This main function estimates true subscores using different methods based on original CTT scores.
CTTsub.RdThis function estimates true subscores using methods introduced in studies of Haberman (2008) <doi:10.3102/1076998607302636> and Wainer et al. (2001) <doi:10.4324/9781410604729>. Hypothesis tests (i.e., Olkin' Z,Williams's t, and Hedges-Olkin's Z) are used to determine whether a subscore or an augmented subscore has added value. Codes for the hypothesis tests are from Sinharay (2019) <doi: 10.3102/1076998618788862>.
Arguments
- test.data
A list that contains item responses of all subtests and the entire test, which can be obtained using function 'data.prep'.
- method
Subscore estimation methods. method="Haberman" (by default) represents the three methods proposed by Haberman (2008) <doi:10.3102/1076998607302636>. method="Wainer" represents Wainer's augmented method.
Value
- summary
Summary of estimated subscores (e.g., mean, sd).
- PRMSE
(a) PRMSE values of estimated subscores (for Haberman's methods only).(b) Decisions on whether subscores have added value - added.value.s (or added.value.sx) = 1 means subscore.s (or subscore.sx) has added value, and added.value.s (or added.value.sx) = 0 vice versa.
- PRMSE.test
All information in PRMSE plus results of hypopthesis testing based on Sinharay (2019) <doi:10.3102/1076998618788862>.
- subscore.original
Original subscores and total score.
- estimated.subscores
Subscores computed using selected method. Three sets of subscores will be returned if method = "Haberman".
References
Haberman, S. J. (2008). "When can subscores have value?." Journal of Educational and Behavioral Statistics, 33(2), 204-229. doi:10.3102/1076998607302636.
Sinharay, S. (2019). "Added Value of Subscores and Hypothesis Testing." Journal of Educational and Behavioral Statistics, 44(1), 25-44. doi:10.3102/1076998618788862.
Wainer, H., Vevea, J., Camacho, F., Reeve, R., Rosa, K., Nelson, L., Swygert, K., & Thissen, D. (2001). "Augmented scores - "Borrowing strength" to compute scores based on small numbers of items." In Thissen, D. & Wainer, H. (Eds.), Test scoring (pp.343 - 387). Mahwah, NJ: Lawrence Erlbaum Associates, Inc. doi:10.4324/9781410604729.
Examples
# Transferring original scored data to a list format
# that can be used in other functions.
test.data<-data.prep(scored.data,c(3,15,15,20),
c("Algebra","Geometry","Measurement", "Math"))
#----------------------------------------------
# Estimating subscores using Haberman's methods
CTTsub(test.data,method="Haberman") # Estimating subscores using Haberman's methods
#> $summary
#> Orig.mean Orig.sd subscore.s.mean subscore.s.sd subscore.x.mean
#> Algebra 9.773333 3.662153 9.773333 2.991654 9.773333
#> Geometry 9.100000 3.626432 9.100000 2.896492 9.100000
#> Measurement 13.060000 4.539506 13.060000 3.788720 13.060000
#> subscore.x.sd subscore.sx.mean subscore.sx.sd
#> Algebra 3.205978 9.773333 3.206067
#> Geometry 3.132737 9.100000 3.133019
#> Measurement 4.009099 13.060000 4.009773
#>
#> $Correlation
#> Algebra Geometry Measurement Math
#> Algebra 1.0000000 0.8143313 0.8336757 0.9357667
#> Geometry 0.8143313 1.0000000 0.8198970 0.9295419
#> Measurement 0.8336757 0.8198970 1.0000000 0.9507132
#> Math 0.9357667 0.9295419 0.9507132 1.0000000
#>
#> $Disattenuated.correlation
#> Algebra Geometry Measurement
#> Algebra 0.8169114 1.0081315 1.0096427
#> Geometry 0.8143313 0.7987169 1.0042016
#> Measurement 0.8336757 0.8198970 0.8346106
#>
#> $PRMSE
#> Alpha PRMSE.s PRMSE.x PRMSE.sx added.value.s
#> Algebra 0.8169114 0.8169114 0.9381521 0.9382038 0
#> Geometry 0.7987169 0.7987169 0.9343207 0.9344893 0
#> Measurement 0.8346106 0.8346106 0.9345284 0.9348423 0
#> Math 0.9311719 NA NA NA NA
#> added.value.sx
#> Algebra 0
#> Geometry 0
#> Measurement 0
#> Math NA
#>
#> $PRMSE.test
#> Alpha PRMSE.s PRMSE.x PRMSE.sx added.value.s
#> Algebra 0.8169114 0.8169114 0.9381521 0.9382038 0
#> Geometry 0.7987169 0.7987169 0.9343207 0.9344893 0
#> Measurement 0.8346106 0.8346106 0.9345284 0.9348423 0
#> Math 0.9311719 NA NA NA NA
#> added.value.sx Olkin.Z Williams.t Hedges.Olkin.Z
#> Algebra 0 -3.558905 -4.089686 0.08235317
#> Geometry 0 -3.624178 -4.170899 0.14110275
#> Measurement 0 -3.484871 -3.994921 0.21136557
#> Math NA NA NA NA
#>
#> $subscore.original
#> Algebra Geometry Measurement Math
#> [1,] 15 15 20 50
#> [2,] 11 10 14 35
#> [3,] 13 13 20 46
#> [4,] 10 11 18 39
#> [5,] 9 11 15 35
#> [6,] 10 12 17 39
#> [7,] 10 11 18 39
#> [8,] 10 10 13 33
#> [9,] 13 11 17 41
#> [10,] 14 11 19 44
#> [11,] 12 12 16 40
#> [12,] 10 10 11 31
#> [13,] 11 12 15 38
#> [14,] 11 10 12 33
#> [15,] 12 13 13 38
#> [16,] 9 9 12 30
#> [17,] 9 5 10 24
#> [18,] 10 9 15 34
#> [19,] 10 8 13 31
#> [20,] 11 13 16 40
#> [21,] 13 11 13 37
#> [22,] 14 15 19 48
#> [23,] 14 15 19 48
#> [24,] 11 13 17 41
#> [25,] 12 11 17 40
#> [26,] 11 12 15 38
#> [27,] 13 12 18 43
#> [28,] 14 11 18 43
#> [29,] 15 13 17 45
#> [30,] 15 13 18 46
#> [31,] 14 11 17 42
#> [32,] 12 13 16 41
#> [33,] 12 13 19 44
#> [34,] 8 5 13 26
#> [35,] 13 13 18 44
#> [36,] 11 13 14 38
#> [37,] 14 14 19 47
#> [38,] 8 5 13 26
#> [39,] 14 13 20 47
#> [40,] 12 10 12 34
#> [41,] 14 11 18 43
#> [42,] 11 11 17 39
#> [43,] 15 14 18 47
#> [44,] 15 13 17 45
#> [45,] 14 10 17 41
#> [46,] 13 13 18 44
#> [47,] 12 10 19 41
#> [48,] 11 13 18 42
#> [49,] 12 8 14 34
#> [50,] 10 13 17 40
#> [51,] 13 14 16 43
#> [52,] 14 12 16 42
#> [53,] 15 13 19 47
#> [54,] 13 13 16 42
#> [55,] 12 13 16 41
#> [56,] 14 12 15 41
#> [57,] 15 8 18 41
#> [58,] 14 14 20 48
#> [59,] 13 13 17 43
#> [60,] 15 13 19 47
#> [61,] 14 13 19 46
#> [62,] 11 10 14 35
#> [63,] 11 5 11 27
#> [64,] 8 8 12 28
#> [65,] 2 2 4 8
#> [66,] 7 6 5 18
#> [67,] 10 7 8 25
#> [68,] 15 15 18 48
#> [69,] 6 7 10 23
#> [70,] 13 11 15 39
#> [71,] 7 2 7 16
#> [72,] 8 5 8 21
#> [73,] 12 10 15 37
#> [74,] 9 7 11 27
#> [75,] 8 9 16 33
#> [76,] 8 2 8 18
#> [77,] 10 9 12 31
#> [78,] 5 7 10 22
#> [79,] 5 4 4 13
#> [80,] 12 11 18 41
#> [81,] 4 7 11 22
#> [82,] 13 12 12 37
#> [83,] 8 5 8 21
#> [84,] 7 9 15 31
#> [85,] 7 8 10 25
#> [86,] 1 2 6 9
#> [87,] 8 7 10 25
#> [88,] 3 2 9 14
#> [89,] 7 10 14 31
#> [90,] 5 8 6 19
#> [91,] 2 4 2 8
#> [92,] 3 4 9 16
#> [93,] 6 4 5 15
#> [94,] 5 5 8 18
#> [95,] 9 10 8 27
#> [96,] 13 11 17 41
#> [97,] 7 1 5 13
#> [98,] 2 3 6 11
#> [99,] 7 8 11 26
#> [100,] 10 10 14 34
#> [101,] 10 9 13 32
#> [102,] 4 2 8 14
#> [103,] 5 1 9 15
#> [104,] 10 10 9 29
#> [105,] 14 13 17 44
#> [106,] 8 8 10 26
#> [107,] 10 11 16 37
#> [108,] 6 3 9 18
#> [109,] 9 9 13 31
#> [110,] 13 12 17 42
#> [111,] 9 6 16 31
#> [112,] 7 4 11 22
#> [113,] 12 11 13 36
#> [114,] 13 11 14 38
#> [115,] 13 10 13 36
#> [116,] 2 5 7 14
#> [117,] 5 4 8 17
#> [118,] 9 5 11 25
#> [119,] 12 12 14 38
#> [120,] 3 4 4 11
#> [121,] 6 5 14 25
#> [122,] 3 4 4 11
#> [123,] 7 8 7 22
#> [124,] 5 4 6 15
#> [125,] 10 7 8 25
#> [126,] 14 10 18 42
#> [127,] 14 12 19 45
#> [128,] 10 5 8 23
#> [129,] 13 12 15 40
#> [130,] 14 11 20 45
#> [131,] 8 11 16 35
#> [132,] 4 2 7 13
#> [133,] 12 11 17 40
#> [134,] 9 9 14 32
#> [135,] 13 9 13 35
#> [136,] 7 10 14 31
#> [137,] 11 10 9 30
#> [138,] 10 10 13 33
#> [139,] 3 6 7 16
#> [140,] 5 7 5 17
#> [141,] 5 9 10 24
#> [142,] 5 5 5 15
#> [143,] 3 6 7 16
#> [144,] 6 8 5 19
#> [145,] 9 12 14 35
#> [146,] 4 4 9 17
#> [147,] 11 14 13 38
#> [148,] 5 7 11 23
#> [149,] 9 2 10 21
#> [150,] 14 12 17 43
#>
#> $subscore.s
#> Subscore.s.Algebra Subscore.s.Geometry Subscore.s.Measurement
#> [1,] 14.043057 13.812430 18.852198
#> [2,] 10.775411 9.818845 13.844534
#> [3,] 12.409234 12.214996 18.852198
#> [4,] 9.958500 10.617562 17.182977
#> [5,] 9.141589 10.617562 14.679145
#> [6,] 9.958500 11.416279 16.348366
#> [7,] 9.958500 10.617562 17.182977
#> [8,] 9.958500 9.818845 13.009923
#> [9,] 12.409234 10.617562 16.348366
#> [10,] 13.226145 10.617562 18.017587
#> [11,] 11.592323 11.416279 15.513755
#> [12,] 9.958500 9.818845 11.340702
#> [13,] 10.775411 11.416279 14.679145
#> [14,] 10.775411 9.818845 12.175313
#> [15,] 11.592323 12.214996 13.009923
#> [16,] 9.141589 9.020128 12.175313
#> [17,] 9.141589 5.825261 10.506091
#> [18,] 9.958500 9.020128 14.679145
#> [19,] 9.958500 8.221411 13.009923
#> [20,] 10.775411 12.214996 15.513755
#> [21,] 12.409234 10.617562 13.009923
#> [22,] 13.226145 13.812430 18.017587
#> [23,] 13.226145 13.812430 18.017587
#> [24,] 10.775411 12.214996 16.348366
#> [25,] 11.592323 10.617562 16.348366
#> [26,] 10.775411 11.416279 14.679145
#> [27,] 12.409234 11.416279 17.182977
#> [28,] 13.226145 10.617562 17.182977
#> [29,] 14.043057 12.214996 16.348366
#> [30,] 14.043057 12.214996 17.182977
#> [31,] 13.226145 10.617562 16.348366
#> [32,] 11.592323 12.214996 15.513755
#> [33,] 11.592323 12.214996 18.017587
#> [34,] 8.324677 5.825261 13.009923
#> [35,] 12.409234 12.214996 17.182977
#> [36,] 10.775411 12.214996 13.844534
#> [37,] 13.226145 13.013713 18.017587
#> [38,] 8.324677 5.825261 13.009923
#> [39,] 13.226145 12.214996 18.852198
#> [40,] 11.592323 9.818845 12.175313
#> [41,] 13.226145 10.617562 17.182977
#> [42,] 10.775411 10.617562 16.348366
#> [43,] 14.043057 13.013713 17.182977
#> [44,] 14.043057 12.214996 16.348366
#> [45,] 13.226145 9.818845 16.348366
#> [46,] 12.409234 12.214996 17.182977
#> [47,] 11.592323 9.818845 18.017587
#> [48,] 10.775411 12.214996 17.182977
#> [49,] 11.592323 8.221411 13.844534
#> [50,] 9.958500 12.214996 16.348366
#> [51,] 12.409234 13.013713 15.513755
#> [52,] 13.226145 11.416279 15.513755
#> [53,] 14.043057 12.214996 18.017587
#> [54,] 12.409234 12.214996 15.513755
#> [55,] 11.592323 12.214996 15.513755
#> [56,] 13.226145 11.416279 14.679145
#> [57,] 14.043057 8.221411 17.182977
#> [58,] 13.226145 13.013713 18.852198
#> [59,] 12.409234 12.214996 16.348366
#> [60,] 14.043057 12.214996 18.017587
#> [61,] 13.226145 12.214996 18.017587
#> [62,] 10.775411 9.818845 13.844534
#> [63,] 10.775411 5.825261 11.340702
#> [64,] 8.324677 8.221411 12.175313
#> [65,] 3.423209 3.429110 5.498428
#> [66,] 7.507766 6.623978 6.333038
#> [67,] 9.958500 7.422695 8.836870
#> [68,] 14.043057 13.812430 17.182977
#> [69,] 6.690854 7.422695 10.506091
#> [70,] 12.409234 10.617562 14.679145
#> [71,] 7.507766 3.429110 8.002260
#> [72,] 8.324677 5.825261 8.836870
#> [73,] 11.592323 9.818845 14.679145
#> [74,] 9.141589 7.422695 11.340702
#> [75,] 8.324677 9.020128 15.513755
#> [76,] 8.324677 3.429110 8.836870
#> [77,] 9.958500 9.020128 12.175313
#> [78,] 5.873943 7.422695 10.506091
#> [79,] 5.873943 5.026544 5.498428
#> [80,] 11.592323 10.617562 17.182977
#> [81,] 5.057032 7.422695 11.340702
#> [82,] 12.409234 11.416279 12.175313
#> [83,] 8.324677 5.825261 8.836870
#> [84,] 7.507766 9.020128 14.679145
#> [85,] 7.507766 8.221411 10.506091
#> [86,] 2.606297 3.429110 7.167649
#> [87,] 8.324677 7.422695 10.506091
#> [88,] 4.240120 3.429110 9.671481
#> [89,] 7.507766 9.818845 13.844534
#> [90,] 5.873943 8.221411 7.167649
#> [91,] 3.423209 5.026544 3.829206
#> [92,] 4.240120 5.026544 9.671481
#> [93,] 6.690854 5.026544 6.333038
#> [94,] 5.873943 5.825261 8.836870
#> [95,] 9.141589 9.818845 8.836870
#> [96,] 12.409234 10.617562 16.348366
#> [97,] 7.507766 2.630393 6.333038
#> [98,] 3.423209 4.227827 7.167649
#> [99,] 7.507766 8.221411 11.340702
#> [100,] 9.958500 9.818845 13.844534
#> [101,] 9.958500 9.020128 13.009923
#> [102,] 5.057032 3.429110 8.836870
#> [103,] 5.873943 2.630393 9.671481
#> [104,] 9.958500 9.818845 9.671481
#> [105,] 13.226145 12.214996 16.348366
#> [106,] 8.324677 8.221411 10.506091
#> [107,] 9.958500 10.617562 15.513755
#> [108,] 6.690854 4.227827 9.671481
#> [109,] 9.141589 9.020128 13.009923
#> [110,] 12.409234 11.416279 16.348366
#> [111,] 9.141589 6.623978 15.513755
#> [112,] 7.507766 5.026544 11.340702
#> [113,] 11.592323 10.617562 13.009923
#> [114,] 12.409234 10.617562 13.844534
#> [115,] 12.409234 9.818845 13.009923
#> [116,] 3.423209 5.825261 8.002260
#> [117,] 5.873943 5.026544 8.836870
#> [118,] 9.141589 5.825261 11.340702
#> [119,] 11.592323 11.416279 13.844534
#> [120,] 4.240120 5.026544 5.498428
#> [121,] 6.690854 5.825261 13.844534
#> [122,] 4.240120 5.026544 5.498428
#> [123,] 7.507766 8.221411 8.002260
#> [124,] 5.873943 5.026544 7.167649
#> [125,] 9.958500 7.422695 8.836870
#> [126,] 13.226145 9.818845 17.182977
#> [127,] 13.226145 11.416279 18.017587
#> [128,] 9.958500 5.825261 8.836870
#> [129,] 12.409234 11.416279 14.679145
#> [130,] 13.226145 10.617562 18.852198
#> [131,] 8.324677 10.617562 15.513755
#> [132,] 5.057032 3.429110 8.002260
#> [133,] 11.592323 10.617562 16.348366
#> [134,] 9.141589 9.020128 13.844534
#> [135,] 12.409234 9.020128 13.009923
#> [136,] 7.507766 9.818845 13.844534
#> [137,] 10.775411 9.818845 9.671481
#> [138,] 9.958500 9.818845 13.009923
#> [139,] 4.240120 6.623978 8.002260
#> [140,] 5.873943 7.422695 6.333038
#> [141,] 5.873943 9.020128 10.506091
#> [142,] 5.873943 5.825261 6.333038
#> [143,] 4.240120 6.623978 8.002260
#> [144,] 6.690854 8.221411 6.333038
#> [145,] 9.141589 11.416279 13.844534
#> [146,] 5.057032 5.026544 9.671481
#> [147,] 10.775411 13.013713 13.009923
#> [148,] 5.873943 7.422695 11.340702
#> [149,] 9.141589 3.429110 10.506091
#> [150,] 13.226145 11.416279 16.348366
#>
#> $subscore.x
#> Subscore.x.Algebra Subscore.x.Geometry Subscore.x.Measurement
#> [1,] 14.985083 14.192685 19.577330
#> [2,] 10.657984 9.964441 14.166263
#> [3,] 13.831190 13.065153 18.134379
#> [4,] 11.811877 11.091973 15.609214
#> [5,] 10.657984 9.964441 14.166263
#> [6,] 11.811877 11.091973 15.609214
#> [7,] 11.811877 11.091973 15.609214
#> [8,] 10.081038 9.400675 13.444787
#> [9,] 12.388824 11.655739 16.330690
#> [10,] 13.254243 12.501387 17.412903
#> [11,] 12.100351 11.373856 15.969952
#> [12,] 9.504092 8.836909 12.723311
#> [13,] 11.523404 10.810090 15.248476
#> [14,] 10.081038 9.400675 13.444787
#> [15,] 11.523404 10.810090 15.248476
#> [16,] 9.215618 8.555026 12.362574
#> [17,] 7.484779 6.863729 10.198147
#> [18,] 10.369511 9.682558 13.805525
#> [19,] 9.504092 8.836909 12.723311
#> [20,] 12.100351 11.373856 15.969952
#> [21,] 11.234931 10.528207 14.887738
#> [22,] 14.408136 13.628919 18.855855
#> [23,] 14.408136 13.628919 18.855855
#> [24,] 12.388824 11.655739 16.330690
#> [25,] 12.100351 11.373856 15.969952
#> [26,] 11.523404 10.810090 15.248476
#> [27,] 12.965770 12.219505 17.052165
#> [28,] 12.965770 12.219505 17.052165
#> [29,] 13.542717 12.783270 17.773641
#> [30,] 13.831190 13.065153 18.134379
#> [31,] 12.677297 11.937622 16.691428
#> [32,] 12.388824 11.655739 16.330690
#> [33,] 13.254243 12.501387 17.412903
#> [34,] 8.061726 7.427495 10.919622
#> [35,] 13.254243 12.501387 17.412903
#> [36,] 11.523404 10.810090 15.248476
#> [37,] 14.119663 13.347036 18.495117
#> [38,] 8.061726 7.427495 10.919622
#> [39,] 14.119663 13.347036 18.495117
#> [40,] 10.369511 9.682558 13.805525
#> [41,] 12.965770 12.219505 17.052165
#> [42,] 11.811877 11.091973 15.609214
#> [43,] 14.119663 13.347036 18.495117
#> [44,] 13.542717 12.783270 17.773641
#> [45,] 12.388824 11.655739 16.330690
#> [46,] 13.254243 12.501387 17.412903
#> [47,] 12.388824 11.655739 16.330690
#> [48,] 12.677297 11.937622 16.691428
#> [49,] 10.369511 9.682558 13.805525
#> [50,] 12.100351 11.373856 15.969952
#> [51,] 12.965770 12.219505 17.052165
#> [52,] 12.677297 11.937622 16.691428
#> [53,] 14.119663 13.347036 18.495117
#> [54,] 12.677297 11.937622 16.691428
#> [55,] 12.388824 11.655739 16.330690
#> [56,] 12.388824 11.655739 16.330690
#> [57,] 12.388824 11.655739 16.330690
#> [58,] 14.408136 13.628919 18.855855
#> [59,] 12.965770 12.219505 17.052165
#> [60,] 14.119663 13.347036 18.495117
#> [61,] 13.831190 13.065153 18.134379
#> [62,] 10.657984 9.964441 14.166263
#> [63,] 8.350199 7.709377 11.280360
#> [64,] 8.638672 7.991260 11.641098
#> [65,] 2.869208 2.353602 4.426341
#> [66,] 5.753940 5.172431 8.033720
#> [67,] 7.773252 7.145612 10.558884
#> [68,] 14.408136 13.628919 18.855855
#> [69,] 7.196306 6.581846 9.837409
#> [70,] 11.811877 11.091973 15.609214
#> [71,] 5.176994 4.608665 7.312244
#> [72,] 6.619360 6.018080 9.115933
#> [73,] 11.234931 10.528207 14.887738
#> [74,] 8.350199 7.709377 11.280360
#> [75,] 10.081038 9.400675 13.444787
#> [76,] 5.753940 5.172431 8.033720
#> [77,] 9.504092 8.836909 12.723311
#> [78,] 6.907833 6.299963 9.476671
#> [79,] 4.311574 3.763016 6.230030
#> [80,] 12.388824 11.655739 16.330690
#> [81,] 6.907833 6.299963 9.476671
#> [82,] 11.234931 10.528207 14.887738
#> [83,] 6.619360 6.018080 9.115933
#> [84,] 9.504092 8.836909 12.723311
#> [85,] 7.773252 7.145612 10.558884
#> [86,] 3.157681 2.635485 4.787079
#> [87,] 7.773252 7.145612 10.558884
#> [88,] 4.600047 4.044899 6.590768
#> [89,] 9.504092 8.836909 12.723311
#> [90,] 6.042413 5.454314 8.394457
#> [91,] 2.869208 2.353602 4.426341
#> [92,] 5.176994 4.608665 7.312244
#> [93,] 4.888520 4.326782 6.951506
#> [94,] 5.753940 5.172431 8.033720
#> [95,] 8.350199 7.709377 11.280360
#> [96,] 12.388824 11.655739 16.330690
#> [97,] 4.311574 3.763016 6.230030
#> [98,] 3.734628 3.199250 5.508555
#> [99,] 8.061726 7.427495 10.919622
#> [100,] 10.369511 9.682558 13.805525
#> [101,] 9.792565 9.118792 13.084049
#> [102,] 4.600047 4.044899 6.590768
#> [103,] 4.888520 4.326782 6.951506
#> [104,] 8.927145 8.273143 12.001836
#> [105,] 13.254243 12.501387 17.412903
#> [106,] 8.061726 7.427495 10.919622
#> [107,] 11.234931 10.528207 14.887738
#> [108,] 5.753940 5.172431 8.033720
#> [109,] 9.504092 8.836909 12.723311
#> [110,] 12.677297 11.937622 16.691428
#> [111,] 9.504092 8.836909 12.723311
#> [112,] 6.907833 6.299963 9.476671
#> [113,] 10.946458 10.246324 14.527001
#> [114,] 11.523404 10.810090 15.248476
#> [115,] 10.946458 10.246324 14.527001
#> [116,] 4.600047 4.044899 6.590768
#> [117,] 5.465467 4.890548 7.672982
#> [118,] 7.773252 7.145612 10.558884
#> [119,] 11.523404 10.810090 15.248476
#> [120,] 3.734628 3.199250 5.508555
#> [121,] 7.773252 7.145612 10.558884
#> [122,] 3.734628 3.199250 5.508555
#> [123,] 6.907833 6.299963 9.476671
#> [124,] 4.888520 4.326782 6.951506
#> [125,] 7.773252 7.145612 10.558884
#> [126,] 12.677297 11.937622 16.691428
#> [127,] 13.542717 12.783270 17.773641
#> [128,] 7.196306 6.581846 9.837409
#> [129,] 12.100351 11.373856 15.969952
#> [130,] 13.542717 12.783270 17.773641
#> [131,] 10.657984 9.964441 14.166263
#> [132,] 4.311574 3.763016 6.230030
#> [133,] 12.100351 11.373856 15.969952
#> [134,] 9.792565 9.118792 13.084049
#> [135,] 10.657984 9.964441 14.166263
#> [136,] 9.504092 8.836909 12.723311
#> [137,] 9.215618 8.555026 12.362574
#> [138,] 10.081038 9.400675 13.444787
#> [139,] 5.176994 4.608665 7.312244
#> [140,] 5.465467 4.890548 7.672982
#> [141,] 7.484779 6.863729 10.198147
#> [142,] 4.888520 4.326782 6.951506
#> [143,] 5.176994 4.608665 7.312244
#> [144,] 6.042413 5.454314 8.394457
#> [145,] 10.657984 9.964441 14.166263
#> [146,] 5.465467 4.890548 7.672982
#> [147,] 11.523404 10.810090 15.248476
#> [148,] 7.196306 6.581846 9.837409
#> [149,] 6.619360 6.018080 9.115933
#> [150,] 12.965770 12.219505 17.052165
#>
#> $subscore.sx
#> Subscore.sx.Algebra Subscore.sx.Geometry Subscore.sx.Measurement
#> [1,] 14.991428 14.179462 19.581290
#> [2,] 10.652804 9.965390 14.179359
#> [3,] 13.851666 13.076693 18.057252
#> [4,] 11.847865 11.099635 15.494590
#> [5,] 10.689669 9.933915 14.127157
#> [6,] 11.847865 11.068160 15.546792
#> [7,] 11.847865 11.099635 15.494590
#> [8,] 10.082923 9.382531 13.469542
#> [9,] 12.380881 11.682494 16.308811
#> [10,] 13.244919 12.556783 17.347435
#> [11,] 12.105156 11.359589 15.980003
#> [12,] 9.494609 8.799671 12.811927
#> [13,] 11.535275 10.776730 15.270186
#> [14,] 10.064490 9.382531 13.521744
#> [15,] 11.516842 10.745255 15.374590
#> [16,] 9.218884 8.539717 12.378716
#> [17,] 7.453943 6.917038 10.197063
#> [18,] 10.377080 9.705436 13.746148
#> [19,] 9.494609 8.862621 12.707523
#> [20,] 12.123589 11.328114 15.980003
#> [21,] 11.204253 10.516775 14.993580
#> [22,] 14.421547 13.596602 18.871473
#> [23,] 14.421547 13.596602 18.871473
#> [24,] 12.417746 11.619544 16.308811
#> [25,] 12.105156 11.391064 15.927801
#> [26,] 11.535275 10.776730 15.270186
#> [27,] 12.969195 12.233879 17.018628
#> [28,] 12.950762 12.265354 17.018628
#> [29,] 13.520643 12.785263 17.832849
#> [30,] 13.814800 13.076693 18.161656
#> [31,] 12.656605 11.973924 16.689820
#> [32,] 12.399313 11.619544 16.361012
#> [33,] 13.281784 12.493833 17.347435
#> [34,] 8.060689 7.499897 10.802476
#> [35,] 13.263352 12.493833 17.399637
#> [36,] 11.535275 10.745255 15.322388
#> [37,] 14.127390 13.336648 18.490464
#> [38,] 8.060689 7.499897 10.802476
#> [39,] 14.127390 13.368123 18.438262
#> [40,] 10.340214 9.673961 13.902754
#> [41,] 12.950762 12.265354 17.018628
#> [42,] 11.829432 11.099635 15.546792
#> [43,] 14.108957 13.336648 18.542666
#> [44,] 13.520643 12.785263 17.832849
#> [45,] 12.362448 11.713969 16.308811
#> [46,] 13.263352 12.493833 17.399637
#> [47,] 12.399313 11.713969 16.204407
#> [48,] 12.711903 11.910974 16.637618
#> [49,] 10.340214 9.736911 13.798350
#> [50,] 12.142022 11.328114 15.927801
#> [51,] 12.969195 12.170929 17.123031
#> [52,] 12.656605 11.942449 16.742022
#> [53,] 14.108957 13.368123 18.490464
#> [54,] 12.675038 11.910974 16.742022
#> [55,] 12.399313 11.619544 16.361012
#> [56,] 12.362448 11.651019 16.413214
#> [57,] 12.344015 11.776919 16.256609
#> [58,] 14.421547 13.628077 18.819271
#> [59,] 12.969195 12.202404 17.070830
#> [60,] 14.108957 13.368123 18.490464
#> [61,] 13.833233 13.076693 18.109454
#> [62,] 10.652804 9.965390 14.179359
#> [63,] 8.299548 7.791327 11.287889
#> [64,] 8.649003 7.988332 11.616697
#> [65,] 2.876459 2.348587 4.414122
#> [66,] 5.725866 5.136984 8.172015
#> [67,] 7.729667 7.145518 10.682476
#> [68,] 14.403114 13.596602 18.923675
#> [69,] 7.215084 6.562658 9.816053
#> [70,] 11.792567 11.099635 15.651195
#> [71,] 5.137552 4.680025 7.305592
#> [72,] 6.589904 6.042749 9.158438
#> [73,] 11.222685 10.548250 14.889176
#> [74,] 8.336413 7.728377 11.287889
#> [75,] 10.119788 9.414006 13.312937
#> [76,] 5.707433 5.262884 8.015409
#> [77,] 9.494609 8.831146 12.759725
#> [78,] 6.939359 6.271229 9.435044
#> [79,] 4.291946 3.742786 6.319169
#> [80,] 12.399313 11.682494 16.256609
#> [81,] 6.957792 6.271229 9.382842
#> [82,] 11.204253 10.485300 15.045782
#> [83,] 6.589904 6.042749 9.158438
#> [84,] 9.549907 8.831146 12.603119
#> [85,] 7.784965 7.114043 10.578072
#> [86,] 3.189049 2.640016 4.690728
#> [87,] 7.766532 7.145518 10.578072
#> [88,] 4.622969 4.097165 6.439170
#> [89,] 9.549907 8.799671 12.655321
#> [90,] 6.056888 5.365464 8.500823
#> [91,] 2.876459 2.285637 4.518526
#> [92,] 5.211283 4.617075 7.201188
#> [93,] 4.861828 4.325645 7.028987
#> [94,] 5.762731 5.168459 8.015409
#> [95,] 8.336413 7.633952 11.444495
#> [96,] 12.380881 11.682494 16.308811
#> [97,] 4.255081 3.837210 6.266968
#> [98,] 3.758930 3.191401 5.452747
#> [99,] 8.079122 7.405473 10.906880
#> [100,] 10.377080 9.673961 13.798350
#> [101,] 9.788766 9.122576 13.088533
#> [102,] 4.604536 4.097165 6.491371
#> [103,] 4.880260 4.420070 6.820179
#> [104,] 8.906295 8.216812 12.154312
#> [105,] 13.244919 12.493833 17.451839
#> [106,] 8.060689 7.405473 10.959081
#> [107,] 11.259551 10.516775 14.836975
#> [108,] 5.744299 5.231409 7.963207
#> [109,] 9.513041 8.831146 12.707523
#> [110,] 12.675038 11.942449 16.689820
#> [111,] 9.513041 8.925571 12.550918
#> [112,] 6.902494 6.365653 9.382842
#> [113,] 10.928528 10.225345 14.612571
#> [114,] 11.498410 10.808205 15.322388
#> [115,] 10.910096 10.256820 14.612571
#> [116,] 4.641401 4.002740 6.543573
#> [117,] 5.468574 4.908505 7.634400
#> [118,] 7.748100 7.208468 10.525870
#> [119,] 11.516842 10.776730 15.322388
#> [120,] 3.740498 3.159926 5.557150
#> [121,] 7.803397 7.208468 10.369264
#> [122,] 3.740498 3.159926 5.557150
#> [123,] 6.902494 6.239754 9.591649
#> [124,] 4.880260 4.325645 6.976785
#> [125,] 7.729667 7.145518 10.682476
#> [126,] 12.656605 12.005399 16.637618
#> [127,] 13.539076 12.816738 17.728445
#> [128,] 7.141353 6.625608 9.920457
#> [129,] 12.086724 11.359589 16.032205
#> [130,] 13.539076 12.848213 17.676243
#> [131,] 10.708102 9.933915 14.074956
#> [132,] 4.310379 3.805735 6.162564
#> [133,] 12.105156 11.391064 15.927801
#> [134,] 9.807198 9.122576 13.036331
#> [135,] 10.615939 9.996865 14.231561
#> [136,] 9.549907 8.799671 12.655321
#> [137,] 9.182019 8.508242 12.535321
#> [138,] 10.082923 9.382531 13.469542
#> [139,] 5.211283 4.554125 7.305592
#> [140,] 5.468574 4.814080 7.791006
#> [141,] 7.527673 6.791138 10.197063
#> [142,] 4.880260 4.294170 7.028987
#> [143,] 5.211283 4.554125 7.305592
#> [144,] 6.038456 5.365464 8.553025
#> [145,] 10.689669 9.902441 14.179359
#> [146,] 5.487007 4.908505 7.582198
#> [147,] 11.535275 10.713780 15.374590
#> [148,] 7.233516 6.562658 9.763851
#> [149,] 6.571472 6.137174 9.054034
#> [150,] 12.950762 12.233879 17.070830
#>
# Obtaining original correlation for the three methods
CTTsub(test.data,method="Haberman")$Correlation
#> Algebra Geometry Measurement Math
#> Algebra 1.0000000 0.8143313 0.8336757 0.9357667
#> Geometry 0.8143313 1.0000000 0.8198970 0.9295419
#> Measurement 0.8336757 0.8198970 1.0000000 0.9507132
#> Math 0.9357667 0.9295419 0.9507132 1.0000000
# Obtaining disattenuated correlation for the three methods
CTTsub(test.data,method="Haberman")$Disattenuated.correlation
#> Algebra Geometry Measurement
#> Algebra 0.8169114 1.0081315 1.0096427
#> Geometry 0.8143313 0.7987169 1.0042016
#> Measurement 0.8336757 0.8198970 0.8346106
# Obtaining PRMSEs for the three methods
CTTsub(test.data,method="Haberman")$PRMSE
#> Alpha PRMSE.s PRMSE.x PRMSE.sx added.value.s
#> Algebra 0.8169114 0.8169114 0.9381521 0.9382038 0
#> Geometry 0.7987169 0.7987169 0.9343207 0.9344893 0
#> Measurement 0.8346106 0.8346106 0.9345284 0.9348423 0
#> Math 0.9311719 NA NA NA NA
#> added.value.sx
#> Algebra 0
#> Geometry 0
#> Measurement 0
#> Math NA
# Obtaining descriptive statistics summary for estimated subscores
CTTsub(test.data,method="Haberman")$summary
#> Orig.mean Orig.sd subscore.s.mean subscore.s.sd subscore.x.mean
#> Algebra 9.773333 3.662153 9.773333 2.991654 9.773333
#> Geometry 9.100000 3.626432 9.100000 2.896492 9.100000
#> Measurement 13.060000 4.539506 13.060000 3.788720 13.060000
#> subscore.x.sd subscore.sx.mean subscore.sx.sd
#> Algebra 3.205978 9.773333 3.206067
#> Geometry 3.132737 9.100000 3.133019
#> Measurement 4.009099 13.060000 4.009773
# Obtaining raw subscores
CTTsub(test.data,method="Haberman")$subscore.original
#> Algebra Geometry Measurement Math
#> [1,] 15 15 20 50
#> [2,] 11 10 14 35
#> [3,] 13 13 20 46
#> [4,] 10 11 18 39
#> [5,] 9 11 15 35
#> [6,] 10 12 17 39
#> [7,] 10 11 18 39
#> [8,] 10 10 13 33
#> [9,] 13 11 17 41
#> [10,] 14 11 19 44
#> [11,] 12 12 16 40
#> [12,] 10 10 11 31
#> [13,] 11 12 15 38
#> [14,] 11 10 12 33
#> [15,] 12 13 13 38
#> [16,] 9 9 12 30
#> [17,] 9 5 10 24
#> [18,] 10 9 15 34
#> [19,] 10 8 13 31
#> [20,] 11 13 16 40
#> [21,] 13 11 13 37
#> [22,] 14 15 19 48
#> [23,] 14 15 19 48
#> [24,] 11 13 17 41
#> [25,] 12 11 17 40
#> [26,] 11 12 15 38
#> [27,] 13 12 18 43
#> [28,] 14 11 18 43
#> [29,] 15 13 17 45
#> [30,] 15 13 18 46
#> [31,] 14 11 17 42
#> [32,] 12 13 16 41
#> [33,] 12 13 19 44
#> [34,] 8 5 13 26
#> [35,] 13 13 18 44
#> [36,] 11 13 14 38
#> [37,] 14 14 19 47
#> [38,] 8 5 13 26
#> [39,] 14 13 20 47
#> [40,] 12 10 12 34
#> [41,] 14 11 18 43
#> [42,] 11 11 17 39
#> [43,] 15 14 18 47
#> [44,] 15 13 17 45
#> [45,] 14 10 17 41
#> [46,] 13 13 18 44
#> [47,] 12 10 19 41
#> [48,] 11 13 18 42
#> [49,] 12 8 14 34
#> [50,] 10 13 17 40
#> [51,] 13 14 16 43
#> [52,] 14 12 16 42
#> [53,] 15 13 19 47
#> [54,] 13 13 16 42
#> [55,] 12 13 16 41
#> [56,] 14 12 15 41
#> [57,] 15 8 18 41
#> [58,] 14 14 20 48
#> [59,] 13 13 17 43
#> [60,] 15 13 19 47
#> [61,] 14 13 19 46
#> [62,] 11 10 14 35
#> [63,] 11 5 11 27
#> [64,] 8 8 12 28
#> [65,] 2 2 4 8
#> [66,] 7 6 5 18
#> [67,] 10 7 8 25
#> [68,] 15 15 18 48
#> [69,] 6 7 10 23
#> [70,] 13 11 15 39
#> [71,] 7 2 7 16
#> [72,] 8 5 8 21
#> [73,] 12 10 15 37
#> [74,] 9 7 11 27
#> [75,] 8 9 16 33
#> [76,] 8 2 8 18
#> [77,] 10 9 12 31
#> [78,] 5 7 10 22
#> [79,] 5 4 4 13
#> [80,] 12 11 18 41
#> [81,] 4 7 11 22
#> [82,] 13 12 12 37
#> [83,] 8 5 8 21
#> [84,] 7 9 15 31
#> [85,] 7 8 10 25
#> [86,] 1 2 6 9
#> [87,] 8 7 10 25
#> [88,] 3 2 9 14
#> [89,] 7 10 14 31
#> [90,] 5 8 6 19
#> [91,] 2 4 2 8
#> [92,] 3 4 9 16
#> [93,] 6 4 5 15
#> [94,] 5 5 8 18
#> [95,] 9 10 8 27
#> [96,] 13 11 17 41
#> [97,] 7 1 5 13
#> [98,] 2 3 6 11
#> [99,] 7 8 11 26
#> [100,] 10 10 14 34
#> [101,] 10 9 13 32
#> [102,] 4 2 8 14
#> [103,] 5 1 9 15
#> [104,] 10 10 9 29
#> [105,] 14 13 17 44
#> [106,] 8 8 10 26
#> [107,] 10 11 16 37
#> [108,] 6 3 9 18
#> [109,] 9 9 13 31
#> [110,] 13 12 17 42
#> [111,] 9 6 16 31
#> [112,] 7 4 11 22
#> [113,] 12 11 13 36
#> [114,] 13 11 14 38
#> [115,] 13 10 13 36
#> [116,] 2 5 7 14
#> [117,] 5 4 8 17
#> [118,] 9 5 11 25
#> [119,] 12 12 14 38
#> [120,] 3 4 4 11
#> [121,] 6 5 14 25
#> [122,] 3 4 4 11
#> [123,] 7 8 7 22
#> [124,] 5 4 6 15
#> [125,] 10 7 8 25
#> [126,] 14 10 18 42
#> [127,] 14 12 19 45
#> [128,] 10 5 8 23
#> [129,] 13 12 15 40
#> [130,] 14 11 20 45
#> [131,] 8 11 16 35
#> [132,] 4 2 7 13
#> [133,] 12 11 17 40
#> [134,] 9 9 14 32
#> [135,] 13 9 13 35
#> [136,] 7 10 14 31
#> [137,] 11 10 9 30
#> [138,] 10 10 13 33
#> [139,] 3 6 7 16
#> [140,] 5 7 5 17
#> [141,] 5 9 10 24
#> [142,] 5 5 5 15
#> [143,] 3 6 7 16
#> [144,] 6 8 5 19
#> [145,] 9 12 14 35
#> [146,] 4 4 9 17
#> [147,] 11 14 13 38
#> [148,] 5 7 11 23
#> [149,] 9 2 10 21
#> [150,] 14 12 17 43
# Obtaining subscores that are estimated as a function of the observed subscores
CTTsub(test.data,method="Haberman")$subscore.s
#> Subscore.s.Algebra Subscore.s.Geometry Subscore.s.Measurement
#> [1,] 14.043057 13.812430 18.852198
#> [2,] 10.775411 9.818845 13.844534
#> [3,] 12.409234 12.214996 18.852198
#> [4,] 9.958500 10.617562 17.182977
#> [5,] 9.141589 10.617562 14.679145
#> [6,] 9.958500 11.416279 16.348366
#> [7,] 9.958500 10.617562 17.182977
#> [8,] 9.958500 9.818845 13.009923
#> [9,] 12.409234 10.617562 16.348366
#> [10,] 13.226145 10.617562 18.017587
#> [11,] 11.592323 11.416279 15.513755
#> [12,] 9.958500 9.818845 11.340702
#> [13,] 10.775411 11.416279 14.679145
#> [14,] 10.775411 9.818845 12.175313
#> [15,] 11.592323 12.214996 13.009923
#> [16,] 9.141589 9.020128 12.175313
#> [17,] 9.141589 5.825261 10.506091
#> [18,] 9.958500 9.020128 14.679145
#> [19,] 9.958500 8.221411 13.009923
#> [20,] 10.775411 12.214996 15.513755
#> [21,] 12.409234 10.617562 13.009923
#> [22,] 13.226145 13.812430 18.017587
#> [23,] 13.226145 13.812430 18.017587
#> [24,] 10.775411 12.214996 16.348366
#> [25,] 11.592323 10.617562 16.348366
#> [26,] 10.775411 11.416279 14.679145
#> [27,] 12.409234 11.416279 17.182977
#> [28,] 13.226145 10.617562 17.182977
#> [29,] 14.043057 12.214996 16.348366
#> [30,] 14.043057 12.214996 17.182977
#> [31,] 13.226145 10.617562 16.348366
#> [32,] 11.592323 12.214996 15.513755
#> [33,] 11.592323 12.214996 18.017587
#> [34,] 8.324677 5.825261 13.009923
#> [35,] 12.409234 12.214996 17.182977
#> [36,] 10.775411 12.214996 13.844534
#> [37,] 13.226145 13.013713 18.017587
#> [38,] 8.324677 5.825261 13.009923
#> [39,] 13.226145 12.214996 18.852198
#> [40,] 11.592323 9.818845 12.175313
#> [41,] 13.226145 10.617562 17.182977
#> [42,] 10.775411 10.617562 16.348366
#> [43,] 14.043057 13.013713 17.182977
#> [44,] 14.043057 12.214996 16.348366
#> [45,] 13.226145 9.818845 16.348366
#> [46,] 12.409234 12.214996 17.182977
#> [47,] 11.592323 9.818845 18.017587
#> [48,] 10.775411 12.214996 17.182977
#> [49,] 11.592323 8.221411 13.844534
#> [50,] 9.958500 12.214996 16.348366
#> [51,] 12.409234 13.013713 15.513755
#> [52,] 13.226145 11.416279 15.513755
#> [53,] 14.043057 12.214996 18.017587
#> [54,] 12.409234 12.214996 15.513755
#> [55,] 11.592323 12.214996 15.513755
#> [56,] 13.226145 11.416279 14.679145
#> [57,] 14.043057 8.221411 17.182977
#> [58,] 13.226145 13.013713 18.852198
#> [59,] 12.409234 12.214996 16.348366
#> [60,] 14.043057 12.214996 18.017587
#> [61,] 13.226145 12.214996 18.017587
#> [62,] 10.775411 9.818845 13.844534
#> [63,] 10.775411 5.825261 11.340702
#> [64,] 8.324677 8.221411 12.175313
#> [65,] 3.423209 3.429110 5.498428
#> [66,] 7.507766 6.623978 6.333038
#> [67,] 9.958500 7.422695 8.836870
#> [68,] 14.043057 13.812430 17.182977
#> [69,] 6.690854 7.422695 10.506091
#> [70,] 12.409234 10.617562 14.679145
#> [71,] 7.507766 3.429110 8.002260
#> [72,] 8.324677 5.825261 8.836870
#> [73,] 11.592323 9.818845 14.679145
#> [74,] 9.141589 7.422695 11.340702
#> [75,] 8.324677 9.020128 15.513755
#> [76,] 8.324677 3.429110 8.836870
#> [77,] 9.958500 9.020128 12.175313
#> [78,] 5.873943 7.422695 10.506091
#> [79,] 5.873943 5.026544 5.498428
#> [80,] 11.592323 10.617562 17.182977
#> [81,] 5.057032 7.422695 11.340702
#> [82,] 12.409234 11.416279 12.175313
#> [83,] 8.324677 5.825261 8.836870
#> [84,] 7.507766 9.020128 14.679145
#> [85,] 7.507766 8.221411 10.506091
#> [86,] 2.606297 3.429110 7.167649
#> [87,] 8.324677 7.422695 10.506091
#> [88,] 4.240120 3.429110 9.671481
#> [89,] 7.507766 9.818845 13.844534
#> [90,] 5.873943 8.221411 7.167649
#> [91,] 3.423209 5.026544 3.829206
#> [92,] 4.240120 5.026544 9.671481
#> [93,] 6.690854 5.026544 6.333038
#> [94,] 5.873943 5.825261 8.836870
#> [95,] 9.141589 9.818845 8.836870
#> [96,] 12.409234 10.617562 16.348366
#> [97,] 7.507766 2.630393 6.333038
#> [98,] 3.423209 4.227827 7.167649
#> [99,] 7.507766 8.221411 11.340702
#> [100,] 9.958500 9.818845 13.844534
#> [101,] 9.958500 9.020128 13.009923
#> [102,] 5.057032 3.429110 8.836870
#> [103,] 5.873943 2.630393 9.671481
#> [104,] 9.958500 9.818845 9.671481
#> [105,] 13.226145 12.214996 16.348366
#> [106,] 8.324677 8.221411 10.506091
#> [107,] 9.958500 10.617562 15.513755
#> [108,] 6.690854 4.227827 9.671481
#> [109,] 9.141589 9.020128 13.009923
#> [110,] 12.409234 11.416279 16.348366
#> [111,] 9.141589 6.623978 15.513755
#> [112,] 7.507766 5.026544 11.340702
#> [113,] 11.592323 10.617562 13.009923
#> [114,] 12.409234 10.617562 13.844534
#> [115,] 12.409234 9.818845 13.009923
#> [116,] 3.423209 5.825261 8.002260
#> [117,] 5.873943 5.026544 8.836870
#> [118,] 9.141589 5.825261 11.340702
#> [119,] 11.592323 11.416279 13.844534
#> [120,] 4.240120 5.026544 5.498428
#> [121,] 6.690854 5.825261 13.844534
#> [122,] 4.240120 5.026544 5.498428
#> [123,] 7.507766 8.221411 8.002260
#> [124,] 5.873943 5.026544 7.167649
#> [125,] 9.958500 7.422695 8.836870
#> [126,] 13.226145 9.818845 17.182977
#> [127,] 13.226145 11.416279 18.017587
#> [128,] 9.958500 5.825261 8.836870
#> [129,] 12.409234 11.416279 14.679145
#> [130,] 13.226145 10.617562 18.852198
#> [131,] 8.324677 10.617562 15.513755
#> [132,] 5.057032 3.429110 8.002260
#> [133,] 11.592323 10.617562 16.348366
#> [134,] 9.141589 9.020128 13.844534
#> [135,] 12.409234 9.020128 13.009923
#> [136,] 7.507766 9.818845 13.844534
#> [137,] 10.775411 9.818845 9.671481
#> [138,] 9.958500 9.818845 13.009923
#> [139,] 4.240120 6.623978 8.002260
#> [140,] 5.873943 7.422695 6.333038
#> [141,] 5.873943 9.020128 10.506091
#> [142,] 5.873943 5.825261 6.333038
#> [143,] 4.240120 6.623978 8.002260
#> [144,] 6.690854 8.221411 6.333038
#> [145,] 9.141589 11.416279 13.844534
#> [146,] 5.057032 5.026544 9.671481
#> [147,] 10.775411 13.013713 13.009923
#> [148,] 5.873943 7.422695 11.340702
#> [149,] 9.141589 3.429110 10.506091
#> [150,] 13.226145 11.416279 16.348366
# Obtaining subscores that are estimated as a function of the observed total score
CTTsub(test.data,method="Haberman")$subscore.x
#> Subscore.x.Algebra Subscore.x.Geometry Subscore.x.Measurement
#> [1,] 14.985083 14.192685 19.577330
#> [2,] 10.657984 9.964441 14.166263
#> [3,] 13.831190 13.065153 18.134379
#> [4,] 11.811877 11.091973 15.609214
#> [5,] 10.657984 9.964441 14.166263
#> [6,] 11.811877 11.091973 15.609214
#> [7,] 11.811877 11.091973 15.609214
#> [8,] 10.081038 9.400675 13.444787
#> [9,] 12.388824 11.655739 16.330690
#> [10,] 13.254243 12.501387 17.412903
#> [11,] 12.100351 11.373856 15.969952
#> [12,] 9.504092 8.836909 12.723311
#> [13,] 11.523404 10.810090 15.248476
#> [14,] 10.081038 9.400675 13.444787
#> [15,] 11.523404 10.810090 15.248476
#> [16,] 9.215618 8.555026 12.362574
#> [17,] 7.484779 6.863729 10.198147
#> [18,] 10.369511 9.682558 13.805525
#> [19,] 9.504092 8.836909 12.723311
#> [20,] 12.100351 11.373856 15.969952
#> [21,] 11.234931 10.528207 14.887738
#> [22,] 14.408136 13.628919 18.855855
#> [23,] 14.408136 13.628919 18.855855
#> [24,] 12.388824 11.655739 16.330690
#> [25,] 12.100351 11.373856 15.969952
#> [26,] 11.523404 10.810090 15.248476
#> [27,] 12.965770 12.219505 17.052165
#> [28,] 12.965770 12.219505 17.052165
#> [29,] 13.542717 12.783270 17.773641
#> [30,] 13.831190 13.065153 18.134379
#> [31,] 12.677297 11.937622 16.691428
#> [32,] 12.388824 11.655739 16.330690
#> [33,] 13.254243 12.501387 17.412903
#> [34,] 8.061726 7.427495 10.919622
#> [35,] 13.254243 12.501387 17.412903
#> [36,] 11.523404 10.810090 15.248476
#> [37,] 14.119663 13.347036 18.495117
#> [38,] 8.061726 7.427495 10.919622
#> [39,] 14.119663 13.347036 18.495117
#> [40,] 10.369511 9.682558 13.805525
#> [41,] 12.965770 12.219505 17.052165
#> [42,] 11.811877 11.091973 15.609214
#> [43,] 14.119663 13.347036 18.495117
#> [44,] 13.542717 12.783270 17.773641
#> [45,] 12.388824 11.655739 16.330690
#> [46,] 13.254243 12.501387 17.412903
#> [47,] 12.388824 11.655739 16.330690
#> [48,] 12.677297 11.937622 16.691428
#> [49,] 10.369511 9.682558 13.805525
#> [50,] 12.100351 11.373856 15.969952
#> [51,] 12.965770 12.219505 17.052165
#> [52,] 12.677297 11.937622 16.691428
#> [53,] 14.119663 13.347036 18.495117
#> [54,] 12.677297 11.937622 16.691428
#> [55,] 12.388824 11.655739 16.330690
#> [56,] 12.388824 11.655739 16.330690
#> [57,] 12.388824 11.655739 16.330690
#> [58,] 14.408136 13.628919 18.855855
#> [59,] 12.965770 12.219505 17.052165
#> [60,] 14.119663 13.347036 18.495117
#> [61,] 13.831190 13.065153 18.134379
#> [62,] 10.657984 9.964441 14.166263
#> [63,] 8.350199 7.709377 11.280360
#> [64,] 8.638672 7.991260 11.641098
#> [65,] 2.869208 2.353602 4.426341
#> [66,] 5.753940 5.172431 8.033720
#> [67,] 7.773252 7.145612 10.558884
#> [68,] 14.408136 13.628919 18.855855
#> [69,] 7.196306 6.581846 9.837409
#> [70,] 11.811877 11.091973 15.609214
#> [71,] 5.176994 4.608665 7.312244
#> [72,] 6.619360 6.018080 9.115933
#> [73,] 11.234931 10.528207 14.887738
#> [74,] 8.350199 7.709377 11.280360
#> [75,] 10.081038 9.400675 13.444787
#> [76,] 5.753940 5.172431 8.033720
#> [77,] 9.504092 8.836909 12.723311
#> [78,] 6.907833 6.299963 9.476671
#> [79,] 4.311574 3.763016 6.230030
#> [80,] 12.388824 11.655739 16.330690
#> [81,] 6.907833 6.299963 9.476671
#> [82,] 11.234931 10.528207 14.887738
#> [83,] 6.619360 6.018080 9.115933
#> [84,] 9.504092 8.836909 12.723311
#> [85,] 7.773252 7.145612 10.558884
#> [86,] 3.157681 2.635485 4.787079
#> [87,] 7.773252 7.145612 10.558884
#> [88,] 4.600047 4.044899 6.590768
#> [89,] 9.504092 8.836909 12.723311
#> [90,] 6.042413 5.454314 8.394457
#> [91,] 2.869208 2.353602 4.426341
#> [92,] 5.176994 4.608665 7.312244
#> [93,] 4.888520 4.326782 6.951506
#> [94,] 5.753940 5.172431 8.033720
#> [95,] 8.350199 7.709377 11.280360
#> [96,] 12.388824 11.655739 16.330690
#> [97,] 4.311574 3.763016 6.230030
#> [98,] 3.734628 3.199250 5.508555
#> [99,] 8.061726 7.427495 10.919622
#> [100,] 10.369511 9.682558 13.805525
#> [101,] 9.792565 9.118792 13.084049
#> [102,] 4.600047 4.044899 6.590768
#> [103,] 4.888520 4.326782 6.951506
#> [104,] 8.927145 8.273143 12.001836
#> [105,] 13.254243 12.501387 17.412903
#> [106,] 8.061726 7.427495 10.919622
#> [107,] 11.234931 10.528207 14.887738
#> [108,] 5.753940 5.172431 8.033720
#> [109,] 9.504092 8.836909 12.723311
#> [110,] 12.677297 11.937622 16.691428
#> [111,] 9.504092 8.836909 12.723311
#> [112,] 6.907833 6.299963 9.476671
#> [113,] 10.946458 10.246324 14.527001
#> [114,] 11.523404 10.810090 15.248476
#> [115,] 10.946458 10.246324 14.527001
#> [116,] 4.600047 4.044899 6.590768
#> [117,] 5.465467 4.890548 7.672982
#> [118,] 7.773252 7.145612 10.558884
#> [119,] 11.523404 10.810090 15.248476
#> [120,] 3.734628 3.199250 5.508555
#> [121,] 7.773252 7.145612 10.558884
#> [122,] 3.734628 3.199250 5.508555
#> [123,] 6.907833 6.299963 9.476671
#> [124,] 4.888520 4.326782 6.951506
#> [125,] 7.773252 7.145612 10.558884
#> [126,] 12.677297 11.937622 16.691428
#> [127,] 13.542717 12.783270 17.773641
#> [128,] 7.196306 6.581846 9.837409
#> [129,] 12.100351 11.373856 15.969952
#> [130,] 13.542717 12.783270 17.773641
#> [131,] 10.657984 9.964441 14.166263
#> [132,] 4.311574 3.763016 6.230030
#> [133,] 12.100351 11.373856 15.969952
#> [134,] 9.792565 9.118792 13.084049
#> [135,] 10.657984 9.964441 14.166263
#> [136,] 9.504092 8.836909 12.723311
#> [137,] 9.215618 8.555026 12.362574
#> [138,] 10.081038 9.400675 13.444787
#> [139,] 5.176994 4.608665 7.312244
#> [140,] 5.465467 4.890548 7.672982
#> [141,] 7.484779 6.863729 10.198147
#> [142,] 4.888520 4.326782 6.951506
#> [143,] 5.176994 4.608665 7.312244
#> [144,] 6.042413 5.454314 8.394457
#> [145,] 10.657984 9.964441 14.166263
#> [146,] 5.465467 4.890548 7.672982
#> [147,] 11.523404 10.810090 15.248476
#> [148,] 7.196306 6.581846 9.837409
#> [149,] 6.619360 6.018080 9.115933
#> [150,] 12.965770 12.219505 17.052165
# Obtaining subscores that are estimated as a function of
# both the observed subscores and the observed total score.
CTTsub(test.data,method="Haberman")$subscore.sx
#> Subscore.sx.Algebra Subscore.sx.Geometry Subscore.sx.Measurement
#> [1,] 14.991428 14.179462 19.581290
#> [2,] 10.652804 9.965390 14.179359
#> [3,] 13.851666 13.076693 18.057252
#> [4,] 11.847865 11.099635 15.494590
#> [5,] 10.689669 9.933915 14.127157
#> [6,] 11.847865 11.068160 15.546792
#> [7,] 11.847865 11.099635 15.494590
#> [8,] 10.082923 9.382531 13.469542
#> [9,] 12.380881 11.682494 16.308811
#> [10,] 13.244919 12.556783 17.347435
#> [11,] 12.105156 11.359589 15.980003
#> [12,] 9.494609 8.799671 12.811927
#> [13,] 11.535275 10.776730 15.270186
#> [14,] 10.064490 9.382531 13.521744
#> [15,] 11.516842 10.745255 15.374590
#> [16,] 9.218884 8.539717 12.378716
#> [17,] 7.453943 6.917038 10.197063
#> [18,] 10.377080 9.705436 13.746148
#> [19,] 9.494609 8.862621 12.707523
#> [20,] 12.123589 11.328114 15.980003
#> [21,] 11.204253 10.516775 14.993580
#> [22,] 14.421547 13.596602 18.871473
#> [23,] 14.421547 13.596602 18.871473
#> [24,] 12.417746 11.619544 16.308811
#> [25,] 12.105156 11.391064 15.927801
#> [26,] 11.535275 10.776730 15.270186
#> [27,] 12.969195 12.233879 17.018628
#> [28,] 12.950762 12.265354 17.018628
#> [29,] 13.520643 12.785263 17.832849
#> [30,] 13.814800 13.076693 18.161656
#> [31,] 12.656605 11.973924 16.689820
#> [32,] 12.399313 11.619544 16.361012
#> [33,] 13.281784 12.493833 17.347435
#> [34,] 8.060689 7.499897 10.802476
#> [35,] 13.263352 12.493833 17.399637
#> [36,] 11.535275 10.745255 15.322388
#> [37,] 14.127390 13.336648 18.490464
#> [38,] 8.060689 7.499897 10.802476
#> [39,] 14.127390 13.368123 18.438262
#> [40,] 10.340214 9.673961 13.902754
#> [41,] 12.950762 12.265354 17.018628
#> [42,] 11.829432 11.099635 15.546792
#> [43,] 14.108957 13.336648 18.542666
#> [44,] 13.520643 12.785263 17.832849
#> [45,] 12.362448 11.713969 16.308811
#> [46,] 13.263352 12.493833 17.399637
#> [47,] 12.399313 11.713969 16.204407
#> [48,] 12.711903 11.910974 16.637618
#> [49,] 10.340214 9.736911 13.798350
#> [50,] 12.142022 11.328114 15.927801
#> [51,] 12.969195 12.170929 17.123031
#> [52,] 12.656605 11.942449 16.742022
#> [53,] 14.108957 13.368123 18.490464
#> [54,] 12.675038 11.910974 16.742022
#> [55,] 12.399313 11.619544 16.361012
#> [56,] 12.362448 11.651019 16.413214
#> [57,] 12.344015 11.776919 16.256609
#> [58,] 14.421547 13.628077 18.819271
#> [59,] 12.969195 12.202404 17.070830
#> [60,] 14.108957 13.368123 18.490464
#> [61,] 13.833233 13.076693 18.109454
#> [62,] 10.652804 9.965390 14.179359
#> [63,] 8.299548 7.791327 11.287889
#> [64,] 8.649003 7.988332 11.616697
#> [65,] 2.876459 2.348587 4.414122
#> [66,] 5.725866 5.136984 8.172015
#> [67,] 7.729667 7.145518 10.682476
#> [68,] 14.403114 13.596602 18.923675
#> [69,] 7.215084 6.562658 9.816053
#> [70,] 11.792567 11.099635 15.651195
#> [71,] 5.137552 4.680025 7.305592
#> [72,] 6.589904 6.042749 9.158438
#> [73,] 11.222685 10.548250 14.889176
#> [74,] 8.336413 7.728377 11.287889
#> [75,] 10.119788 9.414006 13.312937
#> [76,] 5.707433 5.262884 8.015409
#> [77,] 9.494609 8.831146 12.759725
#> [78,] 6.939359 6.271229 9.435044
#> [79,] 4.291946 3.742786 6.319169
#> [80,] 12.399313 11.682494 16.256609
#> [81,] 6.957792 6.271229 9.382842
#> [82,] 11.204253 10.485300 15.045782
#> [83,] 6.589904 6.042749 9.158438
#> [84,] 9.549907 8.831146 12.603119
#> [85,] 7.784965 7.114043 10.578072
#> [86,] 3.189049 2.640016 4.690728
#> [87,] 7.766532 7.145518 10.578072
#> [88,] 4.622969 4.097165 6.439170
#> [89,] 9.549907 8.799671 12.655321
#> [90,] 6.056888 5.365464 8.500823
#> [91,] 2.876459 2.285637 4.518526
#> [92,] 5.211283 4.617075 7.201188
#> [93,] 4.861828 4.325645 7.028987
#> [94,] 5.762731 5.168459 8.015409
#> [95,] 8.336413 7.633952 11.444495
#> [96,] 12.380881 11.682494 16.308811
#> [97,] 4.255081 3.837210 6.266968
#> [98,] 3.758930 3.191401 5.452747
#> [99,] 8.079122 7.405473 10.906880
#> [100,] 10.377080 9.673961 13.798350
#> [101,] 9.788766 9.122576 13.088533
#> [102,] 4.604536 4.097165 6.491371
#> [103,] 4.880260 4.420070 6.820179
#> [104,] 8.906295 8.216812 12.154312
#> [105,] 13.244919 12.493833 17.451839
#> [106,] 8.060689 7.405473 10.959081
#> [107,] 11.259551 10.516775 14.836975
#> [108,] 5.744299 5.231409 7.963207
#> [109,] 9.513041 8.831146 12.707523
#> [110,] 12.675038 11.942449 16.689820
#> [111,] 9.513041 8.925571 12.550918
#> [112,] 6.902494 6.365653 9.382842
#> [113,] 10.928528 10.225345 14.612571
#> [114,] 11.498410 10.808205 15.322388
#> [115,] 10.910096 10.256820 14.612571
#> [116,] 4.641401 4.002740 6.543573
#> [117,] 5.468574 4.908505 7.634400
#> [118,] 7.748100 7.208468 10.525870
#> [119,] 11.516842 10.776730 15.322388
#> [120,] 3.740498 3.159926 5.557150
#> [121,] 7.803397 7.208468 10.369264
#> [122,] 3.740498 3.159926 5.557150
#> [123,] 6.902494 6.239754 9.591649
#> [124,] 4.880260 4.325645 6.976785
#> [125,] 7.729667 7.145518 10.682476
#> [126,] 12.656605 12.005399 16.637618
#> [127,] 13.539076 12.816738 17.728445
#> [128,] 7.141353 6.625608 9.920457
#> [129,] 12.086724 11.359589 16.032205
#> [130,] 13.539076 12.848213 17.676243
#> [131,] 10.708102 9.933915 14.074956
#> [132,] 4.310379 3.805735 6.162564
#> [133,] 12.105156 11.391064 15.927801
#> [134,] 9.807198 9.122576 13.036331
#> [135,] 10.615939 9.996865 14.231561
#> [136,] 9.549907 8.799671 12.655321
#> [137,] 9.182019 8.508242 12.535321
#> [138,] 10.082923 9.382531 13.469542
#> [139,] 5.211283 4.554125 7.305592
#> [140,] 5.468574 4.814080 7.791006
#> [141,] 7.527673 6.791138 10.197063
#> [142,] 4.880260 4.294170 7.028987
#> [143,] 5.211283 4.554125 7.305592
#> [144,] 6.038456 5.365464 8.553025
#> [145,] 10.689669 9.902441 14.179359
#> [146,] 5.487007 4.908505 7.582198
#> [147,] 11.535275 10.713780 15.374590
#> [148,] 7.233516 6.562658 9.763851
#> [149,] 6.571472 6.137174 9.054034
#> [150,] 12.950762 12.233879 17.070830
#-------------------------------------------
# Estimating subscores using Wainer's method
CTTsub(test.data,method="Wainer")
#> $summary
#> mean SD Augmented.reliability
#> Algebra 9.773333 3.206071 0.9308608
#> Geometry 9.100000 3.133385 0.9311427
#> Measurement 13.060000 4.010296 0.9310656
#>
#> $subscore.original
#> Algebra Geometry Measurement Math
#> [1,] 15 15 20 50
#> [2,] 11 10 14 35
#> [3,] 13 13 20 46
#> [4,] 10 11 18 39
#> [5,] 9 11 15 35
#> [6,] 10 12 17 39
#> [7,] 10 11 18 39
#> [8,] 10 10 13 33
#> [9,] 13 11 17 41
#> [10,] 14 11 19 44
#> [11,] 12 12 16 40
#> [12,] 10 10 11 31
#> [13,] 11 12 15 38
#> [14,] 11 10 12 33
#> [15,] 12 13 13 38
#> [16,] 9 9 12 30
#> [17,] 9 5 10 24
#> [18,] 10 9 15 34
#> [19,] 10 8 13 31
#> [20,] 11 13 16 40
#> [21,] 13 11 13 37
#> [22,] 14 15 19 48
#> [23,] 14 15 19 48
#> [24,] 11 13 17 41
#> [25,] 12 11 17 40
#> [26,] 11 12 15 38
#> [27,] 13 12 18 43
#> [28,] 14 11 18 43
#> [29,] 15 13 17 45
#> [30,] 15 13 18 46
#> [31,] 14 11 17 42
#> [32,] 12 13 16 41
#> [33,] 12 13 19 44
#> [34,] 8 5 13 26
#> [35,] 13 13 18 44
#> [36,] 11 13 14 38
#> [37,] 14 14 19 47
#> [38,] 8 5 13 26
#> [39,] 14 13 20 47
#> [40,] 12 10 12 34
#> [41,] 14 11 18 43
#> [42,] 11 11 17 39
#> [43,] 15 14 18 47
#> [44,] 15 13 17 45
#> [45,] 14 10 17 41
#> [46,] 13 13 18 44
#> [47,] 12 10 19 41
#> [48,] 11 13 18 42
#> [49,] 12 8 14 34
#> [50,] 10 13 17 40
#> [51,] 13 14 16 43
#> [52,] 14 12 16 42
#> [53,] 15 13 19 47
#> [54,] 13 13 16 42
#> [55,] 12 13 16 41
#> [56,] 14 12 15 41
#> [57,] 15 8 18 41
#> [58,] 14 14 20 48
#> [59,] 13 13 17 43
#> [60,] 15 13 19 47
#> [61,] 14 13 19 46
#> [62,] 11 10 14 35
#> [63,] 11 5 11 27
#> [64,] 8 8 12 28
#> [65,] 2 2 4 8
#> [66,] 7 6 5 18
#> [67,] 10 7 8 25
#> [68,] 15 15 18 48
#> [69,] 6 7 10 23
#> [70,] 13 11 15 39
#> [71,] 7 2 7 16
#> [72,] 8 5 8 21
#> [73,] 12 10 15 37
#> [74,] 9 7 11 27
#> [75,] 8 9 16 33
#> [76,] 8 2 8 18
#> [77,] 10 9 12 31
#> [78,] 5 7 10 22
#> [79,] 5 4 4 13
#> [80,] 12 11 18 41
#> [81,] 4 7 11 22
#> [82,] 13 12 12 37
#> [83,] 8 5 8 21
#> [84,] 7 9 15 31
#> [85,] 7 8 10 25
#> [86,] 1 2 6 9
#> [87,] 8 7 10 25
#> [88,] 3 2 9 14
#> [89,] 7 10 14 31
#> [90,] 5 8 6 19
#> [91,] 2 4 2 8
#> [92,] 3 4 9 16
#> [93,] 6 4 5 15
#> [94,] 5 5 8 18
#> [95,] 9 10 8 27
#> [96,] 13 11 17 41
#> [97,] 7 1 5 13
#> [98,] 2 3 6 11
#> [99,] 7 8 11 26
#> [100,] 10 10 14 34
#> [101,] 10 9 13 32
#> [102,] 4 2 8 14
#> [103,] 5 1 9 15
#> [104,] 10 10 9 29
#> [105,] 14 13 17 44
#> [106,] 8 8 10 26
#> [107,] 10 11 16 37
#> [108,] 6 3 9 18
#> [109,] 9 9 13 31
#> [110,] 13 12 17 42
#> [111,] 9 6 16 31
#> [112,] 7 4 11 22
#> [113,] 12 11 13 36
#> [114,] 13 11 14 38
#> [115,] 13 10 13 36
#> [116,] 2 5 7 14
#> [117,] 5 4 8 17
#> [118,] 9 5 11 25
#> [119,] 12 12 14 38
#> [120,] 3 4 4 11
#> [121,] 6 5 14 25
#> [122,] 3 4 4 11
#> [123,] 7 8 7 22
#> [124,] 5 4 6 15
#> [125,] 10 7 8 25
#> [126,] 14 10 18 42
#> [127,] 14 12 19 45
#> [128,] 10 5 8 23
#> [129,] 13 12 15 40
#> [130,] 14 11 20 45
#> [131,] 8 11 16 35
#> [132,] 4 2 7 13
#> [133,] 12 11 17 40
#> [134,] 9 9 14 32
#> [135,] 13 9 13 35
#> [136,] 7 10 14 31
#> [137,] 11 10 9 30
#> [138,] 10 10 13 33
#> [139,] 3 6 7 16
#> [140,] 5 7 5 17
#> [141,] 5 9 10 24
#> [142,] 5 5 5 15
#> [143,] 3 6 7 16
#> [144,] 6 8 5 19
#> [145,] 9 12 14 35
#> [146,] 4 4 9 17
#> [147,] 11 14 13 38
#> [148,] 5 7 11 23
#> [149,] 9 2 10 21
#> [150,] 14 12 17 43
#>
#> $subscore.augmented
#> Algebra Geometry Measurement
#> [1,] 14.990343 14.172447 19.559098
#> [2,] 10.652423 9.976406 14.188895
#> [3,] 13.855137 13.024940 18.032893
#> [4,] 11.852344 11.015454 15.440777
#> [5,] 10.688819 9.879820 14.047290
#> [6,] 11.848295 11.000886 15.465543
#> [7,] 11.852344 11.015454 15.440777
#> [8,] 10.080772 9.388084 13.450559
#> [9,] 12.383551 11.685794 16.345484
#> [10,] 13.251138 12.547772 17.411396
#> [11,] 12.103788 11.356561 15.959489
#> [12,] 9.488899 8.840772 12.795408
#> [13,] 11.532137 10.768239 15.221153
#> [14,] 10.060550 9.429093 13.533744
#> [15,] 11.507867 10.794680 15.329105
#> [16,] 9.217232 8.540674 12.359881
#> [17,] 7.457805 6.957008 10.295364
#> [18,] 10.380757 9.676308 13.753368
#> [19,] 9.496995 8.869908 12.745876
#> [20,] 12.119962 11.300984 15.901070
#> [21,] 11.199804 10.591169 15.035183
#> [22,] 14.418692 13.584126 18.820762
#> [23,] 14.418692 13.584126 18.820762
#> [24,] 12.415898 11.574640 16.228645
#> [25,] 12.107836 11.371129 15.934723
#> [26,] 11.532137 10.768239 15.221153
#> [27,] 12.971376 12.218539 17.025401
#> [28,] 12.955202 12.274116 17.083820
#> [29,] 13.518757 12.833302 17.871689
#> [30,] 13.814693 13.106958 18.199264
#> [31,] 12.659265 12.000459 16.756245
#> [32,] 12.395676 11.615649 16.311831
#> [33,] 13.283486 12.436618 17.294557
#> [34,] 8.069901 7.463311 10.867329
#> [35,] 13.263264 12.477627 17.377742
#> [36,] 11.528089 10.753671 15.245919
#> [37,] 14.126804 13.325037 18.468420
#> [38,] 8.069901 7.463311 10.867329
#> [39,] 14.130852 13.339605 18.443654
#> [40,] 10.336265 9.743759 13.944505
#> [41,] 12.955202 12.274116 17.083820
#> [42,] 11.832122 11.056463 15.523962
#> [43,] 14.106582 13.366046 18.551606
#> [44,] 13.518757 12.833302 17.871689
#> [45,] 12.367377 11.741371 16.403904
#> [46,] 13.263264 12.477627 17.377742
#> [47,] 12.407821 11.659353 16.237532
#> [48,] 12.711835 11.848296 16.556221
#> [49,] 10.344361 9.772895 13.894973
#> [50,] 12.140184 11.259975 15.817884
#> [51,] 12.963279 12.189403 17.074933
#> [52,] 12.655217 11.985892 16.781011
#> [53,] 14.110630 13.380614 18.526840
#> [54,] 12.671391 11.930315 16.722592
#> [55,] 12.395676 11.615649 16.311831
#> [56,] 12.359280 11.712235 16.453436
#> [57,] 12.355251 11.811516 16.437557
#> [58,] 14.422740 13.598694 18.795995
#> [59,] 12.967328 12.203971 17.050167
#> [60,] 14.110630 13.380614 18.526840
#> [61,] 13.834915 13.065949 18.116079
#> [62,] 10.652423 9.976406 14.188895
#> [63,] 8.305171 7.859995 11.444461
#> [64,] 8.649629 7.966920 11.596779
#> [65,] 2.876518 2.335147 4.397562
#> [66,] 5.718582 5.218484 8.188307
#> [67,] 7.725424 7.242538 10.755658
#> [68,] 14.398470 13.625135 18.903947
#> [69,] 7.214439 6.531189 9.767765
#> [70,] 11.791677 11.138482 15.690333
#> [71,] 5.142901 4.729443 7.434092
#> [72,] 6.590218 6.095030 9.229453
#> [73,] 11.224074 10.564728 14.927231
#> [74,] 8.337519 7.748841 11.327623
#> [75,] 10.125264 9.320634 13.259421
#> [76,] 5.714552 5.317765 8.172428
#> [77,] 9.492947 8.855340 12.770642
#> [78,] 6.938724 6.216523 9.357004
#> [79,] 4.287439 3.797320 6.334527
#> [80,] 12.403773 11.644785 16.262299
#> [81,] 6.958946 6.175514 9.273818
#> [82,] 11.195756 10.576601 15.059949
#> [83,] 6.590218 6.095030 9.229453
#> [84,] 9.553613 8.732312 12.521085
#> [85,] 7.782042 7.104942 10.530867
#> [86,] 3.192677 2.567794 4.641951
#> [87,] 7.765868 7.160519 10.589286
#> [88,] 4.631916 4.018094 6.446199
#> [89,] 9.549565 8.717744 12.545851
#> [90,] 6.046866 5.380987 8.399044
#> [91,] 2.868422 2.306012 4.447094
#> [92,] 5.215693 4.536271 7.150882
#> [93,] 4.859090 4.385642 7.072863
#> [94,] 5.763074 5.151034 7.997170
#> [95,] 8.325374 7.705138 11.401921
#> [96,] 12.383551 11.685794 16.345484
#> [97,] 4.259139 3.923042 6.426600
#> [98,] 3.760280 3.141548 5.405054
#> [99,] 8.077978 7.378599 10.858442
#> [100,] 10.376709 9.661741 13.778134
#> [101,] 9.788884 9.128996 13.098217
#> [102,] 4.611694 4.059103 6.529385
#> [103,] 4.891457 4.388336 6.915379
#> [104,] 8.897026 8.293459 12.140257
#> [105,] 13.243042 12.518636 17.460928
#> [106,] 8.057756 7.419608 10.941628
#> [107,] 11.260470 10.468142 14.785626
#> [108,] 5.750948 5.221179 8.030823
#> [109,] 9.513169 8.814331 12.687456
#> [110,] 12.675439 11.944882 16.697826
#> [111,] 9.525313 8.858034 12.613158
#> [112,] 6.910424 6.342245 9.449076
#> [113,] 10.924090 10.276504 14.624422
#> [114,] 11.495741 10.864825 15.362758
#> [115,] 10.907916 10.332081 14.682841
#> [116,] 4.639994 3.933381 6.437312
#> [117,] 5.471185 4.891945 7.644829
#> [118,] 7.753742 7.230664 10.622940
#> [119,] 11.511915 10.809248 15.304339
#> [120,] 3.736010 3.167990 5.513005
#> [121,] 7.814408 7.107637 10.373383
#> [122,] 3.736010 3.167990 5.513005
#> [123,] 6.894232 6.283974 9.548141
#> [124,] 4.879312 4.344633 6.989678
#> [125,] 7.725424 7.242538 10.755658
#> [126,] 12.663313 12.015027 16.731479
#> [127,] 13.543027 12.806860 17.763737
#> [128,] 7.141647 6.724361 10.050975
#> [129,] 12.083566 11.397570 16.042675
#> [130,] 13.547075 12.821428 17.738971
#> [131,] 10.709041 9.838811 13.964104
#> [132,] 4.315757 3.785447 6.201809
#> [133,] 12.107836 11.371129 15.934723
#> [134,] 9.809106 9.087987 13.015032
#> [135,] 10.616027 10.072992 14.330500
#> [136,] 9.549565 8.717744 12.545851
#> [137,] 9.172740 8.608125 12.551018
#> [138,] 10.080772 9.388084 13.450559
#> [139,] 5.207597 4.507135 7.200414
#> [140,] 5.459041 4.848242 7.719127
#> [141,] 7.522501 6.734700 10.061687
#> [142,] 4.875264 4.330065 7.014444
#> [143,] 5.207597 4.507135 7.200414
#> [144,] 6.026644 5.421996 8.482229
#> [145,] 10.684771 9.865252 14.072056
#> [146,] 5.491407 4.850936 7.561643
#> [147,] 11.524040 10.739103 15.270685
#> [148,] 7.234661 6.490180 9.684579
#> [149,] 6.582140 6.179743 9.238340
#> [150,] 12.951154 12.259548 17.108587
#>
# Obtaining descriptive statistics summary for subscores
CTTsub(test.data,method="Wainer")$summary
#> mean SD Augmented.reliability
#> Algebra 9.773333 3.206071 0.9308608
#> Geometry 9.100000 3.133385 0.9311427
#> Measurement 13.060000 4.010296 0.9310656
# Obtaining original subscores
CTTsub(test.data,method="Wainer")$subscore.original
#> Algebra Geometry Measurement Math
#> [1,] 15 15 20 50
#> [2,] 11 10 14 35
#> [3,] 13 13 20 46
#> [4,] 10 11 18 39
#> [5,] 9 11 15 35
#> [6,] 10 12 17 39
#> [7,] 10 11 18 39
#> [8,] 10 10 13 33
#> [9,] 13 11 17 41
#> [10,] 14 11 19 44
#> [11,] 12 12 16 40
#> [12,] 10 10 11 31
#> [13,] 11 12 15 38
#> [14,] 11 10 12 33
#> [15,] 12 13 13 38
#> [16,] 9 9 12 30
#> [17,] 9 5 10 24
#> [18,] 10 9 15 34
#> [19,] 10 8 13 31
#> [20,] 11 13 16 40
#> [21,] 13 11 13 37
#> [22,] 14 15 19 48
#> [23,] 14 15 19 48
#> [24,] 11 13 17 41
#> [25,] 12 11 17 40
#> [26,] 11 12 15 38
#> [27,] 13 12 18 43
#> [28,] 14 11 18 43
#> [29,] 15 13 17 45
#> [30,] 15 13 18 46
#> [31,] 14 11 17 42
#> [32,] 12 13 16 41
#> [33,] 12 13 19 44
#> [34,] 8 5 13 26
#> [35,] 13 13 18 44
#> [36,] 11 13 14 38
#> [37,] 14 14 19 47
#> [38,] 8 5 13 26
#> [39,] 14 13 20 47
#> [40,] 12 10 12 34
#> [41,] 14 11 18 43
#> [42,] 11 11 17 39
#> [43,] 15 14 18 47
#> [44,] 15 13 17 45
#> [45,] 14 10 17 41
#> [46,] 13 13 18 44
#> [47,] 12 10 19 41
#> [48,] 11 13 18 42
#> [49,] 12 8 14 34
#> [50,] 10 13 17 40
#> [51,] 13 14 16 43
#> [52,] 14 12 16 42
#> [53,] 15 13 19 47
#> [54,] 13 13 16 42
#> [55,] 12 13 16 41
#> [56,] 14 12 15 41
#> [57,] 15 8 18 41
#> [58,] 14 14 20 48
#> [59,] 13 13 17 43
#> [60,] 15 13 19 47
#> [61,] 14 13 19 46
#> [62,] 11 10 14 35
#> [63,] 11 5 11 27
#> [64,] 8 8 12 28
#> [65,] 2 2 4 8
#> [66,] 7 6 5 18
#> [67,] 10 7 8 25
#> [68,] 15 15 18 48
#> [69,] 6 7 10 23
#> [70,] 13 11 15 39
#> [71,] 7 2 7 16
#> [72,] 8 5 8 21
#> [73,] 12 10 15 37
#> [74,] 9 7 11 27
#> [75,] 8 9 16 33
#> [76,] 8 2 8 18
#> [77,] 10 9 12 31
#> [78,] 5 7 10 22
#> [79,] 5 4 4 13
#> [80,] 12 11 18 41
#> [81,] 4 7 11 22
#> [82,] 13 12 12 37
#> [83,] 8 5 8 21
#> [84,] 7 9 15 31
#> [85,] 7 8 10 25
#> [86,] 1 2 6 9
#> [87,] 8 7 10 25
#> [88,] 3 2 9 14
#> [89,] 7 10 14 31
#> [90,] 5 8 6 19
#> [91,] 2 4 2 8
#> [92,] 3 4 9 16
#> [93,] 6 4 5 15
#> [94,] 5 5 8 18
#> [95,] 9 10 8 27
#> [96,] 13 11 17 41
#> [97,] 7 1 5 13
#> [98,] 2 3 6 11
#> [99,] 7 8 11 26
#> [100,] 10 10 14 34
#> [101,] 10 9 13 32
#> [102,] 4 2 8 14
#> [103,] 5 1 9 15
#> [104,] 10 10 9 29
#> [105,] 14 13 17 44
#> [106,] 8 8 10 26
#> [107,] 10 11 16 37
#> [108,] 6 3 9 18
#> [109,] 9 9 13 31
#> [110,] 13 12 17 42
#> [111,] 9 6 16 31
#> [112,] 7 4 11 22
#> [113,] 12 11 13 36
#> [114,] 13 11 14 38
#> [115,] 13 10 13 36
#> [116,] 2 5 7 14
#> [117,] 5 4 8 17
#> [118,] 9 5 11 25
#> [119,] 12 12 14 38
#> [120,] 3 4 4 11
#> [121,] 6 5 14 25
#> [122,] 3 4 4 11
#> [123,] 7 8 7 22
#> [124,] 5 4 6 15
#> [125,] 10 7 8 25
#> [126,] 14 10 18 42
#> [127,] 14 12 19 45
#> [128,] 10 5 8 23
#> [129,] 13 12 15 40
#> [130,] 14 11 20 45
#> [131,] 8 11 16 35
#> [132,] 4 2 7 13
#> [133,] 12 11 17 40
#> [134,] 9 9 14 32
#> [135,] 13 9 13 35
#> [136,] 7 10 14 31
#> [137,] 11 10 9 30
#> [138,] 10 10 13 33
#> [139,] 3 6 7 16
#> [140,] 5 7 5 17
#> [141,] 5 9 10 24
#> [142,] 5 5 5 15
#> [143,] 3 6 7 16
#> [144,] 6 8 5 19
#> [145,] 9 12 14 35
#> [146,] 4 4 9 17
#> [147,] 11 14 13 38
#> [148,] 5 7 11 23
#> [149,] 9 2 10 21
#> [150,] 14 12 17 43
# Obtaining subscores that are estimated using Wainer's augmentation method
CTTsub(test.data,method="Wainer")$subscore.augmented
#> Algebra Geometry Measurement
#> [1,] 14.990343 14.172447 19.559098
#> [2,] 10.652423 9.976406 14.188895
#> [3,] 13.855137 13.024940 18.032893
#> [4,] 11.852344 11.015454 15.440777
#> [5,] 10.688819 9.879820 14.047290
#> [6,] 11.848295 11.000886 15.465543
#> [7,] 11.852344 11.015454 15.440777
#> [8,] 10.080772 9.388084 13.450559
#> [9,] 12.383551 11.685794 16.345484
#> [10,] 13.251138 12.547772 17.411396
#> [11,] 12.103788 11.356561 15.959489
#> [12,] 9.488899 8.840772 12.795408
#> [13,] 11.532137 10.768239 15.221153
#> [14,] 10.060550 9.429093 13.533744
#> [15,] 11.507867 10.794680 15.329105
#> [16,] 9.217232 8.540674 12.359881
#> [17,] 7.457805 6.957008 10.295364
#> [18,] 10.380757 9.676308 13.753368
#> [19,] 9.496995 8.869908 12.745876
#> [20,] 12.119962 11.300984 15.901070
#> [21,] 11.199804 10.591169 15.035183
#> [22,] 14.418692 13.584126 18.820762
#> [23,] 14.418692 13.584126 18.820762
#> [24,] 12.415898 11.574640 16.228645
#> [25,] 12.107836 11.371129 15.934723
#> [26,] 11.532137 10.768239 15.221153
#> [27,] 12.971376 12.218539 17.025401
#> [28,] 12.955202 12.274116 17.083820
#> [29,] 13.518757 12.833302 17.871689
#> [30,] 13.814693 13.106958 18.199264
#> [31,] 12.659265 12.000459 16.756245
#> [32,] 12.395676 11.615649 16.311831
#> [33,] 13.283486 12.436618 17.294557
#> [34,] 8.069901 7.463311 10.867329
#> [35,] 13.263264 12.477627 17.377742
#> [36,] 11.528089 10.753671 15.245919
#> [37,] 14.126804 13.325037 18.468420
#> [38,] 8.069901 7.463311 10.867329
#> [39,] 14.130852 13.339605 18.443654
#> [40,] 10.336265 9.743759 13.944505
#> [41,] 12.955202 12.274116 17.083820
#> [42,] 11.832122 11.056463 15.523962
#> [43,] 14.106582 13.366046 18.551606
#> [44,] 13.518757 12.833302 17.871689
#> [45,] 12.367377 11.741371 16.403904
#> [46,] 13.263264 12.477627 17.377742
#> [47,] 12.407821 11.659353 16.237532
#> [48,] 12.711835 11.848296 16.556221
#> [49,] 10.344361 9.772895 13.894973
#> [50,] 12.140184 11.259975 15.817884
#> [51,] 12.963279 12.189403 17.074933
#> [52,] 12.655217 11.985892 16.781011
#> [53,] 14.110630 13.380614 18.526840
#> [54,] 12.671391 11.930315 16.722592
#> [55,] 12.395676 11.615649 16.311831
#> [56,] 12.359280 11.712235 16.453436
#> [57,] 12.355251 11.811516 16.437557
#> [58,] 14.422740 13.598694 18.795995
#> [59,] 12.967328 12.203971 17.050167
#> [60,] 14.110630 13.380614 18.526840
#> [61,] 13.834915 13.065949 18.116079
#> [62,] 10.652423 9.976406 14.188895
#> [63,] 8.305171 7.859995 11.444461
#> [64,] 8.649629 7.966920 11.596779
#> [65,] 2.876518 2.335147 4.397562
#> [66,] 5.718582 5.218484 8.188307
#> [67,] 7.725424 7.242538 10.755658
#> [68,] 14.398470 13.625135 18.903947
#> [69,] 7.214439 6.531189 9.767765
#> [70,] 11.791677 11.138482 15.690333
#> [71,] 5.142901 4.729443 7.434092
#> [72,] 6.590218 6.095030 9.229453
#> [73,] 11.224074 10.564728 14.927231
#> [74,] 8.337519 7.748841 11.327623
#> [75,] 10.125264 9.320634 13.259421
#> [76,] 5.714552 5.317765 8.172428
#> [77,] 9.492947 8.855340 12.770642
#> [78,] 6.938724 6.216523 9.357004
#> [79,] 4.287439 3.797320 6.334527
#> [80,] 12.403773 11.644785 16.262299
#> [81,] 6.958946 6.175514 9.273818
#> [82,] 11.195756 10.576601 15.059949
#> [83,] 6.590218 6.095030 9.229453
#> [84,] 9.553613 8.732312 12.521085
#> [85,] 7.782042 7.104942 10.530867
#> [86,] 3.192677 2.567794 4.641951
#> [87,] 7.765868 7.160519 10.589286
#> [88,] 4.631916 4.018094 6.446199
#> [89,] 9.549565 8.717744 12.545851
#> [90,] 6.046866 5.380987 8.399044
#> [91,] 2.868422 2.306012 4.447094
#> [92,] 5.215693 4.536271 7.150882
#> [93,] 4.859090 4.385642 7.072863
#> [94,] 5.763074 5.151034 7.997170
#> [95,] 8.325374 7.705138 11.401921
#> [96,] 12.383551 11.685794 16.345484
#> [97,] 4.259139 3.923042 6.426600
#> [98,] 3.760280 3.141548 5.405054
#> [99,] 8.077978 7.378599 10.858442
#> [100,] 10.376709 9.661741 13.778134
#> [101,] 9.788884 9.128996 13.098217
#> [102,] 4.611694 4.059103 6.529385
#> [103,] 4.891457 4.388336 6.915379
#> [104,] 8.897026 8.293459 12.140257
#> [105,] 13.243042 12.518636 17.460928
#> [106,] 8.057756 7.419608 10.941628
#> [107,] 11.260470 10.468142 14.785626
#> [108,] 5.750948 5.221179 8.030823
#> [109,] 9.513169 8.814331 12.687456
#> [110,] 12.675439 11.944882 16.697826
#> [111,] 9.525313 8.858034 12.613158
#> [112,] 6.910424 6.342245 9.449076
#> [113,] 10.924090 10.276504 14.624422
#> [114,] 11.495741 10.864825 15.362758
#> [115,] 10.907916 10.332081 14.682841
#> [116,] 4.639994 3.933381 6.437312
#> [117,] 5.471185 4.891945 7.644829
#> [118,] 7.753742 7.230664 10.622940
#> [119,] 11.511915 10.809248 15.304339
#> [120,] 3.736010 3.167990 5.513005
#> [121,] 7.814408 7.107637 10.373383
#> [122,] 3.736010 3.167990 5.513005
#> [123,] 6.894232 6.283974 9.548141
#> [124,] 4.879312 4.344633 6.989678
#> [125,] 7.725424 7.242538 10.755658
#> [126,] 12.663313 12.015027 16.731479
#> [127,] 13.543027 12.806860 17.763737
#> [128,] 7.141647 6.724361 10.050975
#> [129,] 12.083566 11.397570 16.042675
#> [130,] 13.547075 12.821428 17.738971
#> [131,] 10.709041 9.838811 13.964104
#> [132,] 4.315757 3.785447 6.201809
#> [133,] 12.107836 11.371129 15.934723
#> [134,] 9.809106 9.087987 13.015032
#> [135,] 10.616027 10.072992 14.330500
#> [136,] 9.549565 8.717744 12.545851
#> [137,] 9.172740 8.608125 12.551018
#> [138,] 10.080772 9.388084 13.450559
#> [139,] 5.207597 4.507135 7.200414
#> [140,] 5.459041 4.848242 7.719127
#> [141,] 7.522501 6.734700 10.061687
#> [142,] 4.875264 4.330065 7.014444
#> [143,] 5.207597 4.507135 7.200414
#> [144,] 6.026644 5.421996 8.482229
#> [145,] 10.684771 9.865252 14.072056
#> [146,] 5.491407 4.850936 7.561643
#> [147,] 11.524040 10.739103 15.270685
#> [148,] 7.234661 6.490180 9.684579
#> [149,] 6.582140 6.179743 9.238340
#> [150,] 12.951154 12.259548 17.108587