Computing subscores using Haberman's method based on observed subscores.
subscore.s.RdThis function estimate true subscores based on observed subscores, using the method introduced by Haberman (2008) <doi:10.3102/1076998607302636>.
Value
- summary
Summary of obtained subscores (e.g., mean, sd).
- PRMSE
PRMSEs of obtained subscores (for Haberman's methods only).
- subscore.original
Original subscores and total score.
- subscore.s
Subscores that are estimated based on the observed subscore.
References
Haberman, S. J. (2008). "When can subscores have value?." Journal of Educational and Behavioral Statistics, 33(2), 204-229. doi:10.3102/1076998607302636.
Examples
# Transferring scored response data to the required list format
test.data<-data.prep(scored.data,c(3,15,15,20),
c("Algebra","Geometry","Measurement", "Math"))
# Estimate true subscores using Haberman's method based on observed subscores
subscore.s(test.data)
#> $summary
#> Orig.mean Orig.sd subscore.s.mean subscore.s.sd
#> Algebra 9.773333 3.662153 9.773333 2.991654
#> Geometry 9.100000 3.626432 9.100000 2.896492
#> Measurement 13.060000 4.539506 13.060000 3.788720
#>
#> $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
#> Original.reliability PRMSE.s
#> Algebra 0.8169114 0.8169114
#> Geometry 0.7987169 0.7987169
#> Measurement 0.8346106 0.8346106
#> Math 0.9311719 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.s(test.data)$summary
#> Orig.mean Orig.sd subscore.s.mean subscore.s.sd
#> Algebra 9.773333 3.662153 9.773333 2.991654
#> Geometry 9.100000 3.626432 9.100000 2.896492
#> Measurement 13.060000 4.539506 13.060000 3.788720
subscore.s(test.data)$Correlation
#> Algebra Geometry Measurement Math
#> Algebra 1.0000000 0.8143313 0.8336757 0.9357667
#> Geometry 0.8143313 1.0000000 0.8198970 0.9295419
#> Measurement 0.8336757 0.8198970 1.0000000 0.9507132
#> Math 0.9357667 0.9295419 0.9507132 1.0000000
subscore.s(test.data)$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
subscore.s(test.data)$PRMSE
#> Original.reliability PRMSE.s
#> Algebra 0.8169114 0.8169114
#> Geometry 0.7987169 0.7987169
#> Measurement 0.8346106 0.8346106
#> Math 0.9311719 NA
subscore.s(test.data)$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