1. Consider the following 2 x 2 contingency table Group X=1 X=2 Total Success (Y=1) 712 Failure (Y=0) n21 122 Total 1.2 H.. and consider the comparison of two groups (X=1,2) with respect to the prob- ability of success of a binary outcome Y. Denote the probability of success in group 1 by p, and the probability of success in group 2 by p2. Then, the odds ratio is defined as: p _ PI/(1-pi) P(Y = 1X = 1)/P(Y = 0|X = 1) p2/(1-p2) P(Y = 1X =2)/P(Y = 0|X = 2) Use Bayes theorem to show that: P= P(X = 1|Y = 1)/Pr(X =1|Y =0) P(X = 2/Y = 1)/P(X = 2|Y =0) In other words, one can transpose the 2 x 2 table and the odds ratio remains the same