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

Here researcher is unaware of the probability of success for men and women which is given ,so he'll go by the null approach and assume that there is no difference between probability of success for men and women and hence both have equal probability, which can be 0.5 for both

So expected value can be found out as follows

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

And true value can be found out by using the given probabilities.

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

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