-  Method for Causal Analysis


Statistical results applied for practical use: Deductive Validity



[dd. 2018|02|07 - 00h:15m (16s:701ms) ]


Predictive power of sample correlation for deduction to N=1 samples


- (5) Table values, selected rows of first significance -


Sample Sizes:


N

0 1000000000;

N

1 1000;

N

2 100;

N

3 20;

Significance criteria levels:


Alpha; Max. accepted random error (type I): (

α

≤ 0.050 ).

Epsilon; Max. accepted estimation error: (

ε

≤ 0.050 ).

I. Sample


(observation)

II. Population


(generalization)

III. Individual


('N=1' prediction)

Overall values


Overall values


Averages for individuals


(max. accuracy of re-test estimation)

Values for individuals


(max. confidence of prediction)



Reliability


Partition prediction (scale segment)



(1)
Sgf.
(2)
Min. Sample corr.
(3)
Min. Sample 'signif.' diff. of effect
(4)
Min. Sample count of hits (balanced)
(5)
Max. Inference improved, average
(6)
Min. Sample count of hits (balanced)
(7)
Max. Mutual information, average
(8)
Max. Popul. corr. (gradient)
(9)
Max. Variance accounted for, total
(10)
Sign (1/2) estimate, overall
(11)
Some 4th (quartile) predicted, overall
(12)
Some 5th (quintile) predicted, overall
(13)
Some 10th (decile) predicted, overall
(14)
Some 20th (vigintile) predicted, overall
(15)
Sign (1/2) predicted, average indiv.
(16)
Some 5th (quintile) predicted, average indiv.
(17)
Some 10th (decile) predicted, average indiv.
(18)
Some 20th (vigintile) predicted, average indiv.
 
 
 
 
 
 
 
 
r  > 0.__
(gradient)
 
 
 
p  ≥ 0.95
(prb.)
 
 
 
h

Χ

 ≥ 75.__

(pct.)
 
 
 
c'  ≥ 1.25
(ratio)
 
 
 
h

Χ

 ≥ 90.__

(pct.)
 
 
 
b  ≥ 1.__
(bits)
 
 

α

 ≤ 0.05

ρ  ≥ 0.95
(gradient)
 
 
 
σ2  ≥ 0.95
(pct.)
segm.  ≥ 0.5_

ε

 ≤ 0.05

 
p  ≥ 95.__
(pct.)
segm.  ≥ 0.25

ε

 ≤ 0.05

 
p  ≥ 95.__
(pct.)
segm.  ≥ 0.2_

ε

 ≤ 0.05

 
p  ≥ 95.__
(pct.)
segm.  ≥ 0.1_

ε

 ≤ 0.05

 
p  ≥ 95.__
(pct.)
segm.  ≥ 0.05

ε

 ≤ 0.05

 
p  ≥ 95.__
(pct.)
segm.  ≥ 0.5_

ε

 ≤ 0.05

 
p  ≥ 95.__
(pct.)
segm.  ≥ 0.2_

ε

 ≤ 0.05

 
p  ≥ 95.__
(pct.)
segm.  ≥ 0.1_

ε

 ≤ 0.05

 
p  ≥ 95.__
(pct.)
segm.  ≥ 0.05

ε

 ≤ 0.05

 
p  ≥ 95.__
(pct.)
 

00

*


01
02
03
00.000060
00.000060
00.000060
00.000060

0.9711114

*


0.5007564
0.5002364
0.5001002
050.0030
050.0030
050.0030
050.0030
000001.000000
000001.000000
000001.000000
000001.000000
050.0030
050.0030
050.0030
050.0030
000000.000000
000000.000000
000000.000000
000000.000000
00.000007
00.000000
00.000000
00.000000
0.000000
0.000000
0.000000
0.000000
050.0002
050.0000
050.0000
050.0000
000.0002
000.0000
000.0000
000.0000
000.0001
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
00

01

*


02
03
00.060000
00.060000
00.060000
00.060000
1.0000000

0.9710675

*


0.7234125
0.5992755
052.9999
052.9999
052.9999
052.9999
000001.001801
000001.000031
000001.000000
000001.000000
052.9999
052.9999
052.9999
052.9999
000000.002597
000000.000045
000000.000000
000000.000000
00.059948
00.007967
00.000000
00.000000
0.003593
0.000063
0.000000
0.000000
051.9093
050.2536
050.0000
050.0000
001.5297
000.2025
000.0000
000.0000
001.2162
000.1610
000.0000
000.0000
000.6032
000.0798
000.0000
000.0000
000.3010
000.0398
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
00
01

02

*


03
00.175000
00.175000
00.175000
00.175000
1.0000000
0.9999999

0.9592121

*


0.7699827
058.7500
058.7500
058.7500
058.7500
000001.015664
000001.007787
000001.000047
000001.000000
058.7500
058.7500
058.7500
058.7500
000000.022423
000000.011190
000000.000068
000000.000000
00.174949
00.124073
00.009773
00.000000
0.030607
0.015394
0.000095
0.000000
055.5976
053.9595
050.3111
050.0000
004.5881
003.2044
000.2485
000.0000
003.6463
002.5472
000.1975
000.0000
001.8076
001.2631
000.0980
000.0000
000.9019
000.6302
000.0489
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
00
01
02

03

*


00.400000
00.400000
00.400000
00.400000
1.0000000
1.0000000
0.9999801

0.9601593

*


070.0000
070.0000
070.0000
070.0000
000001.091066
000001.069820
000001.033103
000001.000303
070.0000
070.0000
070.0000
070.0000
000000.125739
000000.097368
000000.046984
000000.000437
00.399956
00.355341
00.251115
00.024621
0.159965
0.126267
0.063058
0.000606
063.0974
061.5635
058.0797
050.7838
011.8160
010.1990
006.7988
000.6263
009.3682
008.0918
005.4004
000.4980
004.6332
004.0043
002.6756
000.2470
002.3106
001.9972
001.3348
000.1232
000.0163
000.0015
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
 

00

*


01

*


02

*


03

*


00.500000
00.500000
00.500000
00.500000
1.0000000
1.0000000
0.9999999
0.9879133

075.0000

*


075.0000

*


075.0000

*


075.0000

*


000001.154670
000001.126172
000001.073955
000001.011313
075.0000
075.0000
075.0000
075.0000
000000.207481
000000.171427
000000.102934
000000.016230
00.499960
00.459913
00.364668
00.149162
0.249960
0.211520
0.132983
0.022249
066.6652
065.2119
061.8817
054.7657
015.8281
014.1555
010.5285
003.8792
012.5151
011.2089
008.3521
003.0833
006.1847
005.5400
004.1326
001.5287
003.0842
002.7626
002.0611
000.7628
000.4381
000.1494
000.0026
000.0000
000.0006
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
 

00

*


01

*


02
03
00.632455
00.632455
00.632455
00.632455
1.0000000
1.0000000
0.9999999
0.9987005
081.6227
081.6227
081.6227
081.6227

000001.290951

*


000001.250184

*


000001.172020
000001.060625
081.6227
081.6227
081.6227
081.6227
000000.368435
000000.322141
000000.228998
000000.084915
00.632424
00.600157
00.521539
00.333246
0.399960
0.360189
0.272003
0.111053
071.7940
070.4895
067.4642
060.8144
021.5138
020.1113
016.7887
009.4358
017.1714
016.0000
013.2420
007.4886
008.5226
007.9247
006.5445
003.7068
004.2549
003.9546
003.2638
001.8489
004.3936
002.8362
000.7124
000.0003
000.1444
000.0527
000.0020
000.0000
000.0006
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
000.0000
00
01

02

*


03
00.700000
00.700000
00.700000
00.700000
1.0000000
1.0000000
0.9999999
0.9997333
084.9999
084.9999
084.9999
084.9999
000001.400229
000001.351085

000001.255362

*


000001.111660
084.9999
084.9999
084.9999
084.9999
000000.485662
000000.434119
000000.328103
000000.152716
00.699973
00.672446
00.604529
00.436807
0.489962
0.452184
0.365455
0.190800
074.6804
073.4756
070.6638
064.3890
024.6031
023.3121
020.2992
013.2311
019.7150
018.6589
016.1575
010.4826
009.8512
009.2944
008.0046
005.1822
004.9248
004.6437
003.9947
002.5842
009.3305
007.0225
003.0203
000.0705
000.7966
000.4202
000.0610
000.0000
000.0175
000.0051
000.0001
000.0000
000.0000
000.0000
000.0000
000.0000
 

00

*


01

*


02

*


03

*


00.800000
00.800000
00.800000
00.800000
1.0000000
1.0000000
1.0000000
0.9999907
090.0000
090.0000
090.0000
090.0000
000001.666597
000001.599425
000001.466209

000001.254858

*


090.0000

*


090.0000

*


090.0000

*


090.0000

*


000000.736905
000000.677553
000000.552090
000000.327524
00.799981
00.780444
00.731323
00.604107
0.639970
0.609094
0.534833
0.364945
079.5157
078.5007
076.1096
070.6470
030.1613
028.9029
026.1582
020.2810
024.2913
023.2533
020.9927
016.1423
012.2504
011.7075
010.5228
007.9969
006.1380
005.8634
005.2643
003.9908
021.7306
018.7598
012.5032
003.0022
005.1094
003.7206
001.5289
000.0601
000.5803
000.3213
000.0603
000.0001
000.0095
000.0030
000.0001
000.0000
 

00

*


01
02
03
00.870000
00.870000
00.870000
00.870000
1.0000000
1.0000000
1.0000000
0.9999997
093.5000
093.5000
093.5000
093.5000
000002.028092
000001.938957
000001.760419
000001.468884
093.5000
093.5000
093.5000
093.5000

000001.020123

*


000000.955281
000000.815919
000000.554721
00.869987
00.856744
00.822996
00.732479
0.756877
0.734011
0.677323
0.536526
083.5873
082.7516
080.7699
076.1637
036.2635
034.8268
031.8310
026.2178
029.3469
028.1522
025.6704
021.0418
014.9018
014.2728
012.9716
010.5486
007.4798
007.1612
006.5028
005.2773
035.1213
032.2092
025.6246
012.6319
014.0481
011.7444
007.2640
001.5639
003.7110
002.6823
001.1128
000.0629
000.3198
000.1741
000.0330
000.0001
00

01

*


02
03
00.880000
00.880000
00.880000
00.880000
1.0000000
1.0000000
1.0000000
0.9999999
093.9999
093.9999
093.9999
093.9999
000002.105283
000002.011659
000001.823889
000001.516166
093.9999
093.9999
093.9999
093.9999
000001.074014

000001.008385

*


000000.867018
000000.600428
00.879988
00.867692
00.836295
00.751653
0.774379
0.752889
0.699390
0.564982
084.2449
083.4397
081.5283
077.0743
037.4848
036.0009
032.9182
027.2369
030.3652
029.1283
026.5698
021.8806
015.4398
014.7865
013.4425
010.9886
007.7525
007.4214
006.7410
005.4998
037.4620
034.6018
028.0866
014.8929
016.0373
013.6231
008.8183
002.2483
004.7111
003.5105
001.5894
000.1249
000.4990
000.2883
000.0649
000.0005
00
01

02

*


03
00.910000
00.910000
00.910000
00.910000
1.0000000
1.0000000
1.0000000
0.9999999
095.5000
095.5000
095.5000
095.5000
000002.411801
000002.300777
000002.077298
000001.707270
095.5000
095.5000
095.5000
095.5000
000001.270110
000001.202121

000001.054708

*


000000.771691
00.909991
00.900606
00.876504
00.810505
0.828083
0.811091
0.768259
0.656919
086.3911
085.6877
084.0130
080.0807
042.1759
040.5025
037.0442
030.8958
034.3043
032.8937
029.9975
024.8977
017.5400
016.7841
015.2453
012.5675
008.8196
008.4350
007.6539
006.2983
045.3579
042.7304
036.6318
023.4560
023.6016
020.9431
015.3181
006.0177
009.3768
007.5894
004.3379
000.7860
001.7787
001.2064
000.4279
000.0170
00
01
02

03

*


00.940000
00.940000
00.940000
00.940000
1.0000000
1.0000000
1.0000000
0.9999999
097.0000
097.0000
097.0000
097.0000
000002.930908
000002.791409
000002.509655
000002.038714
097.0000
097.0000
097.0000
097.0000
000001.551347
000001.480993
000001.327489

000001.027660

*


00.939993
00.933628
00.917185
00.871438
0.883588
0.871662
0.841228
0.759404
088.9169
088.3376
086.9544
083.6812
049.6685
047.7070
043.6291
036.4327
040.7104
039.0177
035.5349
029.4878
021.0381
020.1024
018.2033
014.9761
010.6074
010.1277
009.1575
007.5175
055.0483
052.7944
047.4862
035.4530
034.5171
031.8313
025.8532
014.3227
018.1871
015.8160
011.0071
003.8430
005.9026
004.5949
002.3837
000.3414
 

00

*


01

*


02
03
00.955000
00.955000
00.955000
00.955000
1.0000000
1.0000000
1.0000000
0.9999999
097.7500
097.7500
097.7500
097.7500
000003.371310
000003.208216
000002.878274
000002.324337
097.7500
097.7500
097.7500
097.7500
000001.753309
000001.681771
000001.525204
000001.216819

00.954995

*


00.950180

*


00.937705
00.902719
0.912016
0.902843
0.879292
0.814902
090.4140
089.9101
088.7054
085.8432
055.6053
053.4528
048.9329
040.8598
045.9145
044.0125
040.0742
033.1944
023.9753
022.8905
020.6853
016.9448
012.1210
011.5605
010.4264
008.5168
060.9427
058.9484
054.2234
043.3082
041.9212
039.3573
033.5243
021.5160
025.3293
022.7607
017.2963
007.9616
010.6185
008.7950
005.3953
001.3175
00
01

02

*


03
00.965000
00.965000
00.965000
00.965000
1.0000000
1.0000000
1.0000000
0.9999999
098.2499
098.2499
098.2499
098.2499
000003.812965
000003.626519
000003.248941
000002.613213
098.2499
098.2499
098.2499
098.2499
000001.930913
000001.858585
000001.699969
000001.385825
00.964996
00.961230

00.951453

*


00.923884
0.931218
0.923963
0.905263
0.853563
091.5531
091.1074
090.0409
087.5004
061.1511
058.8613
053.9954
045.1461
050.9068
048.8282
044.4903
036.8251
026.8941
025.6654
023.1617
018.9030
013.6383
012.9978
011.7004
009.5144
065.4851
063.7028
059.4652
049.5684
047.9677
045.5624
040.0160
028.1381
031.7506
029.1377
023.4114
012.7653
015.7467
013.5661
009.2439
003.1205
 

00

*


01
02
03
00.975000
00.975000
00.975000
00.975000
1.0000000
1.0000000
1.0000000
0.9999999
098.7499
098.7499
098.7499
098.7499
000004.500123
000004.277732
000003.826902
000003.065720
098.7499
098.7499
098.7499
098.7499
000002.169964
000002.096846
000001.936177
000001.616226
00.974997
00.972292
00.965255
00.945305

0.950619

*


0.945352
0.931718
0.893601
092.8670
092.4894
091.5846
089.4235
068.9185
066.5220
061.3191
051.5275
058.1774
055.8937
051.0604
042.3263
031.3714
029.9318
026.9857
021.9398
015.9962
015.2337
013.6862
011.0708
070.7744
069.2493
065.6113
057.0323
055.3349
053.1775
048.1396
036.9497
040.1877
037.6531
031.9401
020.4392
023.5821
021.1081
015.9096
007.2680
00

01

*


02

03

*


00.980000
00.980000
00.980000
00.980000
1.0000000
1.0000000
1.0000000
1.0000000
099.0000
099.0000
099.0000
099.0000
000005.024932
000004.775298
000004.268984
000003.412955
099.0000
099.0000
099.0000
099.0000
000002.329104
000002.255590
000002.093893
000001.771021
00.979997
00.977827
00.972176

00.956112

*


0.960395

0.956147

*


0.945127
0.914150
093.6228
093.2845
092.4737
090.5346
074.1239
071.7267
066.4254
056.1461
063.2907
060.9075
055.8025
046.3952
034.7280
033.1388
029.8750
024.2517
017.7923
016.9386
015.2037
012.2641
073.8364
072.4642
069.1860
061.4214
059.7407
057.7545
053.0885
042.5450
045.5129
043.0883
037.5497
025.9688
029.0847
026.5301
021.0093
011.0935
00
01

02

*


03
00.985000
00.985000
00.985000
00.985000
1.0000000
1.0000000
1.0000000
1.0000000
099.2500
099.2500
099.2500
099.2500
000005.794978
000005.505579
000004.918323
000003.924103
099.2500
099.2500
099.2500
099.2500
000002.534803
000002.460894
000002.298166
000001.972363
00.984998
00.983366
00.979112
00.966984
0.970221
0.967009

0.958660

*


0.935058
094.4795
094.1861
093.4826
091.7978
080.6309
078.3403
073.1176
062.4795
070.0675
067.6234
062.2839
052.1250
039.5368
037.7470
034.0510
027.6238
020.4159
019.4318
017.4279
014.0200
077.3220
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00

*


01
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095.0123

*


094.7469
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00

01

*


02

03

*


00.990000
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0.956333

*


095.4944

095.2545

*


094.6790
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00
01

02

*


03
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096.0988
095.8909

095.3921

*


094.1950
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00

*


01

*


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00.995000
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096.2378

095.2588

*


097.5205

*


096.6827

*


094.2389
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00
01

02

*


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098.2104
097.5315

095.4650

*


088.8126
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00

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01
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090.8052

095.4478

*


094.2314
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00

01

*


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095.0074

*


091.9483
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00
01

02

*


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099.5084
098.7550

095.2042

*


098.1391
097.4397

095.3181

*


088.5234
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00
01
02

03

*


00.998150
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099.5059
098.7469

095.1631

*


085.6188
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00

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099.3051

095.3575

*


094.1184
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072.8472
00

01

*


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096.4328

095.3720

*


092.4067
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074.1930
 

00

*


01

02

*


03
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098.3039
097.6422

095.6057

*


088.9329
076.4324
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068.4391
057.4012

095.0896

*


094.8274
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081.7968
077.1560
00

01

*


02
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00.999350
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095.2682

095.0156

*


094.4088
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077.9665
00
01

02

*


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094.1128
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065.3637
095.8499
095.6282

095.0960

*


093.8166
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00
01
02

03

*


00.999550
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098.8382

095.3668

*


086.1045
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00
01
02

03

*


00.999675
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096.0460

095.0142

*


094.7118
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087.5425
084.3257
 

00

*


01
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095.2902

095.0044

*


094.7378
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085.1841
00

01

*


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095.5404
095.2696

095.0171

*


094.4109
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085.9635
 

00

*


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099.2861

095.3346

*


094.0897
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00

01

*


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096.2041

095.1010

*


092.0402
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00
01

02

*


03
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095.8508
095.6293

095.0974

*


093.8192
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00
01

02

*


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098.1293
097.4224

095.2738

*


088.3668
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088.3035
 

00

*


01
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095.8976
094.8276

095.0917

*


094.8298
094.2009
092.6903
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092.6933
091.8061
089.6769
00

01

*


02

03

*


00.999870
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096.4758
096.0468

095.0156

*


095.2701

095.0176

*


094.4116
092.9555
093.3148
092.9585
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090.0506
00
01
02

03

*


00.999890
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098.9251

095.5869

*


098.0533
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00
01

02

*


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095.8511
095.6296

095.0978

*


093.8200
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093.0717
091.2689
 

00

*


01
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094.8281

095.0920

*


094.8301
094.2013
092.6910
00

01

*


02

03

*


00.999940
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096.6141
096.2020

095.2113

*


095.4557

095.2131

*


094.6308
093.2319
00
01

02

*


03
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095.8513
095.6298

095.0981

*


093.8204
00
01
02

03

*


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096.2021

095.2115

*