The achievement gap in reading competence: the effect of measurement non-invariance across school types

Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Table 4 Effect sizes (Cohen’s d) for school type covariates per estimated model

Type of School	Model 1b	Model 2b	Model 3b	Model 4b
Grade 5
HS	1.26	1.23	1.22	1.21
MS	0.11	0.13	0.08	0.10
CS	− 0.31	− 0.29	− 0.13	− 0.11
AT	− 0.08	− 0.10	− 0.13	− 0.15
LS	− 0.94	− 0.95	− 1.01	− 1.02
Grade 7
HS	1.16	1.16	1.12	1.13
MS	− 0.01	− 0.01	− 0.04	− 0.04
CS	− 0.06	− 0.06	0.06	0.06
AT	− 0.06	− 0.07	− 0.08	− 0.08
LS	− 1.02	− 1.01	− 1.06	− 1.06
Grade 9
HS	1.21	1.21	1.15	1.15
MS	− 0.02	0.00	− 0.04	− 0.03
CS	− 0.01	0.00	0.15	0.16
AT	− 0.17	− 0.20	− 0.20	− 0.23
LS	− 0.98	− 0.97	− 1.03	− 1.02

School level covariates: HS high schools, MS middle secondary schools, CS comprehensive schools, AT schools offering all school tracks except high school, LS lower secondary schools. Cohen’s d effect size: calculated as the difference per value from the average of all other school type effects and divided by the square root of the factor variance per respective latent factor. The average of all school type effects can differ slightly from zero due to effect coding and model re-estimation using the reference group to obtain a reference group estimate. In Models 1b and 3b, no school-type specific item discrimination or item difficulty estimates were accounted for. In Model 2b and 4b, school-type specific item discrimination and item difficulty estimates were taken into account for items exhibiting DIF. The multilevel data structure was taken into account for estimation of Models 1b and 2b but not for Models 3b and 4b