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Table 5 LS and QR estimates of the effects of covariate on mathematics achievement in primary school—fifth grade

From: Beyond the mean estimate: a quantile regression analysis of inequalities in educational outcomes using INVALSI survey data

  LS Mathematics—L5
QR
\(\theta = 0.1\) \(\theta = 0.25\) \(\theta = 0.5\) \(\theta = 0.75\) \(\theta = 0.9\) p value equiv.test
(Intercept) 206.60 154.20 177.62 207.41 235.34 259.17  
  (1.07) (2.05) (1.50) (1.56) (1.62) (2.14)  
Female −7.74 −2.07 −5.91 −8.85 −10.94 −10.77 < 0.01
  (0.55) (1.01) (0.74) (0.72) (0.74) (1.07)  
Early enrolment −1.45 5.05 5.33 −4.13 −7.70 −5.69 < 0.01
  (2.61) (3.63) (2.26) (2.25) (2.88) (5.44)  
Late enrolment −13.93 −19.97 −15.44 −12.13 −9.07 −9.96 < 0.05
  (1.93) (3.62) (2.62) (3.30) (3.13) (3.24)  
Kindergarten:yes 0.77 3.18 3.07 0.24 −1.78 −2.30 0.06
  (0.99) (1.94) (1.36) (1.47) (1.58) (2.00)  
Non-native −8.24 −8.57 −7.44 −9.04 −8.21 −7.05 0.55
  (1.01) (1.66) (1.44) (1.35) (1.75) (1.82)  
Centre-Italy −1.55 −0.79 −1.39 −1.36 −1.43 −2.75 0.80
  (0.75) (1.27) (0.89) (1.01) (1.08) (1.52)  
South-Italy −7.73 −9.71 −8.36 −8.59 −7.39 −5.59 < 0.05
  (0.75) (1.19) (0.83) (0.72) (0.85) (1.18)  
ESCS 10.15 9.66 10.70 10.84 10.24 9.46 < 0.01
  (0.30) (0.56) (0.38) (0.43) (0.48) (0.57)  
  1. In Italic estimates with p < 0.05.Standard errors in parenthesis computed with non-clustered bootstrap estimation. In the last column the p value of the equivalence test (equiv.test) results