Suppose you have a large bag of 400 marbles, each marble is one of 10 colors. Suppose your friend selectively removes 30 marbles and places them in a box, which you may look through.
you know: the total number of marbles in each bag, the total number of marbles of each color in each bag, the total number of colors in each bag.
If you want to rank the colors by importance to your friend, what formula would you use? Assuming he selected marbles he preferred. It seems that affinity towards a color would be a function of both the probability of its selection and the number of times it is selected, for example, O(O-E).
Would you have to change E with each selected marble? For example, if the larger bag contains 50 red marbles, then E_red of the first marble would be 50/400, but would the second be 49/399?
What if your friend instead made 10 rows of marbles, and you wanted to rank his preference for having particular colors in particular positions relative to the row overall, how would you do so?