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March 21st, 2012, 02:28 AM   #1
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Chi Square Sample Size

Hello,

I want to do a test of distribution. That is, I want to find out what the statistical distribution is of a certain variable. Let's say it's the weight of apples, since I like fruit analogies. Let's say I want to know if the weight of apples are normally distributed (or log-normal or whatever). So I weigh n apples and enter the data into a list and divide the weights into c classes and count the amount of apples that belong to each class.

From what I've read, the only requirement on the sample size n, in the chi^2-test, is that the expected frequency of any one class must be at least five. But this seems like an insufficient measurement of reliability, doesn't it? Weighing 15 apples and dividing it into 3 classes can't possibly be equally good to weighing 1500 apples and dividing it into 300 classes. It appears to me that I would trust the result in the latter case more than in the first case. It seems plausible to believe that the variance of the resulting p-value should be inversely correlated to n and c.

But this is just a hunch I'm having and I can't prove it. So I'm asking you, how many apples do I need to weigh?

Thank you!
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