Computing subscores using Haberman's method based on both observed total scores and observed subscores.
subscore.sx.RdThis function estimate true subscores based on both observed total scores and 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 observed subscores and total score.
- subscore.sx
Subscores that are estimated based on both the observed total score and 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
test.data<-data.prep(scored.data,c(3,15,15,20),
c("Algebra","Geometry","Measurement", "Math"))
subscore.sx(test.data)
#> $summary
#> Orig.mean Orig.sd subscore.sx.mean subscore.sx.sd
#> Algebra 9.773333 3.662153 9.773333 3.206067
#> Geometry 9.100000 3.626432 9.100000 3.133019
#> Measurement 13.060000 4.539506 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
#> Original.reliability PRMSE.sx
#> Algebra 0.8169114 0.9382038
#> Geometry 0.7987169 0.9344893
#> Measurement 0.8346106 0.9348423
#> 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.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
#>
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)$Disattenuated.correlation
#> Algebra Geometry Measurement
#> Algebra 0.8169114 1.0081315 1.0096427
#> Geometry 0.8143313 0.7987169 1.0042016
#> Measurement 0.8336757 0.8198970 0.8346106
subscore.sx(test.data)$summary
#> Orig.mean Orig.sd subscore.sx.mean subscore.sx.sd
#> Algebra 9.773333 3.662153 9.773333 3.206067
#> Geometry 9.100000 3.626432 9.100000 3.133019
#> Measurement 13.060000 4.539506 13.060000 4.009773
subscore.sx(test.data)$PRMSE
#> Original.reliability PRMSE.sx
#> Algebra 0.8169114 0.9382038
#> Geometry 0.7987169 0.9344893
#> Measurement 0.8346106 0.9348423
#> Math 0.9311719 NA
subscore.sx(test.data)$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