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.

null assumption(hypothesis) they would have assumed that there is no difference between probability of success for men and women will be 0.5 for both men and women

So the expected value can be found out as

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

and the true value can be found out by using the true probability of success given

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

Bias=expected value - True value= 10.5 - 11.9 = -1. 4

For male it is, bias= 7*0.5 - 7*0.7 = -1. 4

For female it is, bias = 14*0.5 - 14*0.5=0

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