Discriminant Analysis by
Mahalanobis Distance
Calculation
Discriminant calibration data file = C:\WHEATDSC.JCM
Discriminant equation file name = C:\WHEATDSC.MDL
Date = Tue Mar 25 2003
Time = 19:33:11
Number of samples in each group:
1 COARSE GRIND 30
2 WHOLE WHEAT 35
3 FINE GRIND 31
Results:
Wavelengths: 1282 1149 1163
Means:
COARSE GRIND 0.2393440 0.2264164 0.2451990
WHOLE WHEAT 0.2148125 0.1732105 0.2132334
FINE GRIND 0.1267060 0.1128753 0.1239823
Std. Devs.: 0.0108633 0.00884742 0.0102018
Mahalanobis distance between groups:
From group #1, COARSE GRIND
to group #2, WHOLE WHEAT = 42.3454
to group #3, FINE GRIND = 26.0376
From group #2, WHOLE WHEAT
to group #3, FINE GRIND = 61.5706
Sum of 1 / D^2 = 0.0022965
Sums 1 / D^2 with wavelength eliminated:
Wavelength eliminated = 1282: 0.012522
Wavelength eliminated = 1149: 0.027272
Wavelength eliminated = 1163: 0.021293
Mahalanobis distances for each sample:
Sample COARSE GRIND WHOLE WHEAT FINE GRIND Classif. as:
COARSE GRIND 1.4872 42.600 25.111 COARSE GRIND
COARSE GRIND 1.4872 42.600 25.111 COARSE GRIND
COARSE GRIND 1.1068 43.431 25.293 COARSE GRIND
COARSE GRIND 1.1068 43.431 25.293 COARSE GRIND
COARSE GRIND 0.3832 42.052 26.35 COARSE GRIND
COARSE GRIND 0.3832 42.052 26.35 COARSE GRIND
COARSE GRIND 1.4355 41.490 25.809 COARSE GRIND
COARSE GRIND 1.4355 41.490 25.809 COARSE GRIND
COARSE GRIND 2.2937 43.972 26.480 COARSE GRIND
COARSE GRIND 2.2937 43.972 26.480 COARSE GRIND
COARSE GRIND 1.7703 42.663 27.108 COARSE GRIND
COARSE GRIND 1.7703 42.663 27.108 COARSE GRIND
COARSE GRIND 0.9577 41.811 26.097 COARSE GRIND
COARSE GRIND 0.9577 41.811 26.097 COARSE GRIND
COARSE GRIND 1.002 41.718 26.614 COARSE GRIND
COARSE GRIND 1.002 41.718 26.614 COARSE GRIND
COARSE GRIND 0.9003 42.076 25.553 COARSE GRIND
COARSE GRIND 0.9003 42.076 25.553 COARSE GRIND
COARSE GRIND 0.7344 42.305 25.937 COARSE GRIND
COARSE GRIND 0.7344 42.305 25.937 COARSE GRIND
COARSE GRIND 1.8957 40.491 27.479 COARSE GRIND
COARSE GRIND 1.8957 40.491 27.479 COARSE GRIND
COARSE GRIND 1.5631 40.788 26.894 COARSE GRIND
COARSE GRIND 1.5631 40.788 26.894 COARSE GRIND
COARSE GRIND 1.6599 43.855 24.830 COARSE GRIND
COARSE GRIND 1.6599 43.855 24.830 COARSE GRIND
COARSE GRIND 0.9566 42.175 25.863 COARSE GRIND
COARSE GRIND 0.9566 42.175 25.863 COARSE GRIND
COARSE GRIND 1.7531 43.911 25.565 COARSE GRIND
COARSE GRIND 1.7531 43.911 25.565 COARSE GRIND
WHOLE WHEAT 41.168 3.8675 61.357 WHOLE WHEAT
WHOLE WHEAT 42.934 4.8022 63.277 WHOLE WHEAT
WHOLE WHEAT 40.075 2.3516 59.281 WHOLE WHEAT
WHOLE WHEAT 40.277 2.3583 59.837 WHOLE WHEAT
WHOLE WHEAT 41.533 2.6225 61.180 WHOLE WHEAT
WHOLE WHEAT 40.640 1.8023 59.805 WHOLE WHEAT
WHOLE WHEAT 43.921 1.8170 62.753 WHOLE WHEAT
WHOLE WHEAT 42.85 1.4066 62.444 WHOLE WHEAT
WHOLE WHEAT 42.774 0.8003 61.995 WHOLE WHEAT
WHOLE WHEAT 43.261 1.3433 62.749 WHOLE WHEAT
WHOLE WHEAT 42.42 2.1102 61.834 WHOLE WHEAT
WHOLE WHEAT 42.114 3.4572 61.651 WHOLE WHEAT
WHOLE WHEAT 42.471 3.6584 60.441 WHOLE WHEAT
WHOLE WHEAT 39.600 3.0384 58.704 WHOLE WHEAT
WHOLE WHEAT 42.878 2.5438 61.257 WHOLE WHEAT
WHOLE WHEAT 44.013 1.8800 63.252 WHOLE WHEAT
WHOLE WHEAT 41.179 2.2626 59.978 WHOLE WHEAT
WHOLE WHEAT 42.227 3.9463 61.386 WHOLE WHEAT
WHOLE WHEAT 41.201 1.4543 60.187 WHOLE WHEAT
WHOLE WHEAT 41.966 0.5107 61.242 WHOLE WHEAT
WHOLE WHEAT 42.733 2.4023 62.685 WHOLE WHEAT
WHOLE WHEAT 42.801 1.6000 61.665 WHOLE WHEAT
WHOLE WHEAT 42.737 1.7726 62.41 WHOLE WHEAT
WHOLE WHEAT 42.858 1.5694 61.597 WHOLE WHEAT
WHOLE WHEAT 43.704 2.1799 62.361 WHOLE WHEAT
WHOLE WHEAT 42.957 1.0323 62.306 WHOLE WHEAT
WHOLE WHEAT 42.408 1.6403 61.381 WHOLE WHEAT
WHOLE WHEAT 41.793 1.3658 60.732 WHOLE WHEAT
WHOLE WHEAT 42.749 1.2435 62.111 WHOLE WHEAT
WHOLE WHEAT 42.009 2.6357 60.361 WHOLE WHEAT
WHOLE WHEAT 43.656 1.8327 63.193 WHOLE WHEAT
WHOLE WHEAT 42.125 0.8171 61.278 WHOLE WHEAT
WHOLE WHEAT 43.160 2.9626 62.442 WHOLE WHEAT
WHOLE WHEAT 46.068 3.8958 65.198 WHOLE WHEAT
WHOLE WHEAT 42.610 2.0217 61.814 WHOLE WHEAT
FINE GRIND 25.842 61.463 0.2403 FINE GRIND
FINE GRIND 25.97 61.508 0.1388 FINE GRIND
FINE GRIND 26.436 62.272 0.7882 FINE GRIND
FINE GRIND 26.077 61.621 0.4111 FINE GRIND
FINE GRIND 25.404 61.758 1.5853 FINE GRIND
FINE GRIND 25.628 61.186 0.4406 FINE GRIND
FINE GRIND 26.313 62.045 0.5252 FINE GRIND
FINE GRIND 25.649 61.152 0.4245 FINE GRIND
FINE GRIND 25.574 61.069 0.5079 FINE GRIND
FINE GRIND 26.012 61.475 0.1364 FINE GRIND
FINE GRIND 25.441 60.978 0.6347 FINE GRIND
FINE GRIND 25.738 61.386 0.3346 FINE GRIND
FINE GRIND 25.917 61.534 0.1686 FINE GRIND
FINE GRIND 25.759 61.123 0.5259 FINE GRIND
FINE GRIND 25.223 60.590 0.9841 FINE GRIND
FINE GRIND 26.195 61.629 0.2170 FINE GRIND
FINE GRIND 26.335 61.714 0.4179 FINE GRIND
FINE GRIND 27.274 62.853 1.3542 FINE GRIND
FINE GRIND 26.440 61.969 0.4286 FINE GRIND
FINE GRIND 26.574 61.943 0.6299 FINE GRIND
FINE GRIND 25.892 61.210 0.4900 FINE GRIND
FINE GRIND 26.205 61.562 0.4507 FINE GRIND
FINE GRIND 25.728 61.51 0.5205 FINE GRIND
FINE GRIND 27.366 63.155 1.5914 FINE GRIND
FINE GRIND 26.572 62.016 0.5643 FINE GRIND
FINE GRIND 25.432 60.810 0.7648 FINE GRIND
FINE GRIND 25.699 61.013 0.6495 FINE GRIND
FINE GRIND 26.771 62.233 0.8295 FINE GRIND
FINE GRIND 26.310 61.738 0.3025 FINE GRIND
FINE GRIND 26.096 61.423 0.4035 FINE GRIND
FINE GRIND 25.412 60.778 0.7954 FINE GRIND
CLASSIFICATION MATRIX
Class Actual class
Found.
| COAR WHOL FINE
V
COARSE GRIND 30 0 0
WHOLE WHEAT 0 35 0
FINE GRIND 0 0 31
RMS groupsizes
COARSE GRIND: 1.4163898
WHOLE WHEAT: 2.4138575
FINE GRIND: 0.69282997
Inverse Covariance Matrix & other things more useful to computers than to people
8854447.5471396632 7537736.6808868274 -15829581.815224703
7537736.6808868088 6957039.9331944697 -13938546.555546027
-15829581.815224688 -13938546.555546047 28705709.589367542
Mahalanobis distances for each sample
excluded from calculations:
Sample # COARSE GRIND WHOLE WHEAT FINE GRIND Classif. as:
COARSE GRIND COARSE 1 1.5488 42.388 25.087 COARSE GRIND
COARSE GRIND COARSE 2 1.5488 42.388 25.087 COARSE GRIND
COARSE GRIND COARSE 3 1.1463 43.474 25.230 COARSE GRIND
COARSE GRIND COARSE 4 1.1463 43.474 25.230 COARSE GRIND
COARSE GRIND COARSE 5 0.3946 41.844 26.220 COARSE GRIND
COARSE GRIND COARSE 6 0.3946 41.844 26.220 COARSE GRIND
COARSE GRIND COARSE 7 1.4936 41.426 25.675 COARSE GRIND
COARSE GRIND COARSE 8 1.4936 41.426 25.675 COARSE GRIND
COARSE GRIND COARSE 9 2.4298 44.414 26.381 COARSE GRIND
COARSE GRIND COARSE 10 2.4298 44.414 26.381 COARSE GRIND
COARSE GRIND COARSE 11 1.8529 42.463 27.145 COARSE GRIND
COARSE GRIND COARSE 12 1.8529 42.463 27.145 COARSE GRIND
COARSE GRIND COARSE 13 0.9903 41.648 25.957 COARSE GRIND
COARSE GRIND COARSE 14 0.9903 41.648 25.957 COARSE GRIND
COARSE GRIND COARSE 15 1.0365 41.580 26.521 COARSE GRIND
COARSE GRIND COARSE 16 1.0365 41.580 26.521 COARSE GRIND
COARSE GRIND COARSE 17 0.9304 41.864 25.446 COARSE GRIND
COARSE GRIND COARSE 18 0.9304 41.864 25.446 COARSE GRIND
COARSE GRIND COARSE 19 0.7578 42.078 25.8 COARSE GRIND
COARSE GRIND COARSE 20 0.7578 42.078 25.8 COARSE GRIND
COARSE GRIND COARSE 21 1.9893 41.038 27.659 COARSE GRIND
COARSE GRIND COARSE 22 1.9893 41.038 27.659 COARSE GRIND
COARSE GRIND COARSE 23 1.6298 41.107 26.865 COARSE GRIND
COARSE GRIND COARSE 24 1.6298 41.107 26.865 COARSE GRIND
COARSE GRIND COARSE 25 1.7338 44.170 24.887 COARSE GRIND
COARSE GRIND COARSE 26 1.7338 44.170 24.887 COARSE GRIND
COARSE GRIND COARSE 27 0.9891 41.953 25.727 COARSE GRIND
COARSE GRIND COARSE 28 0.9891 41.953 25.727 COARSE GRIND
COARSE GRIND COARSE 29 1.8343 44.271 25.452 COARSE GRIND
COARSE GRIND COARSE 30 1.8343 44.271 25.452 COARSE GRIND
WHOLE WHEAT WHOLE 1 41.214 4.3227 61.029 WHOLE WHEAT
WHOLE WHEAT WHOLE 2 42.924 5.6698 64.485 WHOLE WHEAT
WHOLE WHEAT WHOLE 3 41.012 2.4827 60.698 WHOLE WHEAT
WHOLE WHEAT WHOLE 4 41.013 2.4902 60.503 WHOLE WHEAT
WHOLE WHEAT WHOLE 5 41.439 2.7902 60.890 WHOLE WHEAT
WHOLE WHEAT WHOLE 6 41.067 1.8785 60.505 WHOLE WHEAT
WHOLE WHEAT WHOLE 7 44.293 1.8943 62.913 WHOLE WHEAT
WHOLE WHEAT WHOLE 8 42.682 1.4558 62.373 WHOLE WHEAT
WHOLE WHEAT WHOLE 9 42.586 0.8222 61.722 WHOLE WHEAT
WHOLE WHEAT WHOLE 10 43.230 1.3889 62.887 WHOLE WHEAT
WHOLE WHEAT WHOLE 11 42.195 2.2143 61.532 WHOLE WHEAT
WHOLE WHEAT WHOLE 12 41.889 3.7918 61.330 WHOLE WHEAT
WHOLE WHEAT WHOLE 13 42.263 4.0483 60.514 WHOLE WHEAT
WHOLE WHEAT WHOLE 14 41.093 3.2778 61.167 WHOLE WHEAT
WHOLE WHEAT WHOLE 15 42.738 2.7001 60.951 WHOLE WHEAT
WHOLE WHEAT WHOLE 16 44.457 1.9626 63.904 WHOLE WHEAT
WHOLE WHEAT WHOLE 17 41.248 2.3832 60.486 WHOLE WHEAT
WHOLE WHEAT WHOLE 18 42.001 4.4282 61.056 WHOLE WHEAT
WHOLE WHEAT WHOLE 19 41.268 1.5063 60.488 WHOLE WHEAT
WHOLE WHEAT WHOLE 20 41.772 0.5236 60.947 WHOLE WHEAT
WHOLE WHEAT WHOLE 21 42.553 2.5397 62.820 WHOLE WHEAT
WHOLE WHEAT WHOLE 22 42.625 1.6612 61.338 WHOLE WHEAT
WHOLE WHEAT WHOLE 23 42.550 1.8464 62.327 WHOLE WHEAT
WHOLE WHEAT WHOLE 24 42.696 1.6285 61.266 WHOLE WHEAT
WHOLE WHEAT WHOLE 25 43.943 2.2912 62.263 WHOLE WHEAT
WHOLE WHEAT WHOLE 26 42.815 1.0631 62.154 WHOLE WHEAT
WHOLE WHEAT WHOLE 27 42.182 1.7043 61.060 WHOLE WHEAT
WHOLE WHEAT WHOLE 28 41.632 1.4126 60.632 WHOLE WHEAT
WHOLE WHEAT WHOLE 29 42.560 1.2839 61.879 WHOLE WHEAT
WHOLE WHEAT WHOLE 30 41.798 2.8054 60.506 WHOLE WHEAT
WHOLE WHEAT WHOLE 31 43.847 1.9113 63.776 WHOLE WHEAT
WHOLE WHEAT WHOLE 32 41.908 0.8396 60.975 WHOLE WHEAT
WHOLE WHEAT WHOLE 33 43.138 3.1875 62.427 WHOLE WHEAT
WHOLE WHEAT WHOLE 34 49.763 4.3604 70.160 WHOLE WHEAT
WHOLE WHEAT WHOLE 35 42.403 2.1170 61.507 WHOLE WHEAT
FINE GRIND FINE 1 25.708 61.135 0.2471 FINE GRIND
FINE GRIND FINE 2 25.829 61.177 0.1427 FINE GRIND
FINE GRIND FINE 3 26.317 62.102 0.8128 FINE GRIND
FINE GRIND FINE 4 25.936 61.290 0.4229 FINE GRIND
FINE GRIND FINE 5 25.315 61.439 1.6517 FINE GRIND
FINE GRIND FINE 6 25.513 60.905 0.4533 FINE GRIND
FINE GRIND FINE 7 26.183 61.785 0.5406 FINE GRIND
FINE GRIND FINE 8 25.532 60.879 0.4367 FINE GRIND
FINE GRIND FINE 9 25.465 60.822 0.5227 FINE GRIND
FINE GRIND FINE 10 25.872 61.147 0.1402 FINE GRIND
FINE GRIND FINE 11 25.353 60.764 0.6537 FINE GRIND
FINE GRIND FINE 12 25.611 61.066 0.3441 FINE GRIND
FINE GRIND FINE 13 25.780 61.203 0.1733 FINE GRIND
FINE GRIND FINE 14 25.631 60.859 0.5413 FINE GRIND
FINE GRIND FINE 15 25.176 60.577 1.0168 FINE GRIND
FINE GRIND FINE 16 26.057 61.298 0.2231 FINE GRIND
FINE GRIND FINE 17 26.206 61.4 0.4299 FINE GRIND
FINE GRIND FINE 18 27.355 63.077 1.4058 FINE GRIND
FINE GRIND FINE 19 26.321 61.688 0.4410 FINE GRIND
FINE GRIND FINE 20 26.472 61.656 0.6488 FINE GRIND
FINE GRIND FINE 21 25.756 60.922 0.5043 FINE GRIND
FINE GRIND FINE 22 26.067 61.230 0.4637 FINE GRIND
FINE GRIND FINE 23 25.602 61.179 0.5357 FINE GRIND
FINE GRIND FINE 24 27.488 63.682 1.6583 FINE GRIND
FINE GRIND FINE 25 26.470 61.748 0.5810 FINE GRIND
FINE GRIND FINE 26 25.344 60.671 0.7886 FINE GRIND
FINE GRIND FINE 27 25.575 60.785 0.6690 FINE GRIND
FINE GRIND FINE 28 26.705 62.046 0.8557 FINE GRIND
FINE GRIND FINE 29 26.179 61.414 0.3111 FINE GRIND
FINE GRIND FINE 30 25.955 61.098 0.4151 FINE GRIND
FINE GRIND FINE 31 25.328 60.655 0.8203 FINE GRIND
CLASSIFICATION MATRIX
Class Actual class
Found.
| COAR WHOL FINE
V
COARSE GRIND 30 0 0
WHOLE WHEAT 0 35 0
FINE GRIND 0 0 31