# Impact of counterfactual hiring decisions

As the hiring manager for my widget company, in order to decide whether to progress an applicant to an interview I administer an IQ test. If the applicant's score is above 110 on the test I let them through to an interview with the hiring manager, if not they are immediately rejected.

My company has been doing this for many years, so there is plenty of data on how many candidates passed and failed at the subsequent interview.

Now, I want to increase the number of successful applicants, so I'd like to know what would happen if I also let through all applicants who either achieve 110 on my IQ test or those who stated that they have a Bachelor's degree in their application. For the sake of this question, suppose I have records of previous applicants and I know whether or not they stated that they had bachelor's degrees (even though that wasn't a criterion for their admission to interview at the time).

What methodology can I employ to predict the success rate of applicants at the interview stage under the counterfactual scenario where either and IQ of >110 or a Bachelor's degree had been used (as opposed to just the IQ test, for which I have the actual data). What are the limitations / assumptions of such an approach?

The answer should allow for IQ test results and the presence of a Bachelor's degree being dependent variables.

• Since you only have 2 dummy variables (IQ>110 and Bachelor) you could just calculate conditional probabilities: $P(pass | IQ>110)$, $P(pass | Bachelor)$, $P(pass | IQ>110, Bachelor)$. A fancier thing would be logistic regression. Mar 27 at 10:18
• Well P(pass|Bachelor) is what I'm trying to find I think, but how can I calculate it given I only have P(pass|IQ > 110) and P(pass|IQ > 110, Bachelor)? Mar 27 at 11:03
• You mentioned you know if applicants had a Bachelor's or not, so you could just calculate it directly by filtering all applicants for $Bachelor = 1$ and taking the mean of $pass \in {0,1}$. Then you calculated the conditional relative frequency, which is an estimate for $P(pass|Bachelor)$. Mar 27 at 11:40