Maximum consistency of incomplete data
via non-invasive imputation
(SIMULATION DATA)
 
G. Gediga & I. Düntsch

This document contains the simulation data for

Maximum consistency of incomplete data via non-invasive imputation

The variable parameters are

      Number of different granules $\displaystyle n$ $\displaystyle = 500,400,300,200,100$
      Number of attributes $\displaystyle k$ $\displaystyle = 10,8,6,4$
      Number of attribute values $\displaystyle m$ $\displaystyle = 6,5,4,3,2$
      Percentage of missing values $\displaystyle p$ $\displaystyle = 0.5, 0.2, 0.15, 0.10, 0.05, 0.02$
      Number of missing values $\displaystyle s$ $\displaystyle = 500 \cdot p$

Not all combinations were possible, since we have to observe

    $\displaystyle n \le m^k.$

For each combination we have randomly generated 100 information systems, each with $ N = 500$ objects.

Reported are the the mean ($ \mu$) and variance ($ \sigma$) of the following functions:

  1. The percentage of missing values which were replaced by one value (Certain replacements).
  2. $ \operatorname{len}= \frac{\sum_{i=1}^ s\ensuremath{\lvert t_i \rvert}}{s \cdot m}$, the average size of a replacement list when taken over all lists, relative to the number $ m$ of possible values.
  3. The number of replacement errors, i.e. those incidences for which the original value was not among the suggested values.


Table 1: p = 0.5
    Attr. Certain repl $ \operatorname{len}$ Error ($ e$)
Grans. ($ n$) Attr. ($ k$) values ($ m$) $ \mu$ $ \sigma$ $ \mu$ $ \sigma$ $ \mu$ $ \sigma$
500 10 6 0.005 0.002 0.900 0.006 136.910 20.775
500 10 5 0.003 0.001 0.944 0.004 73.420 8.399
500 10 4 0.001 0.001 0.980 0.002 26.330 5.567
500 10 3 0.000 0.000 0.998 0.001 3.010 1.605
500 10 2 0.000 0.000 1.000 0.000 0.000 0.000
400 10 6 0.005 0.002 0.900 0.007 122.910 15.304
400 10 5 0.003 0.001 0.944 0.004 66.150 9.753
400 10 4 0.001 0.001 0.980 0.003 23.150 5.502
400 10 3 0.000 0.000 0.998 0.001 2.170 1.272
400 10 2 0.000 0.000 1.000 0.000 0.000 0.000
300 10 6 0.005 0.002 0.901 0.006 100.110 12.529
300 10 5 0.002 0.001 0.945 0.005 52.810 9.270
300 10 4 0.001 0.001 0.980 0.002 19.110 4.546
300 10 3 0.000 0.000 0.998 0.001 1.930 1.533
300 10 2 0.000 0.000 1.000 0.000 0.010 0.100
200 10 6 0.004 0.002 0.900 0.006 68.770 10.526
200 10 5 0.002 0.001 0.945 0.004 36.690 7.183
200 10 4 0.001 0.000 0.979 0.002 13.430 4.493
200 10 3 0.000 0.000 0.998 0.001 1.440 1.297
200 10 2 0.000 0.000 1.000 0.000 0.000 0.000
100 10 6 0.003 0.001 0.896 0.006 20.650 5.515
100 10 5 0.002 0.001 0.942 0.005 11.870 4.141
100 10 4 0.001 0.001 0.978 0.003 3.950 2.157
100 10 3 0.000 0.000 0.997 0.001 0.540 0.688
100 10 2 0.000 0.000 1.000 0.000 0.000 0.000
500 8 6 0.000 0.000 0.969 0.004 33.080 7.289
500 8 5 0.000 0.000 0.987 0.002 13.450 3.860
500 8 4 0.000 0.000 0.997 0.001 3.250 1.533
500 8 3 0.000 0.000 1.000 0.000 0.150 0.386
400 8 6 0.000 0.000 0.970 0.004 28.630 6.314
400 8 5 0.000 0.000 0.986 0.002 13.010 4.331
400 8 4 0.000 0.000 0.997 0.001 3.090 1.875
400 8 3 0.000 0.000 1.000 0.000 0.140 0.450
300 8 6 0.000 0.000 0.970 0.004 24.430 5.151
300 8 5 0.000 0.000 0.987 0.002 10.540 3.611
300 8 4 0.000 0.000 0.997 0.001 2.530 1.761
300 8 3 0.000 0.000 1.000 0.000 0.140 0.377
200 8 6 0.000 0.000 0.969 0.004 16.890 4.662
200 8 5 0.000 0.000 0.986 0.003 7.180 3.514
200 8 4 0.000 0.000 0.996 0.001 1.940 1.549
200 8 3 0.000 0.000 1.000 0.000 0.120 0.327
200 8 2 0.000 0.000 1.000 0.000 0.000 0.000
100 8 6 0.000 0.000 0.965 0.005 5.380 2.987
100 8 5 0.000 0.000 0.984 0.003 2.420 1.843
100 8 4 0.000 0.000 0.996 0.001 0.720 0.911
100 8 3 0.000 0.000 1.000 0.000 0.020 0.141
100 8 2 0.000 0.000 1.000 0.000 0.000 0.000
500 6 6 0.000 0.000 0.996 0.001 3.340 2.208
500 6 5 0.000 0.000 0.999 0.001 0.980 0.985
500 6 4 0.000 0.000 1.000 0.000 0.110 0.345
500 6 3 0.000 0.000 1.000 0.000 0.000 0.000
400 6 6 0.000 0.000 0.996 0.002 2.750 2.022
400 6 5 0.000 0.000 0.999 0.001 0.800 0.853
400 6 4 0.000 0.000 1.000 0.000 0.070 0.256
400 6 3 0.000 0.000 1.000 0.000 0.000 0.000
300 6 6 0.000 0.000 0.996 0.001 2.260 1.857
300 6 5 0.000 0.000 0.999 0.001 0.730 0.802
300 6 4 0.000 0.000 1.000 0.000 0.180 0.435
300 6 3 0.000 0.000 1.000 0.000 0.000 0.000
200 6 6 0.000 0.000 0.995 0.002 1.840 1.434
200 6 5 0.000 0.000 0.999 0.001 0.620 0.814
200 6 4 0.000 0.000 1.000 0.000 0.090 0.351
200 6 3 0.000 0.000 1.000 0.000 0.000 0.000
100 6 6 0.000 0.000 0.994 0.002 0.780 0.991
100 6 5 0.000 0.000 0.998 0.001 0.250 0.500
100 6 4 0.000 0.000 1.000 0.000 0.030 0.171
100 6 3 0.000 0.000 1.000 0.000 0.000 0.000
500 4 6 0.000 0.000 1.000 0.000 0.050 0.219
500 4 5 0.000 0.000 1.000 0.000 0.000 0.000
400 4 6 0.000 0.000 1.000 0.000 0.020 0.141
400 4 5 0.000 0.000 1.000 0.000 0.000 0.000
300 4 6 0.000 0.000 1.000 0.000 0.010 0.100
300 4 5 0.000 0.000 1.000 0.000 0.000 0.000
200 4 6 0.000 0.000 1.000 0.000 0.010 0.100
200 4 5 0.000 0.000 1.000 0.000 0.010 0.100
200 4 4 0.000 0.000 1.000 0.000 0.000 0.000
100 4 6 0.000 0.000 1.000 0.001 0.020 0.141
100 4 5 0.000 0.000 1.000 0.000 0.000 0.000
100 4 4 0.000 0.000 1.000 0.000 0.000 0.000


Table 2: p = 0.2
    Attr. Certain repl $ \operatorname{len}$ Error ($ e$)
Grans. ($ n$) Attr. ($ k$) values ($ m$) $ \mu$ $ \sigma$ $ \mu$ $ \sigma$ $ \mu$ $ \sigma$
500 10 6 0.918 0.022 0.022 0.008 453.840 453.078
500 10 5 0.871 0.032 0.046 0.014 442.780 445.770
500 10 4 0.767 0.034 0.111 0.019 406.450 409.343
500 10 3 0.505 0.033 0.345 0.029 280.440 264.119
500 10 2 0.053 0.008 0.947 0.008 21.190 4.541
400 10 6 0.910 0.032 0.025 0.011 379.640 375.534
400 10 5 0.861 0.034 0.049 0.015 369.780 368.444
400 10 4 0.744 0.039 0.122 0.024 335.560 344.317
400 10 3 0.486 0.032 0.358 0.030 231.510 255.206
400 10 2 0.053 0.008 0.947 0.008 17.540 4.333
300 10 6 0.893 0.028 0.029 0.010 280.180 264.112
300 10 5 0.839 0.039 0.056 0.017 272.760 259.015
300 10 4 0.726 0.034 0.129 0.020 247.280 256.432
300 10 3 0.470 0.027 0.367 0.023 172.600 137.786
300 10 2 0.052 0.008 0.948 0.008 13.820 4.253
200 10 6 0.872 0.031 0.035 0.011 147.060 32.194
200 10 5 0.817 0.036 0.063 0.016 144.590 15.932
200 10 4 0.687 0.039 0.147 0.023 132.260 17.820
200 10 3 0.441 0.031 0.386 0.028 90.120 13.429
200 10 2 0.054 0.009 0.946 0.009 8.290 2.948
100 10 6 0.858 0.027 0.038 0.009 21.420 8.315
100 10 5 0.796 0.039 0.069 0.016 21.800 8.739
100 10 4 0.664 0.039 0.155 0.023 19.860 7.934
100 10 3 0.427 0.029 0.390 0.026 13.290 5.756
100 10 2 0.067 0.009 0.933 0.009 1.290 1.343
500 8 6 0.620 0.047 0.148 0.027 318.450 321.500
500 8 5 0.519 0.040 0.228 0.027 276.610 266.215
500 8 4 0.359 0.031 0.395 0.028 207.910 251.562
500 8 3 0.139 0.017 0.718 0.020 90.820 10.576
400 8 6 0.598 0.043 0.157 0.025 261.110 256.479
400 8 5 0.500 0.044 0.237 0.030 229.930 256.649
400 8 4 0.351 0.029 0.396 0.027 175.360 149.107
400 8 3 0.134 0.017 0.722 0.020 74.240 10.761
300 8 6 0.581 0.041 0.158 0.022 192.740 220.712
300 8 5 0.483 0.040 0.244 0.029 173.560 149.133
300 8 4 0.327 0.028 0.411 0.024 125.460 11.962
300 8 3 0.126 0.016 0.726 0.022 55.350 8.721
200 8 6 0.552 0.047 0.168 0.025 106.760 14.415
200 8 5 0.450 0.044 0.253 0.031 92.240 11.098
200 8 4 0.305 0.036 0.420 0.032 68.010 10.775
200 8 3 0.116 0.016 0.731 0.021 29.240 6.459
200 8 2 0.002 0.002 0.998 0.002 0.490 0.810
100 8 6 0.518 0.039 0.175 0.021 15.440 6.531
100 8 5 0.424 0.042 0.259 0.027 12.140 5.416
100 8 4 0.294 0.032 0.416 0.030 9.500 4.756
100 8 3 0.123 0.018 0.711 0.024 4.110 2.636
100 8 2 0.005 0.003 0.995 0.003 0.120 0.383
500 6 6 0.151 0.022 0.502 0.026 127.500 12.377
500 6 5 0.093 0.018 0.633 0.027 92.130 11.175
500 6 4 0.036 0.010 0.809 0.019 47.320 8.164
500 6 3 0.003 0.003 0.972 0.006 9.050 3.707
400 6 6 0.142 0.026 0.505 0.028 104.760 12.624
400 6 5 0.088 0.018 0.636 0.029 75.980 10.747
400 6 4 0.031 0.009 0.815 0.018 38.580 6.673
400 6 3 0.002 0.002 0.972 0.006 7.530 2.761
300 6 6 0.128 0.026 0.516 0.031 74.950 11.158
300 6 5 0.082 0.017 0.636 0.030 55.520 9.464
300 6 4 0.029 0.008 0.816 0.017 28.600 6.024
300 6 3 0.003 0.002 0.971 0.008 5.530 2.508
200 6 6 0.121 0.022 0.510 0.028 39.990 6.965
200 6 5 0.072 0.015 0.641 0.024 29.550 6.891
200 6 4 0.028 0.009 0.809 0.019 15.250 4.549
200 6 3 0.003 0.002 0.969 0.006 2.900 2.062
100 6 6 0.111 0.024 0.504 0.031 6.020 3.225
100 6 5 0.068 0.017 0.625 0.030 4.370 2.665
100 6 4 0.029 0.008 0.791 0.020 2.300 1.801
100 6 3 0.005 0.003 0.957 0.008 0.480 0.759
500 4 6 0.000 0.000 0.946 0.011 11.130 3.776
500 4 5 0.000 0.000 0.985 0.005 4.350 2.397
400 4 6 0.000 0.000 0.941 0.011 10.100 3.799
400 4 5 0.000 0.000 0.983 0.007 3.610 2.550
300 4 6 0.000 0.000 0.939 0.012 6.700 2.646
300 4 5 0.000 0.000 0.982 0.006 2.700 1.856
200 4 6 0.000 0.000 0.938 0.015 3.760 2.375
200 4 5 0.000 0.000 0.978 0.008 1.550 1.452
200 4 4 0.000 0.000 0.998 0.002 0.260 0.661
100 4 6 0.000 0.001 0.920 0.018 0.650 1.086
100 4 5 0.000 0.000 0.968 0.010 0.320 0.680
100 4 4 0.000 0.000 0.996 0.004 0.030 0.171


Table 3: p = 0.15
    Attr. Certain repl $ \operatorname{len}$ Error ($ e$)
Grans. ($ n$) Attr. ($ k$) values ($ m$) $ \mu$ $ \sigma$ $ \mu$ $ \sigma$ $ \mu$ $ \sigma$
500 10 6 0.974 0.015 0.006 0.004 323.740 334.635
500 10 5 0.956 0.016 0.013 0.006 321.030 330.918
500 10 4 0.906 0.023 0.038 0.011 308.760 302.643
500 10 3 0.734 0.032 0.165 0.024 258.100 256.452
500 10 2 0.152 0.017 0.848 0.017 46.080 6.683
400 10 6 0.968 0.017 0.007 0.005 261.840 257.938
400 10 5 0.950 0.020 0.015 0.007 262.150 256.523
400 10 4 0.893 0.028 0.043 0.013 253.050 256.573
400 10 3 0.721 0.033 0.172 0.025 213.490 251.462
400 10 2 0.148 0.016 0.852 0.016 37.820 6.904
300 10 6 0.966 0.016 0.008 0.004 185.310 191.863
300 10 5 0.940 0.020 0.018 0.007 182.670 177.483
300 10 4 0.883 0.029 0.047 0.013 178.460 165.797
300 10 3 0.699 0.033 0.185 0.024 153.550 12.085
300 10 2 0.149 0.015 0.851 0.015 28.320 5.414
200 10 6 0.960 0.021 0.009 0.006 91.570 13.486
200 10 5 0.931 0.026 0.021 0.009 91.630 10.952
200 10 4 0.869 0.027 0.052 0.013 89.960 12.218
200 10 3 0.669 0.033 0.202 0.023 77.230 11.187
200 10 2 0.153 0.018 0.847 0.018 15.350 4.520
100 10 6 0.951 0.020 0.011 0.005 11.420 4.967
100 10 5 0.924 0.026 0.022 0.008 10.230 4.756
100 10 4 0.853 0.031 0.058 0.014 11.450 5.433
100 10 3 0.668 0.035 0.199 0.024 9.800 4.367
100 10 2 0.179 0.019 0.821 0.019 2.010 1.817
500 8 6 0.833 0.038 0.051 0.016 246.320 256.849
500 8 5 0.760 0.039 0.091 0.020 237.310 256.658
500 8 4 0.601 0.033 0.204 0.023 199.700 236.693
500 8 3 0.320 0.026 0.504 0.026 116.500 12.148
400 8 6 0.809 0.037 0.059 0.015 201.560 246.361
400 8 5 0.738 0.044 0.100 0.022 189.910 213.179
400 8 4 0.589 0.045 0.207 0.028 166.780 104.826
400 8 3 0.304 0.026 0.516 0.027 95.810 11.639
300 8 6 0.803 0.037 0.057 0.015 142.980 21.392
300 8 5 0.719 0.046 0.106 0.022 138.390 13.370
300 8 4 0.568 0.043 0.217 0.029 117.930 12.082
300 8 3 0.292 0.027 0.524 0.026 67.690 9.169
200 8 6 0.773 0.042 0.066 0.017 72.520 11.102
200 8 5 0.695 0.045 0.112 0.023 70.240 8.487
200 8 4 0.537 0.041 0.232 0.028 57.690 9.345
200 8 3 0.287 0.026 0.521 0.025 36.890 6.495
200 8 2 0.010 0.005 0.990 0.005 1.610 1.340
100 8 6 0.763 0.042 0.068 0.016 8.840 4.380
100 8 5 0.675 0.045 0.118 0.021 8.660 4.083
100 8 4 0.532 0.041 0.227 0.026 7.040 4.170
100 8 3 0.296 0.029 0.503 0.030 4.860 2.878
100 8 2 0.022 0.008 0.978 0.008 0.270 0.649
500 6 6 0.348 0.039 0.300 0.028 131.270 11.570
500 6 5 0.244 0.030 0.432 0.028 103.170 10.528
500 6 4 0.115 0.017 0.648 0.027 64.100 8.230
500 6 3 0.016 0.007 0.920 0.015 18.700 4.792
400 6 6 0.339 0.047 0.301 0.036 107.160 11.452
400 6 5 0.227 0.034 0.441 0.031 84.580 10.660
400 6 4 0.110 0.023 0.646 0.030 53.370 8.092
400 6 3 0.016 0.007 0.917 0.012 15.930 4.100
300 6 6 0.316 0.040 0.310 0.029 76.560 9.297
300 6 5 0.217 0.030 0.439 0.030 60.970 8.747
300 6 4 0.109 0.021 0.643 0.025 38.700 6.371
300 6 3 0.016 0.007 0.915 0.012 11.630 3.749
200 6 6 0.302 0.037 0.310 0.032 38.250 6.795
200 6 5 0.209 0.033 0.436 0.034 31.910 6.104
200 6 4 0.098 0.020 0.644 0.026 19.240 5.525
200 6 3 0.016 0.007 0.910 0.014 6.030 2.316
100 6 6 0.283 0.045 0.309 0.033 5.000 2.828
100 6 5 0.203 0.036 0.425 0.035 4.060 2.339
100 6 4 0.103 0.022 0.619 0.030 2.570 2.128
100 6 3 0.024 0.010 0.883 0.018 1.020 1.206
500 4 6 0.000 0.001 0.864 0.020 20.030 4.959
500 4 5 0.000 0.001 0.950 0.011 9.980 3.241
400 4 6 0.000 0.001 0.869 0.019 15.270 3.863
400 4 5 0.000 0.000 0.947 0.011 8.500 3.249
300 4 6 0.000 0.001 0.862 0.020 11.400 3.806
300 4 5 0.000 0.001 0.944 0.013 5.670 2.551
200 4 6 0.001 0.001 0.849 0.024 6.180 2.779
200 4 5 0.000 0.000 0.938 0.013 2.840 1.968
200 4 4 0.000 0.000 0.992 0.004 0.850 1.077
100 4 6 0.001 0.002 0.821 0.027 0.970 1.114
100 4 5 0.000 0.002 0.907 0.018 0.400 0.667
100 4 4 0.000 0.000 0.981 0.008 0.120 0.409


Table 4: p = 0.10
    Attr. Certain repl $ \operatorname{len}$ Error ($ e$)
Grans. ($ n$) Attr. ($ k$) values ($ m$) $ \mu$ $ \sigma$ $ \mu$ $ \sigma$ $ \mu$ $ \sigma$
500 10 6 0.994 0.007 0.001 0.002 202.250 249.051
500 10 5 0.988 0.009 0.003 0.003 206.080 251.687
500 10 4 0.969 0.015 0.011 0.006 199.960 242.308
500 10 3 0.883 0.028 0.065 0.019 185.510 193.640
500 10 2 0.331 0.025 0.669 0.025 68.750 8.708
400 10 6 0.994 0.008 0.001 0.002 163.530 80.219
400 10 5 0.986 0.010 0.004 0.003 163.710 71.563
400 10 4 0.968 0.017 0.012 0.007 161.930 80.090
400 10 3 0.875 0.026 0.069 0.016 150.730 33.983
400 10 2 0.325 0.025 0.675 0.025 54.750 7.653
300 10 6 0.993 0.008 0.002 0.002 113.340 11.558
300 10 5 0.985 0.012 0.004 0.003 111.250 13.218
300 10 4 0.963 0.015 0.013 0.006 110.090 11.632
300 10 3 0.867 0.028 0.073 0.017 105.900 11.047
300 10 2 0.327 0.028 0.673 0.028 39.720 6.472
200 10 6 0.992 0.009 0.002 0.002 53.790 8.468
200 10 5 0.981 0.013 0.005 0.004 54.380 8.802
200 10 4 0.954 0.018 0.016 0.006 52.150 8.844
200 10 3 0.852 0.033 0.082 0.019 50.900 9.516
200 10 2 0.333 0.029 0.667 0.029 20.050 4.711
100 10 6 0.991 0.011 0.002 0.003 5.400 3.309
100 10 5 0.981 0.014 0.005 0.004 5.250 2.973
100 10 4 0.953 0.021 0.017 0.008 5.700 3.211
100 10 3 0.851 0.031 0.082 0.018 5.560 3.105
100 10 2 0.370 0.031 0.630 0.031 2.630 2.281
500 8 6 0.945 0.026 0.014 0.008 160.510 49.915
500 8 5 0.911 0.032 0.027 0.012 159.910 56.049
500 8 4 0.821 0.036 0.075 0.017 147.690 10.778
500 8 3 0.556 0.038 0.290 0.031 111.710 11.614
400 8 6 0.939 0.025 0.015 0.008 128.240 12.431
400 8 5 0.902 0.029 0.030 0.010 127.350 12.085
400 8 4 0.805 0.041 0.082 0.021 119.940 11.075
400 8 3 0.546 0.042 0.294 0.033 89.310 10.401
300 8 6 0.930 0.027 0.017 0.008 89.150 10.664
300 8 5 0.890 0.029 0.033 0.011 87.790 10.391
300 8 4 0.784 0.041 0.090 0.021 83.250 10.923
300 8 3 0.535 0.046 0.301 0.034 62.990 9.065
200 8 6 0.921 0.029 0.019 0.008 42.380 8.554
200 8 5 0.880 0.034 0.036 0.013 42.480 7.769
200 8 4 0.771 0.043 0.095 0.022 40.250 6.875
200 8 3 0.517 0.041 0.307 0.032 30.490 6.640
200 8 2 0.040 0.010 0.960 0.010 4.120 2.114
100 8 6 0.922 0.029 0.018 0.008 4.810 3.087
100 8 5 0.875 0.040 0.037 0.014 4.700 3.060
100 8 4 0.770 0.037 0.092 0.018 4.440 2.500
100 8 3 0.531 0.042 0.293 0.031 3.370 2.394
100 8 2 0.080 0.017 0.920 0.017 0.540 0.869
500 6 6 0.619 0.046 0.134 0.025 104.490 9.776
500 6 5 0.493 0.048 0.224 0.032 91.450 8.047
500 6 4 0.307 0.039 0.414 0.033 70.320 9.634
500 6 3 0.069 0.016 0.799 0.021 30.880 5.911
400 6 6 0.599 0.051 0.140 0.027 83.360 8.744
400 6 5 0.471 0.047 0.232 0.030 73.300 9.344
400 6 4 0.290 0.040 0.424 0.036 56.290 8.645
400 6 3 0.068 0.015 0.796 0.021 26.080 4.769
300 6 6 0.572 0.051 0.146 0.028 57.680 7.693
300 6 5 0.463 0.049 0.230 0.032 52.080 7.992
300 6 4 0.277 0.035 0.426 0.032 38.240 6.418
300 6 3 0.068 0.018 0.793 0.025 17.140 4.231
200 6 6 0.556 0.054 0.147 0.026 27.690 6.101
200 6 5 0.440 0.055 0.238 0.035 25.140 5.821
200 6 4 0.267 0.042 0.422 0.038 19.200 5.015
200 6 3 0.070 0.017 0.778 0.024 8.590 3.306
100 6 6 0.547 0.056 0.145 0.025 2.770 2.059
100 6 5 0.451 0.054 0.223 0.032 2.350 1.789
100 6 4 0.286 0.040 0.396 0.036 2.170 1.949
100 6 3 0.095 0.026 0.729 0.029 1.140 1.181
500 4 6 0.011 0.009 0.722 0.033 26.990 4.817
500 4 5 0.001 0.003 0.866 0.021 16.900 4.554
400 4 6 0.009 0.009 0.715 0.032 21.340 4.957
400 4 5 0.002 0.003 0.863 0.023 13.720 3.939
300 4 6 0.009 0.008 0.709 0.032 15.600 4.662
300 4 5 0.002 0.004 0.850 0.021 9.910 3.266
200 4 6 0.009 0.008 0.689 0.036 8.000 3.275
200 4 5 0.003 0.004 0.831 0.024 4.880 2.516
200 4 4 0.000 0.001 0.969 0.010 1.940 1.483
100 4 6 0.012 0.010 0.658 0.037 0.840 0.972
100 4 5 0.004 0.005 0.788 0.028 0.580 0.912
100 4 4 0.000 0.002 0.932 0.016 0.190 0.563


Table 5: p = 0.05
    Attr. Certain repl $ \operatorname{len}$ Error ($ e$)
Grans. ($ n$) Attr. ($ k$) values ($ m$) $ \mu$ $ \sigma$ $ \mu$ $ \sigma$ $ \mu$ $ \sigma$
500 10 6 0.999 0.004 0.000 0.001 95.620 8.753
500 10 5 0.998 0.005 0.001 0.001 97.060 10.039
500 10 4 0.994 0.008 0.002 0.003 96.430 9.476
500 10 3 0.963 0.018 0.020 0.010 95.960 8.832
500 10 2 0.571 0.037 0.429 0.037 60.880 7.227
400 10 6 0.999 0.002 0.000 0.000 75.940 8.091
400 10 5 0.998 0.006 0.001 0.002 75.670 8.260
400 10 4 0.993 0.010 0.002 0.003 75.870 7.888
400 10 3 0.959 0.020 0.021 0.011 73.840 9.126
400 10 2 0.563 0.035 0.437 0.035 48.620 6.740
300 10 6 0.999 0.004 0.000 0.001 51.290 7.027
300 10 5 0.997 0.006 0.001 0.002 51.530 7.520
300 10 4 0.992 0.008 0.003 0.003 52.790 7.563
300 10 3 0.957 0.020 0.022 0.011 50.270 7.614
300 10 2 0.560 0.039 0.440 0.039 33.590 6.122
200 10 6 0.999 0.005 0.000 0.001 23.030 5.040
200 10 5 0.998 0.005 0.000 0.001 23.250 5.480
200 10 4 0.993 0.011 0.002 0.004 22.550 5.213
200 10 3 0.954 0.020 0.024 0.011 23.220 4.717
200 10 2 0.582 0.045 0.418 0.045 16.090 4.085
100 10 6 1.000 0.002 0.000 0.000 1.780 1.460
100 10 5 0.997 0.008 0.001 0.002 1.910 1.747
100 10 4 0.991 0.011 0.003 0.004 2.380 1.994
100 10 3 0.954 0.023 0.023 0.012 1.860 1.747
100 10 2 0.639 0.049 0.361 0.049 1.760 1.571
500 8 6 0.990 0.011 0.002 0.003 77.360 7.411
500 8 5 0.978 0.016 0.006 0.005 76.960 8.043
500 8 4 0.945 0.024 0.020 0.009 76.390 7.098
500 8 3 0.792 0.038 0.118 0.024 67.430 7.685
400 8 6 0.990 0.012 0.002 0.002 61.930 7.757
400 8 5 0.975 0.018 0.007 0.006 61.200 7.506
400 8 4 0.937 0.026 0.023 0.011 58.600 6.057
400 8 3 0.779 0.041 0.126 0.026 54.040 7.513
300 8 6 0.984 0.015 0.003 0.003 40.190 6.932
300 8 5 0.971 0.021 0.008 0.006 41.460 5.870
300 8 4 0.929 0.029 0.025 0.011 40.050 6.172
300 8 3 0.768 0.044 0.132 0.028 36.270 5.263
200 8 6 0.983 0.019 0.004 0.006 17.730 4.653
200 8 5 0.969 0.021 0.008 0.006 19.880 5.205
200 8 4 0.927 0.031 0.026 0.012 18.300 4.391
200 8 3 0.765 0.038 0.132 0.023 16.840 4.855
200 8 2 0.136 0.025 0.864 0.025 6.690 2.766
100 8 6 0.984 0.016 0.003 0.004 1.530 1.381
100 8 5 0.969 0.023 0.008 0.006 1.600 1.537
100 8 4 0.928 0.031 0.026 0.012 1.410 1.518
100 8 3 0.797 0.048 0.111 0.029 1.750 1.585
100 8 2 0.246 0.037 0.754 0.037 0.660 0.807
500 6 6 0.850 0.048 0.039 0.015 55.190 7.602
500 6 5 0.763 0.052 0.078 0.021 54.070 6.569
500 6 4 0.582 0.060 0.198 0.037 47.460 6.620
500 6 3 0.218 0.038 0.591 0.036 32.060 5.416
400 6 6 0.846 0.042 0.039 0.014 43.990 5.571
400 6 5 0.747 0.052 0.085 0.021 41.960 5.642
400 6 4 0.567 0.051 0.202 0.032 37.280 5.061
400 6 3 0.224 0.039 0.577 0.037 26.060 4.649
300 6 6 0.836 0.042 0.041 0.014 29.950 5.008
300 6 5 0.731 0.051 0.087 0.021 28.750 5.030
300 6 4 0.561 0.063 0.203 0.036 24.360 5.454
300 6 3 0.223 0.038 0.570 0.039 17.650 3.804
200 6 6 0.831 0.055 0.043 0.018 13.540 3.617
200 6 5 0.733 0.057 0.086 0.023 13.430 4.063
200 6 4 0.549 0.057 0.201 0.032 11.600 3.094
200 6 3 0.238 0.039 0.540 0.036 8.620 2.810
100 6 6 0.826 0.052 0.042 0.015 1.240 1.357
100 6 5 0.749 0.062 0.077 0.022 1.530 1.267
100 6 4 0.585 0.060 0.179 0.033 1.140 1.164
100 6 3 0.298 0.049 0.476 0.039 0.850 0.968
500 4 6 0.084 0.031 0.479 0.043 23.610 4.197
500 4 5 0.019 0.015 0.693 0.031 19.870 4.211
400 4 6 0.086 0.031 0.473 0.041 18.930 4.056
400 4 5 0.021 0.016 0.685 0.035 15.100 3.419
300 4 6 0.089 0.032 0.464 0.042 13.070 3.427
300 4 5 0.026 0.017 0.665 0.032 10.180 3.092
200 4 6 0.086 0.033 0.443 0.045 5.800 2.507
200 4 5 0.033 0.021 0.632 0.043 4.980 2.256
200 4 4 0.001 0.003 0.894 0.019 2.940 1.890
100 4 6 0.115 0.040 0.396 0.046 0.520 0.858
100 4 5 0.054 0.026 0.553 0.051 0.370 0.661
100 4 4 0.015 0.014 0.786 0.035 0.290 0.518


Table 6: p = 0.02
    Attr. Certain repl $ \operatorname{len}$ Error ($ e$)
Grans. ($ n$) Attr. ($ k$) values ($ m$) $ \mu$ $ \sigma$ $ \mu$ $ \sigma$ $ \mu$ $ \sigma$
500 10 6 1.000 0.000 0.000 0.000 37.090 5.334
500 10 5 0.999 0.003 0.000 0.001 37.270 5.327
500 10 4 0.999 0.004 0.000 0.001 36.720 5.414
500 10 3 0.987 0.016 0.006 0.008 37.030 5.729
500 10 2 0.723 0.046 0.277 0.046 33.050 5.254
400 10 6 1.000 0.000 0.000 0.000 29.950 5.108
400 10 5 1.000 0.002 0.000 0.000 30.190 4.890
400 10 4 0.998 0.006 0.001 0.002 29.550 5.311
400 10 3 0.985 0.014 0.007 0.007 29.010 5.060
400 10 2 0.722 0.055 0.278 0.055 25.540 4.021
300 10 6 1.000 0.000 0.000 0.000 19.230 4.442
300 10 5 1.000 0.001 0.000 0.000 20.010 4.143
300 10 4 1.000 0.002 0.000 0.001 19.420 4.137
300 10 3 0.983 0.017 0.009 0.008 19.790 4.309
300 10 2 0.717 0.053 0.284 0.053 16.370 3.472
200 10 6 1.000 0.000 0.000 0.000 7.960 2.874
200 10 5 0.999 0.004 0.000 0.001 8.380 2.838
200 10 4 0.998 0.006 0.001 0.002 8.780 3.445
200 10 3 0.983 0.016 0.009 0.008 8.440 2.897
200 10 2 0.744 0.049 0.256 0.049 7.470 2.841
100 10 6 1.000 0.000 0.000 0.000 0.630 0.960
100 10 5 0.999 0.003 0.000 0.001 0.770 1.004
100 10 4 1.000 0.003 0.000 0.001 0.700 0.870
100 10 3 0.988 0.016 0.006 0.008 0.700 0.969
100 10 2 0.815 0.052 0.185 0.052 0.720 0.900
500 8 6 0.998 0.009 0.000 0.002 29.880 3.993
500 8 5 0.994 0.012 0.002 0.003 29.790 4.648
500 8 4 0.978 0.023 0.008 0.008 28.980 4.738
500 8 3 0.887 0.040 0.060 0.022 28.750 4.024
400 8 6 0.998 0.007 0.000 0.001 22.460 4.193
400 8 5 0.992 0.014 0.002 0.004 23.830 4.568
400 8 4 0.977 0.019 0.008 0.006 23.800 4.262
400 8 3 0.888 0.042 0.059 0.023 22.930 4.276
300 8 6 0.999 0.005 0.000 0.001 15.790 4.123
300 8 5 0.995 0.012 0.001 0.003 16.150 3.804
300 8 4 0.975 0.024 0.009 0.008 15.620 3.698
300 8 3 0.882 0.041 0.062 0.023 15.440 3.630
200 8 6 0.997 0.009 0.001 0.002 7.030 2.649
200 8 5 0.994 0.012 0.002 0.003 6.860 2.184
200 8 4 0.972 0.027 0.009 0.009 6.770 2.441
200 8 3 0.889 0.042 0.057 0.022 6.550 2.840
200 8 2 0.241 0.049 0.759 0.049 4.530 2.267
100 8 6 0.999 0.006 0.000 0.001 0.610 0.875
100 8 5 0.993 0.017 0.002 0.004 0.630 0.849
100 8 4 0.979 0.025 0.007 0.008 0.740 0.949
100 8 3 0.914 0.044 0.044 0.023 0.490 0.798
100 8 2 0.436 0.060 0.564 0.060 0.410 0.683
500 6 6 0.938 0.038 0.013 0.009 22.280 3.556
500 6 5 0.890 0.052 0.031 0.017 21.810 3.733
500 6 4 0.750 0.070 0.102 0.033 21.280 3.893
500 6 3 0.371 0.071 0.426 0.061 18.230 3.604
400 6 6 0.939 0.037 0.013 0.009 17.240 3.423
400 6 5 0.884 0.056 0.032 0.016 17.220 3.871
400 6 4 0.755 0.070 0.095 0.031 16.890 3.345
400 6 3 0.377 0.061 0.420 0.050 13.980 3.188
300 6 6 0.943 0.037 0.012 0.009 11.250 3.403
300 6 5 0.882 0.052 0.032 0.014 11.290 3.204
300 6 4 0.735 0.071 0.104 0.033 10.610 3.467
300 6 3 0.368 0.062 0.415 0.050 9.230 2.428
200 6 6 0.935 0.041 0.014 0.010 4.570 2.512
200 6 5 0.891 0.048 0.030 0.015 4.950 2.086
200 6 4 0.755 0.064 0.093 0.027 5.120 2.380
200 6 3 0.409 0.071 0.370 0.052 4.200 2.025
100 6 6 0.948 0.040 0.011 0.008 0.510 0.772
100 6 5 0.897 0.052 0.027 0.015 0.440 0.686
100 6 4 0.802 0.068 0.073 0.029 0.440 0.701
100 6 3 0.526 0.077 0.281 0.051 0.350 0.626
500 4 6 0.240 0.077 0.299 0.049 12.600 2.825
500 4 5 0.071 0.043 0.538 0.052 12.150 3.252
400 4 6 0.225 0.072 0.302 0.051 10.220 2.608
400 4 5 0.085 0.045 0.517 0.047 9.060 2.469
300 4 6 0.251 0.078 0.276 0.059 7.130 2.596
300 4 5 0.098 0.048 0.482 0.053 6.030 2.072
200 4 6 0.258 0.082 0.258 0.050 2.940 1.699
200 4 5 0.130 0.063 0.429 0.051 3.000 1.664
200 4 4 0.014 0.026 0.792 0.040 2.280 1.422
100 4 6 0.346 0.088 0.206 0.040 0.280 0.514
100 4 5 0.214 0.072 0.333 0.049 0.280 0.533
100 4 4 0.072 0.045 0.590 0.058 0.160 0.420



1999-11-28