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Table 6 Variance of the discrimination parameter \(c_{gi}\) across countries (given item i), \(\chi ^2\)-value and asymmetric confidence interval (\(CI_l\) lower bound, \(CI_u\) upper bound; items ordered in descending order of \(s^{2}_{gi|i}\))

From: Assuming measurement invariance of background indicators in international comparative educational achievement studies: a challenge for the interpretation of achievement differences

Item \(s^{2}_{gi|i}\) \(\chi ^{2}\) \(CI_{l}\) \(CI_{u}\)  
ASDHED 1.75 11,800.07 1.09 3.24  
ASDG05 0.63 4285.24 0.40 1.18  
ASBH15 0.58 3896.91 0.36 1.07  
ASBG04 0.44 2966.86 0.27 0.81  
ASDHOC 0.22 1498.92 0.14 0.41 \(\blacktriangle\)
  1. \(\blacktriangle\), item variance is statistically different from ASDHED; ASBG04, number of books in the home (student-reported); ASDG05, number of home study supports (student-reported); ASBH15, number of children’s books in the home (parent-reported); ASDHED, highest level of education of either parent (parent-reported); ASDHOC, highest level of occupation of either parent (parent-reported)