Effect size in regression

#1
Hi everyone,
I am reading an article at which authors used an effect size that it's totally new to me and I do not know how to interpret it. I would appreciate if anyone could explain its meaning or provide any reference about its interpretation. Below, I paste some sentences from the original article at which the authors' explain how data were analyzed, highlighting in bold the effect size description.

We used linear regression model (...) Analytically, we regressed one of the outcomes on the indicator for opposite sex (β) and the set of control variables (λ). C In the main regressions, the estimate on opposite sex (β) compared the mean outcomes between females exposed to a male and females exposed to a female. Figs 1 and 2 plot effect sizes, that is, the point estimate divided by mean of an outcome in the estimation sample

My questions are: 1) why beta (which I assume is the standardized regression weight) was divided by the mean of the estimation sample?; 2) Would not have been better just to use the b (unstandardized) weights as a measure of effect size (or to divide b by the SD of the sample to have an approximation to Cohen's d)?

Thanks in advance for any answer
 

hlsmith

Not a robit
#2
I could not tell from that snippet, but it does seem as though they are trying to get at a standardized coefficient, which seem popular in the social sciences since you can try to rank the coefficients by it. Not well versed in the methods.
 
#3
Hi hlsmith,
Thanks for your answer.
Unfortunately, the methods section is very short and table/ figure legends do not provide further details. Let's see if anyone else has seen this procedure before and can provide further details. In any case, your answer is very much appreciated
 

noetsi

Fortran must die
#6
I think they are trying to standardize the slopes as well. Generally this is doubtful with dummy variables like gender which can take on only two levels.
 
#7
Hi Noetsi,
thanks for your reply.
I have a doubt on your (and Hlsmith) comment: You both coincide when suggesting that the authors of this report might be trying to standardize the slope coefficient. However: 1) if that would be the goal, would it not be achieved when dividing by the standard deviation of the Y variable (instead of dividing by the mean of Y)? ; 2) since the slope coefficient is provided as a beta (in greek letter) I assumed it is an already standardized coefficient, so why to "re-standardize" it?

On the other hand, I agree with your comment about the difficulties to interpret standardized coefficients for a dummy variable. This prompts me to think that perhaps (despite reporting as beta) the provided coefficient might be the unstandardized regression coefficient. However, I do not yet understand why to divide it by the Y mean (instead of by its SD)...
 

noetsi

Fortran must die
#8
As for 1 there are likely many ways to standardize. Just because some feel dividing by the standard deviation is the best way, does not mean the authors agree. As for 2 I would be cautious in assuming anything based on nomenclature. Again the authors may depart from common procedures (and this is very common with nomenclature).

I think the only way to answer the question is to contact the authors (normally a contact is provided in the journal and sometimes which author to contact).