That's the sort of question we address with this model, as shown in the example of the sport preferences of a sample of boys and girls. The word contingency in the name of the model refers, I guess, to the relationship between the two variables.
Table speaks for itself.
It's pretty obvious that there's a strong relationship in the example. Whether the relationship is significant would depend on the number of boys and girls. We don't normally think about parameters for this model, but they would be the probabilities of opting for each sport, for each sex. Those outcome measures that we have already met, the relative risk and odds ratio , make sense only for 2 x 2 tables or for comparing 2 x 2 cells in a bigger table. The funny thing is, there is no tradition for doing such pairwise tests in a contingency table, or for controlling the type I error , not that I know of anyway.