Statistics Help: Determining Randomness

[ZutAlors!]

I've got a statistics problem, dealing with a number of tests using slightly different procedures, and it's equivalent to this:

Suppose I've got a few hundred marbles, some of which are black, some white. Say, three hundred marbles split 60/40, if you want some approximate numbers. These marbles are split into bags: some bags have more marbles, some have less; let's say in the range of 10 to 50 marbles in each bag.

Obviously the proportion of marbles in each bag varies. But how can I determine whether the variance is random (by which, I assume, I mean "matches a normal distribution" Right?) Is there an exact or approximate test I can apply?

And, assuming, the variance is not random (or, rather, probably not random with some confidence), as I expect, what's a reasonable way to identify which bags are the culprits?

[Borodog]

A few things to consider:

1) I don't really know the answer to your question. I could hack out something practicable, but whether it would be "correct" according to a statistician would be highly improbable.

2) The distribution of marbles is most definitely not normal, but Poisson (this does not mean it's not random, just that the random deviates form a different distribution than the one you assumed).

3) If the distribution of marbles is non-random, then it is not any subset of individual bags that is the "problem." The whole distribution is non-random, period.

4) My first instinct is that the expected distribution should be calculable (even if by brute force methods such as Monte Carlo simulation). From this and the data construct some normalized summed deviation. The larger the deviation, the more likely the distribution is non-random.

5) Given the numbers you quoted, the statistics are likely too low to be meaningful.


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[ZutAlors!]

Thanks, Boro. I was thinking that the numbers for a lot of these groups were too small -- ten seems far too small to draw conclusions from, although forty samples might be reasonable. That was why it occured to me to look at the distribution of all three hundred or so into groups. If that distribution did indeed look random, then I could forget about any further analysis.

If I were to do a Monte Carlo simulation, how would I calculate an overall standard deviation? It occurs to me that the groups with greater numbers of marbles should be weighted more heavily. If I distributed marbles, calculated B/W percentages in each bag, calculated the deviations from the overall B/W percentage, then weighted the deviations by the number of marbles in the bag, would that be a good start?

Thanks.