Question

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

The formula for bias is

Bias= expected value - true value

Since researchers are unaware of the probability of success for men and women which is given here as 0.7 and 0.5 , so they will go with the null approach which is there is no difference between the probability of success for men and women and hence both have equal probability which can be 0.5 for both.

So the expected value that researchers must be expecting as per the null approach will be

Expected value= 7*0.5+14*0.5=10.5

And the true value can be obtained by using the given probabilities

True value=7*0.7+14*0.5 = 11.9

Hence Bias= 10.5-11.9 = -1. 4

Bias for men = 7*0.5-7*0.7= -1. 4

Bias for women = 14*0.5-14*0.5=0