- Thread starter nicegirl
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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??

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...

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.

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?

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...

View attachment 4796

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.

it's not good to automatically use tool, we need to ask why.do we really find the best method to solve problem?

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.

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?

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.

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?

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.

how to evaluate a test is the most powerful test?