Hi all, I am trying to conduct a field experiment (a correspondence study) and have a question about which method I should use.

So to give you some background, the experiment is on discrimination and aims to measure the effect of the variables of race, gender, and parental status on the probability of receiving a callback for a job interview. In addition, the applications were sent to jobs of six different types, from low education jobs to high education jobs. Based on the literature, I have formulated three hypotheses:

H1a Employers systematically disfavor applicants who are black over those who are white;
H1b The effect hypothesized by H1a will be stronger for jobs requiring higher levels of education.

H2a Employers systematically disfavor female applicants among those applicants who are black;
H2b The effect hypothesized by H2a will be stronger for jobs requiring higher levels of education.

H3a Employers systematically disfavor parents among applicants who are black and female;
H3b This effect will be stronger for jobs requiring higher levels of education.

The way that I have now tested these hypotheses is by running regressions on samples of the data. In particular, I have run the following regressions:

H1
regress callback black
regress callback black if occupation==1
regress callback black if occupation==2
regress callback black if occupation==3
regress callback black if occupation==4
regress callback black if occupation==5
regress callback black if occupation==6

* H2
regress callback woman if black==1
regress callback woman if black==1 & occupation==1
regress callback woman if black==1 & occupation==2
regress callback woman if black==1 & occupation==3
regress callback woman if black==1 & occupation==4
regress callback woman if black==1 & occupation==5
regress callback woman if black==1 & occupation==6

* H3
regress callback parent if black==1 & woman==1
regress callback parent if black==1 & woman==1 & occupation==1
regress callback parent if black==1 & woman==1 & occupation==2
regress callback parent if black==1 & woman==1 & occupation==3
regress callback parent if black==1 & woman==1 & occupation==4
regress callback parent if black==1 & woman==1 & occupation==5
regress callback parent if black==1 & woman==1 & occupation==6

(FYI: occupation==6 = high education job, occupation==1 = low education job.)

Now here is my question. It has been suggested to me that I may need to test my hypotheses by looking at interaction effects (between, respectively, black and occupation, gender and occupation, and parent and occupation). But I'm not quite sure on why that would be appropriate here, and insofar as it is, which interaction effects I would need to look at. For instance, taking H2, wouldn't I need to look at the interaction effects of both woman-black and woman-occupation? I was hoping to get some feedback from people on this forum

Thanks a lot for your time!