-  Method for Causal Analysis


Statistical results applied for practical use: Deductive Validity



[dd. 2018|02|06 - 23h:08m (27s:072ms) ]


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


- (3) Table values, marking those 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
00.000001
00.000001
00.000001
00.000001
0.5126191
0.5000126
0.5000039
0.5000016
050.000050
050.000050
050.000050
050.000050
000001.000000
000001.000000
000001.000000
000001.000000
050.000050
050.000050
050.000050
050.000050
000000.000000
000000.000000
000000.000000
000000.000000
00.000000
00.000000
00.000000
00.000000
0.000000
0.000000
0.000000
0.000000
050.000
050.000
050.000
050.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.000005
00.000005
00.000005
00.000005
0.5628221
0.5000630
0.5000197
0.5000083
050.000250
050.000250
050.000250
050.000250
000001.000000
000001.000000
000001.000000
000001.000000
050.000250
050.000250
050.000250
050.000250
000000.000000
000000.000000
000000.000000
000000.000000
00.000000
00.000000
00.000000
00.000000
0.000000
0.000000
0.000000
0.000000
050.000
050.000
050.000
050.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.000010
00.000010
00.000010
00.000010
0.6240794
0.5001260
0.5000394
0.5000167
050.000500
050.000500
050.000500
050.000500
000001.000000
000001.000000
000001.000000
000001.000000
050.000500
050.000500
050.000500
050.000500
000000.000000
000000.000000
000000.000000
000000.000000
00.000000
00.000000
00.000000
00.000000
0.000000
0.000000
0.000000
0.000000
050.000
050.000
050.000
050.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.000020
00.000020
00.000020
00.000020
0.7364550
0.5002521
0.5000788
0.5000334
050.001000
050.001000
050.001000
050.001000
000001.000000
000001.000000
000001.000000
000001.000000
050.001000
050.001000
050.001000
050.001000
000000.000000
000000.000000
000000.000000
000000.000000
00.000000
00.000000
00.000000
00.000000
0.000000
0.000000
0.000000
0.000000
050.000
050.000
050.000
050.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.000030
00.000030
00.000030
00.000030
0.8286164
0.5003782
0.5001182
0.5000501
050.001499
050.001499
050.001499
050.001499
000001.000000
000001.000000
000001.000000
000001.000000
050.001499
050.001499
050.001499
050.001499
000000.000000
000000.000000
000000.000000
000000.000000
00.000000
00.000000
00.000000
00.000000
0.000000
0.000000
0.000000
0.000000
050.000
050.000
050.000
050.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.000040
00.000040
00.000040
00.000040
0.8970453
0.5005042
0.5001576
0.5000668
050.001999
050.001999
050.001999
050.001999
000001.000000
000001.000000
000001.000000
000001.000000
050.001999
050.001999
050.001999
050.001999
000000.000000
000000.000000
000000.000000
000000.000000
00.000000
00.000000
00.000000
00.000000
0.000000
0.000000
0.000000
0.000000
050.000
050.000
050.000
050.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.000050
00.000050
00.000050
00.000050
0.9430695
0.5006303
0.5001970
0.5000835
050.002499
050.002499
050.002499
050.002499
000001.000000
000001.000000
000001.000000
000001.000000
050.002499
050.002499
050.002499
050.002499
000000.000000
000000.000000
000000.000000
000000.000000
00.000000
00.000000
00.000000
00.000000
0.000000
0.000000
0.000000
0.000000
050.000
050.000
050.000
050.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
 

00

*


01
02
03
00.000060
00.000060
00.000060
00.000060

0.9711114

*


0.5007564
0.5002364
0.5001002
050.003000
050.003000
050.003000
050.003000
000001.000000
000001.000000
000001.000000
000001.000000
050.003000
050.003000
050.003000
050.003000
000000.000000
000000.000000
000000.000000
000000.000000
00.000007
00.000000
00.000000
00.000000
0.000000
0.000000
0.000000
0.000000
050.000
050.000
050.000
050.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.000070
00.000070
00.000070
00.000070
0.9865798
0.5008824
0.5002758
0.5001169
050.003500
050.003500
050.003500
050.003500
000001.000000
000001.000000
000001.000000
000001.000000
050.003500
050.003500
050.003500
050.003500
000000.000000
000000.000000
000000.000000
000000.000000
00.000017
00.000000
00.000000
00.000000
0.000000
0.000000
0.000000
0.000000
050.000
050.000
050.000
050.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.000080
00.000080
00.000080
00.000080
0.9942991
0.5010085
0.5003152
0.5001336
050.004000
050.004000
050.004000
050.004000
000001.000000
000001.000000
000001.000000
000001.000000
050.004000
050.004000
050.004000
050.004000
000000.000000
000000.000000
000000.000000
000000.000000
00.000027
00.000000
00.000000
00.000000
0.000000
0.000000
0.000000
0.000000
050.000
050.000
050.000
050.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.000090
00.000090
00.000090
00.000090
0.9977840
0.5011345
0.5003546
0.5001503
050.004499
050.004499
050.004499
050.004499
000001.000000
000001.000000
000001.000000
000001.000000
050.004499
050.004499
050.004499
050.004499
000000.000000
000000.000000
000000.000000
000000.000000
00.000037
00.000000
00.000000
00.000000
0.000000
0.000000
0.000000
0.000000
050.001
050.000
050.000
050.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.000100
00.000100
00.000100
00.000100
0.9992095
0.5012606
0.5003940
0.5001670
050.004999
050.004999
050.004999
050.004999
000001.000000
000001.000000
000001.000000
000001.000000
050.004999
050.004999
050.004999
050.004999
000000.000000
000000.000000
000000.000000
000000.000000
00.000047
00.000000
00.000000
00.000000
0.000000
0.000000
0.000000
0.000000
050.001
050.000
050.000
050.000
000.001
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.000500
00.000500
00.000500
00.000500
1.0000000
0.5063026
0.5019701
0.5008352
050.024999
050.024999
050.024999
050.024999
000001.000000
000001.000000
000001.000000
000001.000000
050.024999
050.024999
050.024999
050.024999
000000.000000
000000.000000
000000.000000
000000.000000
00.000447
00.000000
00.000000
00.000000
0.000000
0.000000
0.000000
0.000000
050.014
050.000
050.000
050.000
000.011
000.000
000.000
000.000
000.009
000.000
000.000
000.000
000.004
000.000
000.000
000.000
000.002
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.001000
00.001000
00.001000
00.001000
1.0000000
0.5126030
0.5039401
0.5016705
050.049999
050.049999
050.049999
050.049999
000001.000000
000001.000000
000001.000000
000001.000000
050.049999
050.049999
050.049999
050.049999
000000.000000
000000.000000
000000.000000
000000.000000
00.000947
00.000000
00.000000
00.000000
0.000000
0.000000
0.000000
0.000000
050.030
050.000
050.000
050.000
000.024
000.000
000.000
000.000
000.019
000.000
000.000
000.000
000.009
000.000
000.000
000.000
000.004
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.005000
00.005000
00.005000
00.005000
1.0000000
0.5627441
0.5196918
0.5083520
050.249999
050.249999
050.249999
050.249999
000001.000012
000001.000000
000001.000000
000001.000000
050.249999
050.249999
050.249999
050.249999
000000.000017
000000.000000
000000.000000
000000.000000
00.004947
00.000000
00.000000
00.000000
0.000024
0.000000
0.000000
0.000000
050.157
050.000
050.000
050.000
000.125
000.000
000.000
000.000
000.100
000.000
000.000
000.000
000.049
000.000
000.000
000.000
000.024
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.010000
00.010000
00.010000
00.010000
1.0000000
0.6239326
0.5393339
0.5167007
050.500000
050.500000
050.500000
050.500000
000001.000049
000001.000000
000001.000000
000001.000000
050.500000
050.500000
050.500000
050.500000
000000.000071
000000.000000
000000.000000
000000.000000
00.009947
00.000000
00.000000
00.000000
0.000098
0.000000
0.000000
0.000000
050.316
050.000
050.000
050.000
000.252
000.000
000.000
000.000
000.201
000.000
000.000
000.000
000.099
000.000
000.000
000.000
000.049
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.025000
00.025000
00.025000
00.025000
1.0000000
0.7851556
0.5975067
0.5416928
051.250000
051.250000
051.250000
051.250000
000001.000311
000001.000000
000001.000000
000001.000000
051.250000
051.250000
051.250000
051.250000
000000.000449
000000.000000
000000.000000
000000.000000
00.024948
00.000000
00.000000
00.000000
0.000622
0.000000
0.000000
0.000000
050.794
050.000
050.000
050.000
000.634
000.000
000.000
000.000
000.504
000.000
000.000
000.000
000.250
000.000
000.000
000.000
000.124
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.050000
00.050000
00.050000
00.050000
1.0000000
0.9429568
0.6893576
0.5829709
052.500000
052.500000
052.500000
052.500000
000001.001249
000001.000000
000001.000000
000001.000000
052.500000
052.500000
052.500000
052.500000
000000.001801
000000.000000
000000.000000
000000.000000
00.049948
00.000000
00.000000
00.000000
0.002494
0.000000
0.000000
0.000000
051.590
050.000
050.000
050.000
001.273
000.000
000.000
000.000
001.012
000.000
000.000
000.000
000.502
000.000
000.000
000.000
000.250
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00

01

*


02
03
00.060000
00.060000
00.060000
00.060000
1.0000000

0.9710675

*


0.7234125
0.5992755
052.999999
052.999999
052.999999
052.999999
000001.001801
000001.000031
000001.000000
000001.000000
052.999999
052.999999
052.999999
052.999999
000000.002597
000000.000045
000000.000000
000000.000000
00.059948
00.007967
00.000000
00.000000
0.003593
0.000063
0.000000
0.000000
051.909
050.253
050.000
050.000
001.529
000.202
000.000
000.000
001.216
000.161
000.000
000.000
000.603
000.079
000.000
000.000
000.301
000.039
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
000.000
00
01
02
03
00.075000
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*


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00

*


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*


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*


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075.000000

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*


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000.025
000.000
 

00

*


01
02
03
00.870000
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000002.028092
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000001.468884
093.500000
093.500000
093.500000
093.500000

000001.020123

*


000000.955281
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000.033
000.000
00

01

*


02
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00.880000
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093.999999
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093.999999
000001.074014

000001.008385

*


000000.867018
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000.005
00
01

02

*


03
00.910000
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000001.270110
000001.202121

000001.054708

*


000000.771691
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002.965
001.365
000.132
00
01
02

03

*


00.940000
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1.0000000
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000001.551347
000001.480993
000001.327489

000001.027660

*


00.939993
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00
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004.117
000.847
 

00

*


01

*


02
03
00.955000
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097.750000
097.750000
000001.753309
000001.681771
000001.525204
000001.216819

00.954995

*


00.950180

*


00.937705
00.902719
0.912016
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00
01
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00.960000
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036.603
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028.335
025.733
020.112
010.089
012.922
010.917
007.062
002.033
00
01

02

*


03
00.965000
00.965000
00.965000
00.965000
1.0000000
1.0000000
1.0000000
0.9999999
098.249999
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098.249999
098.249999
000001.930913
000001.858585
000001.699969
000001.385825
00.964996
00.961230

00.951453

*


00.923884
0.931218
0.923963
0.905263
0.853563
091.553
091.107
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087.500
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00
01
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049.155
043.830
032.210
035.660
033.067
027.303
016.143
019.234
016.892
012.110
004.767
 

00

*


01
02
03
00.975000
00.975000
00.975000
00.975000
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0.9999999
098.749999
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000002.096846
000001.936177
000001.616226
00.974997
00.972292
00.965255
00.945305

0.950619

*


0.945352
0.931718
0.893601
092.867
092.489
091.584
089.423
068.918
066.522
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053.177
048.139
036.949
040.187
037.653
031.940
020.439
023.582
021.108
015.909
007.268
00

01

*


02

03

*


00.980000
00.980000
00.980000
00.980000
1.0000000
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099.000000
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000002.255590
000002.093893
000001.771021
00.979997
00.977827
00.972176

00.956112

*


0.960395

0.956147

*


0.945127
0.914150
093.622
093.284
092.473
090.534
074.123
071.726
066.425
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053.088
042.545
045.512
043.088
037.549
025.968
029.084
026.530
021.009
011.093
00
01

02

*


03
00.985000
00.985000
00.985000
00.985000
1.0000000
1.0000000
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099.250000
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000002.298166
000001.972363
00.984998
00.983366
00.979112
00.966984
0.970221
0.967009

0.958660

*


0.935058
094.479
094.186
093.482
091.797
080.630
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070.067
067.623
062.283
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00

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095.012

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00

01

*


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0.956333

*


095.494

095.254

*


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01

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095.890

095.392

*


094.195
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00

*


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095.258

*


097.520

*


096.682

*


094.238
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00
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097.531

095.465

*


088.812
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00

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095.447

*


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095.007

*


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00
01

02

*


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095.204

*


098.139
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095.318

*


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095.163

*


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