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In mathematics, the QR results showed a steady increase of the gender gap from the lower to the upper tail of the conditional distribution of performances.
It is important to note that all the estimated LS and QR relationships between predictors and the conditional distribution of performances should not be interpreted as causal relations.
QR findings for the second grade indicate that the effect of parent education is significant and positive along the entire conditional distribution of performances in mathematics and reading.
Subsequently, in middle school, the gender gap becomes less pronounced throughout the distribution of performances and the largest reduction can be assessed at the tails of the conditional distribution.
To better understand the determinants and mechanism of inequality it would be important to assess if and how educational predictors relate differently to the conditional distribution of performances, that is, according to the students' proficiency level.
Besides, the information about whether the estimated QR effects of predictors are significantly different across the conditional distribution of performances can be gathered from the equivalence test results reported in the last column.
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