I ran the following model, with exam scores in science as my outcome variable, and parental income group divided into 5 groups and a binary gender variable with the results below:

regress test_score i.quantiles_parent_income i.gender_dummy

 Source |       SS           df       MS      Number of obs   =     2,268
-------------+----------------------------------   F(6, 2261)      =    318.19
       Model |  76430.8521         6  12738.4753   Prob > F        =    0.0000
    Residual |    90516.86     2,261  40.0339938   R-squared       =    0.4578
-------------+----------------------------------   Adj R-squared   =    0.4564
       Total |  166947.712     2,267  73.6425726   Root MSE        =    6.3272

                   test_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
                        2  |  -.9545663   .5365921    -1.78   0.075    -2.006831    .0976982
                        3  |   .0265901   .5395947     0.05   0.961    -1.031563    1.084743
                        4  |   5.121439   .5328825     9.61   0.000      4.07645    6.166429
                        5  |   7.491982   .5170866    14.49   0.000     6.477968    8.505996
              gender_dummy |
                     male  |  -8.225431   .2901021   -28.35   0.000    -8.794325   -7.656537

I then ran an F-test between students whose parents fall in the 2nd quantile, relative to the top 20th percentile:

test i2.quantiles_parent_income== i5.quantiles_parent_income
       F(  1,  2261) =  415.54
            Prob > F =    0.0000

Can I say that a student living in the top 20th percentile scores on average, 7.5 points higher than a student in 2nd quantile, and the result is significant at the 99 significance level. Is it possible to compute how being a male in the top 20th percentile impacts one's test scores in science compared to a female student in the same parental income group?


1 Answer 1


You can say that in your data, on average, belonging to the fifth quantile of parental income instead of the second leads to an increase in the score equal to: 7.49 - (-0.95) = 8.44. And this difference was statistically significant at an alpha level of 0.01.

Regarding your second question: given your model, the difference in score between two people of the opposite gender who are in the same quantile of parental income is given exclusively by the estimate related to gender (males score 8.23 ​​lower than females). Note that this statement holds regardless of what quantile the two people are in (whether they are both in the fifth or both in the second, the male will have, on average, an 8.23 ​​lower score than the female). Now, this estimate was obtained as an average considering all quantiles.

If you want to focus precisely on a quantile (say the fifth) and to study the effect of gender on score specifically for this group of people, I recommend that you perform a stratified analysis: consider only the data of the people who belong to the fifth quantile and repeat the analysis using gender as the only covariate. This will give you the gender specific effect in the fifth quintile subjects.

A possible alternative is to consider the complete dataset, but add the interaction term between gender and quantile of parental income to the covariates. This second option is equally valid, but if you've never used interactions before I recommend that you study the topic first (it's nothing complicated but the interpretation of the estimates becomes slightly more challenging).


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