- #1

Swatje

- 35

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I was wondering, if you have a certain sample set. How can you quantify the probability of a certain statistical fluctuation?

For example, let's say you have a poisson distribution of high numbers, up into the fifties. You have one peak... How do you determine the probability of this being a statistical fluctuation?

The simple answer would be for me, calculate the the mean, take the square root of the mean as the standard deviance of a poisson, and then see how much sigma's this is. You could then use the gauss tables, (for high numbers the poisson will look like a gauss), and see the probability.

Some things bother me with this, for example: the standard deviance is an estimation, therefor you should use the t-distribution. But the t-distribution requires the knowledge of the actual mean. Would it be better to use the t-distribution anyways, because the lack of knowledge of the standard deviance is a more weighing factor? How ever, if you would use the estimated mean in the t-distribution, you would still be wrong. Is there a distribution that gives values for both an estimated mean and an estimated standard deviation?

My second question lies in the fact, that if a poisson goes to a gauss for high numbers, would it mean you could estimate the standard deviation by using the square root of 1/(N-1) summation rule? Or do these meet at high numbers, so it's always better to use the poisson way?

I thank you in advance for your time.

EDIT: I forgot to ask this:

If you were to analyse this sample, would it be better to count the fluctation into your mean, or leave it out...? So do you consider it a part of your sample set, or do you take it away and see if it is consistent with the rest of your sample set...?