A DISSERTATION Measurement and Quantitative Methods Doctor of Philosophy 20 20 LIST OF FIGURES KEY TO ABBREVIATIONS 1.1. 1.2. 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 - 16 - 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 2.7. 2.8. 2.9. 3.1. 2015 Winter Applied Academic Spring Applied Academic Table 3 . Gender and Achievement Level Frequencies of Winter 2015 Academic Math Assessment Male (%) Female (%) Row Total (%) Below Level 1 54 (0) 29 (0) 83 (0) Level 1 819 (2) 1103 (2.7) 1922 (4.7) Level 2 2113 (5.2) 2662 (6.5) 4375 (11.7) Level 3 14518 (35.5) 14802 (36.2) 29320 (71.7) Level 4 2569 (6.3) 2269 (5.6) 4838 (11.9) Column Total (%) 20073 (53) 20865 (47) 40939 (100) Table 4 . Gender and Achievement Level Frequencies of Winter 2015 Applied Math Assessment Male (%) Female (%) Row Total (%) Below Level 1 318 (2) 270 (2) 588 (4) Level 1 1124 (7) 963 (6) 2087 (13) Level 2 3087 (19) 2550 (16) 5637 (35) Level 3 3445 (21.6) 2574 (16) 6019 (38) Level 4 1021 (6.4) 642 (4) 1663 (10) Column Total (%) 8995 (56) 6999 (44) 15994 (100) Table 5 . Gender and Achievement Level Frequencies of Spring 2015 Academic Math Assessment Male (%) Female (%) Row Total (%) Below Level 1 47 (0) 35 (0) 82 (0) Level 1 856 (1.9) 939 (2.1) 1795(4) Level 2 2210 (4.9) 2663 (5.9) 4873 (10.8) Level 3 15928 (35) 16612 (37) 32540 (72) Level 4 3048 (6.7) 3065 (6.8) 6113 (13.5) Column Total (%) 22089 (48) 23314 (52) 45403 (100) Table 6 . Gender and Achievemen t Level Frequencies of Spring 2015 Applied Math Assessment Male (%) Female (%) Row Total (%) Below Level 1 447 (2.8) 261 (1.6) 588 (4.4) Level 1 1031 (6.4) 862 (5.3) 2087 (11.7) Level 2 2935 (18) 2568 (16) 5637 (34) Level 3 3605 (22) 2739 (16.9) 6019 (36.9) Level 4 1065 (6.7) 704 (4.3) 1663 (11) Column Total (%) 9083 (56) 7134 (44) 16217 (100) 3.2. 3.3. 3.3.1. 3.3.2. 3.3.3. When students at the standard level a nd insufficient level (group 3 and group 1 ) have been compared, items 1,3,12, and 19 (0.23 0.37) presented negligible DIF, items 4,13,17,20,21,22,23 indicated moderate DIF (0.50 0.93) , and items 6,15,16 had large DIF (1.82 3.61) based on signed area difference statistics. All these items were favoring students at the province standard. Unsigned area measures conclude that items 12, and 24 favor respectively higher achievers ( 0.38, 0.26), while items 1,3, and 19 have s mall or negligible DIF (0.21 0.34) favoring lower achievers. (0.21 0.48) (0.50 0.72) (0.61 0.74) 0.50). (0.21 APPENDIX Table A 1. Winter 2015 Applied Math Assessment DIF Effect Size Measures for Achievement Groups 1 and 2 (Reference = Group 1, Focal = Group 2) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A 2. Winter 2015 Applied Math Assessment DIF Effect Size Measures for Achievement Groups 1 and 3 (Reference = Group 1, Focal = Group 3) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A 3. Winter 2015 Applied Math Assessment DIF Effect Size Measures for Achievement Groups 1 and 4 (Reference = Group 1, Focal = Group 4) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r - 0.202 - 0.05 | [ - 0.55, 0.45] MC02r 0.715 0.18 | [ - 0.32, 0.68] MC03r 0.743 0.19 | [ - 0.31, 0.69] MC04r - 0.485 - 0.12 | [ - 0.62, 0.38] MC05r 1.959 0.50 | [ 0.00, 1.00] MC06r - 0.448 - 0.11 | [ - 0.62, 0.39] MC07r - 0.245 - 0.06 | [ - 0.56, 0.44] MC08r 0.329 0.08 | [ - 0.42, 0.59] MC09r 0.283 0.07 | [ - 0.43, 0.57] MC10r 1.067 0.27 | [ - 0.23, 0.77] MC11r - 0.985 - 0.25 | [ - 0.75, 0.25] MC12r - 0.189 - 0.05 | [ - 0.55, 0.45] MC13r 0.834 0.21 | [ - 0.29, 0.71] MC14r - 0.003 0.00 | [ - 0.50, 0.50] MC15r 0.938 0.24 | [ - 0.26, 0.74] MC16r 0.491 0.13 | [ - 0.38, 0.63] MC17r - 0.892 - 0.23 | [ - 0.73, 0.27] MC18r - 0.656 - 0.17 | [ - 0.67, 0.33] MC19r 0.134 0.03 | [ - 0.47, 0.54] MC20r 1.175 0.30 | [ - 0.20, 0.80] MC21r 0.514 0.13 | [ - 0.37, 0.63] MC22r 0.363 0.09 | [ - 0.41, 0.59] MC23r - 0.202 - 0.05 | [ - 0.55, 0.45] MC24r 0.669 0.17 | [ - 0.33, 0.67] Table A 4. Winter 2015 Applied Math Assessment DIF Effect Size Measures for Achievement Groups 2 and 3 (Reference = Group 2, Focal = Group 3) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A 5. Winter 2015 Applied Math Assessment DIF Effect Size Measures for Achievement Groups 2 and 4 (Reference = Group 2, Focal = Group 4) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A 6. Winter 2015 Applied Math Assessment DIF Effect Size Measures for Achievement Groups 3 and 4 (Reference = Group 3, Focal = Group 4) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A 7. Winter 2015 Applied Math Assessment DIF Effect Size Measures for Gender Groups (Reference = Males, Focal = Females) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A 8. Winter 2015 Academic Math Assessment DIF Effect Size Measures for Achievement Groups 1 and 2 (Reference = Group 1, Focal = Group = 2) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A 9. Winter 2015 Academic Math Assessment DIF Effect Size Measures for Achievement Groups 1 and 3 (Reference = Group 1, Focal = Group 3) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A1 0. Winter 2015 Academic Math Assessment DIF Effect Size Measures for Achievement Groups 1 and 4 (Reference = Group 1, Focal = Group 4) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A1 1. Winter 2015 Academic Math Assessment DIF Effect Size Measures for Achievement Groups 2 and 3 (Reference = Group 2, Focal Group 3) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A1 2. Winter 2015 Academic Math Assessment DIF Effect Size Measures for Achievement Groups 2 and 4 (Reference = Group 2, Focal = Group 4) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A1 3. Winter 2015 Academic Math Assessment DIF Effect Size Measures for Achievement Groups 3 and 4 (Reference = Group 3, Focal = Group 4) Z(SA) d | [95% CI] Z(UA) d | [95% CI] MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A1 4. Winter 2015 Academic Math Assessment DIF Effect Size Measures for Gender Groups (Reference = Males, Focal = Males) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A1 5. Spring 2015 Applied Math Assessment DIF Effect Size Measures for Achievement Groups 1 and 2 (Reference = Group 1, Focal = Group 2) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A1 6. Spring 2015 Applied Math Assessment DIF Effect Size Measures for Achievement Groups 1 and 3 (Reference = Group 1, Focal = Group 3) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A1 7. Spring 2015 Applied Math Assessment DIF Effect Size Measures for Achievement Groups 1 and 4 (Reference = Group 1, Focal = Group 4) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A1 8. Spring 2015 Applied Math Assessment DIF Effect Size Measures for Achievement Groups 2 and 3 (Reference = Group 2, Focal = Group 3) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A1 9. Spring 2015 Applied Math Assessment DIF Effect Size Measures for Achievement Groups 2 and 4 (Reference = Group 2, Focal = Group 4) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A2 0. Spring 2015 Applied Math Assessment DIF Effect Size Measures for Achievement Groups 3 and 4 (Reference = Group 3, Focal = Group 4) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A2 1. Spring 2015 Applied Math Assessment DIF Effect Size Measures for Gender Groups (Reference = Males, Focal = Females) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r MC20r MC21r MC22r MC23r MC24r Table A2 2. Spring 2015 A cademic Math Assessment DIF Effect Size Measures for Achievement Groups 1 and 2 (Reference = Group 1, Focal = Group 2) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r Table A2 3. Spring 2015 A cademic Math Assessment DIF Effect Size Measures for Achievement Groups 1 and 3 (Reference = Group 1, Focal = Group 3) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r Table A2 4. Spring 2015 A cademic Math Assessment DIF Effect Size Measures for Achievement Groups 1 and 4 (Reference = Group 1, Focal = Group 4) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r Table A2 5. Spring 2015 A cademic Math Assessment DIF Effect Size Measures for Achievement Groups 2 and 3 (Reference = Group 2, Focal = Group 3) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r - 0.580 - 0.08 | [ - 0.37, 0.20] 0.500 0.07 | [ - 0.21, 0.35] MC02r - 0.305 - 0.04 | [ - 0.33, 0.24] 0.303 0.04 | [ - 0.24, 0.33] MC03r - 20.069 - 2.89 | [ - 3.17, - 2.60] - 14.886 - 2.14 | [ - 2.42, - 1.86] MC04r - 2.146 - 0.31 | [ - 0.59, - 0.03] 1.472 0.21 | [ - 0.07, 0.49] MC05r 1.375 0.20 | [ - 0.08, 0.48] - 1.648 - 0.24 | [ - 0.52, 0.04] MC06r - 1.825 - 0.26 | [ - 0.54, 0.02] 1.532 0.22 | [ - 0.06, 0.50] MC07r 2.246 0.32 | [ 0.04, 0.60] - 3.925 - 0.56 | [ - 0.85, - 0.28] MC08r - 3.753 - 0.54 | [ - 0.82, - 0.26] - 5.573 - 0.80 | [ - 1.08, - 0.52] MC09r 0.038 0.01 | [ - 0.28, 0.29] - 0.038 - 0.01 | [ - 0.29, 0.28] MC10r - 4.214 - 0.61 | [ - 0.89, - 0.32] 1.897 0.27 | [ - 0.01, 0.55] MC11r - 0.419 - 0.06 | [ - 0.34, 0.22] 0.409 0.06 | [ - 0.22, 0.34] MC12r - 2.167 - 0.31 | [ - 0.59, - 0.03] 2.089 0.30 | [ 0.02, 0.58] MC13r - 3.336 - 0.48 | [ - 0.76, - 0.20] 2.932 0.42 | [ 0.14, 0.70] MC14r - 2.371 - 0.34 | [ - 0.62, - 0.06] - 7.467 - 1.07 | [ - 1.36, - 0.79] MC15r - 1.579 - 0.23 | [ - 0.51, 0.05] 1.515 0.22 | [ - 0.06, 0.50] MC16r 0.717 0.10 | [ - 0.18, 0.38] - 5.706 - 0.82 | [ - 1.10, - 0.54] MC17r 0.482 0.07 | [ - 0.21, 0.35] - 0.526 - 0.08 | [ - 0.36, 0.21] MC18r - 1.712 - 0.25 | [ - 0.53, 0.04] - 1.130 - 0.16 | [ - 0.44, 0.12] MC19r - 2.262 - 0.33 | [ - 0.61, - 0.04] - 2.018 - 0.29 | [ - 0.57, - 0.01] MC20r 1.946 0.28 | [ 0.00, 0.56] - 6.134 - 0.88 | [ - 1.16, - 0.60] MC21r 0.796 0.11 | [ - 0.17, 0.40] - 7.549 - 1.09 | [ - 1.37, - 0.80] MC22r 3.364 0.48 | [ 0.20, 0.77] - 8.682 - 1.25 | [ - 1.53, - 0.97] MC23r - 9.426 - 1.36 | [ - 1.64, - 1.07] 4.196 0.60 | [ 0.32, 0.89] MC24r - 22.178 - 3.19 | [ - 3.47, - 2.91] 10.815 1.56 | [ 1.27, 1.84] Table A2 6. Spring 2015 A cademic Math Assessment DIF Effect Size Measures for Achievement Groups 2 and 4 (Reference = Group 2, Focal = Group 4) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r Table A2 7. Spring 2015 A cademic Math Assessment DIF Effect Size Measures for Achievement Groups 3 and 4 (Reference = Group 3, Focal = Group 4) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r Table A2 8. Spring 2015 A cademic Math Assessment DIF Effect Size Measures for Gender Groups (Reference = Males, Focal = Females) Item Z(SA) d (95% CI) Z (UA) d (95% CI) MC01r MC02r MC03r MC04r MC05r MC06r MC07r MC08r MC09r MC10r MC11r MC12r MC13r MC14r MC15r MC16r MC17r MC18r MC19r Gierl, M. J., Tan, X., Wang, C. ( 2005). Identifying Content and Cognitive Dimensions on the SAT. The College Board: New York. Overcoming inequality: why governance matters; EFA global monitoring report, 2009 . Paris: UNESCO. Retrieved from https://unesdoc.unesco.org/ark:/48223/pf0000177683