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I am currently studying the relationship between having a supervisory job and having traditional values when it comes to child care (woman staying home). I want to find the relationship with differences in gender. So woman probably have a negative correlation and men a positive one.

It is logical to add interaction terms traditional value * female and traditional value * men to find the difference in "stata"?

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If you think a priori that gender will modify the effect of traditional values on having a supervisory job, than yes, add the interaction term. The p value given for the interaction term will tell you whether there is a significant difference in the way gender modifies traditional values effect on having a supervisory position.

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