Changing a discrete variable into a dummy and loosing significance

[Luisa Fried]

Dear all,

I am writing an essay using an unbalanced panel dataset. Right now I am using a Linear Probability Model with time and company fixed effects.
My research question is if the number of women in a department increases the probability of the head of the department to be female as well.

I'm using the discrete variable for the number of women in the department as the main dependent variable. I ran the regression in Stata with the xtreg command the coefficient of my main x-variable was significant on the 5 % level and positive.

Now I wanted to transform my discrete variable into a dummy variable which is equal to 1 if four or more women work in the department.
When running the new regression with the same control variables as before, the coefficient of the dummy variable becomes insignificant. It is just above 0.

How can this be since the discrete variable was statistically significant? How can a change from 0 to 1 woman for example have an impact on the probability of Y=1 but not the change of 0 to 4 women?

I really appreciate your help. Thank you.

[Mike Lacy]

Any change in the coding of a variable will change the sampling distribution of the associated coefficient. In your case, you have thrown away a lot of information (using a bad idea) by converting "number of women" into "Is it 4 or less?". (I'm presuming that by saying "using the discrete variable" that you mean you are entering it as a numeric but discrete variable." I would further add that your "is it significant or not" approach to data analysis is 1) does not fit with contemporary thibking, in which significance testing, particularly as an automatic decision mechanism, is not well-regarded; and 2) not very meaningful once you begin fishing around for different cutpoints for a variable.

[Carlo Lazzaro]

Luisa:
in addition to Mike's helpful reply, I think that a reverse causality issue may affect your results: wouldn't it be possible that a female boss increases the probability of having (more) women working in a given department?