themusicgod1's Journal: Poissonian Statistics & OKCupid

Statistics has never really been my strong suit, but one of the equations we used in our astronomy labs was one out of poisson statistics, that is

P(r,u) = (e^{-u})*(u^r)/r!

and P(F) = P(r,u) * Number_Of_Stars_Surveyed,

where F is the total number of stars

or, perhaps written differently,

(defun stars (T U S) (* T (* (/ (* (expt 2.71828183 (- U)) (expt U S)) (* 1.0 (! S))) 100.0)))

with

(defun ! (int) (if (eq 0 int) 1 (* int (! (- int 1)))))

This is what you should use if you have a system of magnitudes of stars that are ordered in a poisson distribution, to determine what probability you have, given 'r' discrete categories of stars(in our case, r=5) that are each in turn less likely according to the poisson distribution, what is the probability that your data set can be picked. That is to say, what is the likelyhood that your ratio U of 'number-of-stars in category N and above vs. the number of stars' came about purely by chance? At least if I'm understanding this correctly, which I'm not sure.

According to my calculation,

(stars 85.0 (/ 7.0 85.0) 5) should be .0002%
(stars 85.0 (/ 27.0 85.0) 5) .2%
(stars 85.0 (/ 38.0 85.0) 5) .8%
(stars 85.0 (/ 53.0 85.0) 5) 4%
(stars 85.0 (/ 85.0 85.0) 5) 26%

That last one makes my head hurt. Under what condition could we be more certain that some order of stars was likely? 26% isn't very likely. In our lab my results for the Pleiades cluster was .002%, it should have been 4e-6%, but still... you can't seem to do much better than 26%, which isn't very likely at all. Yet looking at the graph in the wikipedia makes this at least *look* right...

Seems like I'm missing something here...what is the likelyhood that there are 53 "2 or greater" star women given a sample size of 85 given a poisson distribution? What about 85 1 or greater? How am I messing this up?

DATA
5 stars 7
4 stars 11 (- 38 11) 27 4 or greater
3 stars 15 (- 53 15) 38 3 or greater
2 stars 20 (- 85 32) 53 2 or greater
1 stars 32
(+ 7 11 15 20 32) total 85