other die other than it is "non-normal" then if you want to do something other than a classical hypothesis test you would need to put a prior over the probabilities for the other die. In that case you could use Baye's theorem to get the probability of each die given your data.

12. ## Re: Is the dice normal?

Originally Posted by nicegirl
is that a hard question or too easy??
no one post the solution and answer.
You are a person, you could post the solution!

Then we can chime in with our feedback.

13. ## Re: Is the dice normal?

The people patiently helping you have given you all the tools you need to answer this question yourself. You need to interpret the data and results yourself or you will not learn.

But I will chime in with my opinion. There is no evidence that the dice is not-normal. The dice does not constitute an anomaly, it should be considered normal.

Originally Posted by nicegirl
which means only 11.1% confidence to say the dice is normal. less than 50%,even less than 25%.
so, i say this dice is not normal.
You are interpreting the p-value wrong. The p-value if not the "chance" that the null-hypothesis is wrong. You may interpret the above as this: a normal dice will give the above result or an even more extremely skewed result 11.1% of the time.

11.1% is within the realm of reasonable doubt. So most people will opt to avoid type-1 error, and accept the null hypothesis. Usually only when the p-value drops below 5% do we reject the null-hypothesis. This is the convention in statistics.

However take note that if:
We reject the null hypothesis and the null hypothesis is true. We make a Type I error.
We fail to reject the null hypothesis and the alternative hypothesis is true. We make a Type II error.

In cases where the type-II error is very costly, people may opt for another choice (i.e. type 1 error causes discomfort but type-II error causes death) -->
A doctor tests you for a highly infectious disease. The test comes in that their is a 10% chance that you do not have the disease, while the treatment is taking some relatively harmless pills and the effect of not taking the pills is your death and maybe those of the people close to you. A doctor may choose to give you the pills. Does your dice fall in this class of problems? Otherwise you have no logical ground to conclude what you did.

In your case there is no defined cost function, so you should accept the null hypothesis: the dice is normal.

14. ## Re: Is the dice normal?

i am not sure if this case indicate the hypothesis method cannot help to make decision.
And, my own thought:the probability is not existing in the world. only possiblity:yes or no. it means when you say one thing have 11.1% chance to happen, it's reay meaning is this thing will not happen.
this is only a theory discussion, about the basic concept and method.
PLS LET ME KNOW IF I WAS WRONG.

15. ## Re: Is the dice normal?

If you flipped a coin three times and it came up heads three times in a row would your immediate conclusion be that the coin isn't fair?