Question

1. Suppose that, in a given population, the probability of success for a given drug is 0.7 for men and 0.5 for women (the researchers cannot be aware of this). In a study to determine the probability of success, 7 men and 14 women were assigned to receive the drug (no blocking was performed; all were lumped in to the treatment group). What is the bias in this study for each biological sex? (This may be a positive or a negative number).

Answer 1

If there is an equal effect of drug on men and women then the probability of success for a given drug will be 0.5 for men and 0.5 for women. So among 7 men and 14 women, there should be 7*0.5= 3.5 men and 14*0.5 = 7 women who has positve effect of drug.

Now since there is probability of success for a given drug is 0.7 for men and 0.5 for women, then we expect 7*0.7= 4.9 men and 14*0.5= 7 women who has positve effect of drug.

So the bais for men = 4.9 - 3.5=1.4 and bais for women = 7 - 7 =0.