[Multinomial Distribution] Help with applying Multinomial to a biological problem

Hello all, I need help with a stats question I'm trying to solve for a biological question.


Say you have a town and each street on it will have a different number of bins. In each bin you will find a different number of baseballs, most will have 0 but some will have a baseball or more. Whats interesting is if one particular bin on one street has many baseballs relative to the other bins on that street. How can you statistically compare different streets to say that someone is choosing one street over another to non-randomly add baseballs to particular bins of particular streets. I have tried using multinomial.... say n= (total number of baseballs on a street) , X= number of baseballs in any particular bin on a street, L= number of bins on a street, Pi = probability of randomly getting a baseball in a bin or 1/L. The formula would then be

[(N)! /(Xsub1! ..... Xsubk!)] * [(1/L)^(Xsub1) .... (1/L)^(Xsubk)]


Now this seems to work well, except as your L increases your p-value will also decrease which doesn't make sense. For example a street with 10 bins and 20 baseballs in just one of those 10 bins should be more significant than a street with 1000 bins and 10 baseballs all in different bins out of the 10000 (so 10 bins with 1 baseball each out of 10000 total). How do I normalize for L?

Any help would be greatly appreciated I know this explanation sucks but its the least abstract one I could think of!


Ambassador to the humans
One of the issues is that you're only looking at the probability of that specific event occurring. When calculating p-values we typically look at the probability that an event as or more extreme than the one we observed occurs.

But really it just sounds like you want a chi-square goodness of fit test.