RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-17_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.23 14.8150 0.391197
2 to 25 15.67 11.5259 0.172042
3 to 26 15.55 16.0857 0.482229
4 to 27 15.43 31.6950 0.983585
5 to 28 15.68 28.1406 0.956678
6 to 29 15.50 19.2863 0.687650
7 to 30 15.60 22.7860 0.843652
8 to 31 15.54 24.0335 0.881474
9 to 32 15.64 21.3989 0.791047
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.072609
Tough bday spacings test for dh-ranFile-2015-07-17_10:31: 4096 birthdays, year=2^32 days
Table of Expected vs. Observed counts:
Duplicates 0 1 2 3 4 5 6 7 8 9 >=10
Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1
Observed 7 31 71 89 96 89 59 26 18 10 4
(O-E)^2/E 0.5 0.9 0.1 0.8 0.0 1.5 0.9 0.5 0.7 1.7 0.0
Birthday Spacings: Sum(O-E)^2/E= 7.528, p= 0.325
RESULTS OF GCD FOR dh-ranFile-2015-07-17_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.167125
p-value, dist. of gcd's: 0.671937
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-17_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.125 0.727 0.045 0.922 0.511 0.529 0.414 0.782
Bits 8 to 15---> 0.780 0.042 0.531 0.559 0.376 0.442 0.627 0.173
Bits 16 to 23---> 0.334 0.790 0.133 0.662 0.044 0.255 0.033 0.375
Bits 24 to 31---> 0.152 0.684 0.645 0.808 0.801 0.892 0.336 0.211
KS test for the above 32 p values: 0.380
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-17_10:31,
p-values for 5 runs: 0.2862, 0.3613, 0.4079, 0.9768, 0.5037
Rank test for binary matrices (31x31) for dh-ranFile-2015-07-17_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 198 211.4 0.852 0.852
r= 29 5135 5134.0 0.000 0.852
r= 30 23122 23103.0 0.016 0.867
r= 31 11545 11551.5 0.004 0.871
chi-square = 0.871 with df = 3; p-value = 0.168
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2015-07-17_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 192 211.4 1.783 1.783
r= 30 5139 5134.0 0.005 1.788
r= 31 23146 23103.0 0.080 1.868
r= 32 11523 11551.5 0.070 1.939
chi-square = 1.939 with df = 3; p-value = 0.415
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2015-07-17_10:31
b-rank test for bits 1 to 8, p=0.20350
b-rank test for bits 2 to 9, p=0.16508
b-rank test for bits 3 to 10, p=0.00591
b-rank test for bits 4 to 11, p=0.15916
b-rank test for bits 5 to 12, p=0.75291
b-rank test for bits 6 to 13, p=0.37675
b-rank test for bits 7 to 14, p=0.21701
b-rank test for bits 8 to 15, p=0.50871
b-rank test for bits 9 to 16, p=0.20049
b-rank test for bits 10 to 17, p=0.16457
b-rank test for bits 11 to 18, p=0.17558
b-rank test for bits 12 to 19, p=0.36397
b-rank test for bits 13 to 20, p=0.54794
b-rank test for bits 14 to 21, p=0.93201
b-rank test for bits 15 to 22, p=0.75844
b-rank test for bits 16 to 23, p=0.32131
b-rank test for bits 17 to 24, p=0.27410
b-rank test for bits 18 to 25, p=0.67208
b-rank test for bits 19 to 26, p=0.83605
b-rank test for bits 20 to 27, p=0.72655
b-rank test for bits 21 to 28, p=0.94529
b-rank test for bits 22 to 29, p=0.59304
b-rank test for bits 23 to 30, p=0.28018
b-rank test for bits 24 to 31, p=0.37161
b-rank test for bits 25 to 32, p=0.29461
TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices
The above should be 25 uniform [0,1] random variables:
The KS test for those 25 supposed UNI's yields p = 0.277499
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-17_10:31
(20 bits/word, 2097152 words 20 bitstreams. No. missing words
should average 141909.33 with sigma=428.00.)
----------------------------------------------------------------
BITSTREAM test results.
Bitstream No. missing words z-score p-value
1 142311 0.94 0.826001
2 142190 0.66 0.744014
3 142327 0.98 0.835434
4 141851 -0.14 0.445798
5 142158 0.58 0.719381
6 142055 0.34 0.633204
7 142074 0.38 0.649786
8 142406 1.16 0.877066
9 142285 0.88 0.809956
10 142534 1.46 0.927788
11 142216 0.72 0.763164
12 141333 -1.35 0.089060
13 142018 0.25 0.600214
14 142170 0.61 0.728752
15 142180 0.63 0.736439
16 141157 -1.76 0.039392
17 142633 1.69 0.954564
18 142216 0.72 0.763164
19 142601 1.62 0.946958
20 141619 -0.68 0.248778
----------------------------------------------------------------
OPSO test for dh-ranFile-2015-07-17_10:31
Bits used No. missing words z-score p-value
23 to 32 141838 -0.2460 0.402855
22 to 31 141456 -1.5632 0.059002
21 to 30 141798 -0.3839 0.350528
20 to 29 141938 0.0989 0.539376
19 to 28 141856 -0.1839 0.427047
18 to 27 141899 -0.0356 0.485792
17 to 26 142126 0.7471 0.772510
16 to 25 141595 -1.0839 0.139205
15 to 24 141634 -0.9494 0.171205
14 to 23 141929 0.0678 0.527039
13 to 22 141428 -1.6598 0.048482
12 to 21 141964 0.1885 0.574764
11 to 20 141430 -1.6529 0.049179
10 to 19 142051 0.4885 0.687408
9 to 18 141932 0.0782 0.531155
8 to 17 142484 1.9816 0.976239
7 to 16 141615 -1.0149 0.155069
6 to 15 142208 1.0299 0.848471
5 to 14 141995 0.2954 0.616161
4 to 13 142108 0.6851 0.753350
3 to 12 142321 1.4196 0.922131
2 to 11 142421 1.7644 0.961166
1 to 10 141829 -0.2770 0.390890
-----------------------------------------------------------------
OQSO test for dh-ranFile-2015-07-17_10:31
Bits used No. missing words z-score p-value
28 to 32 142004 0.3209 0.625863
27 to 31 142030 0.4091 0.658749
26 to 30 141929 0.0667 0.526581
25 to 29 141741 -0.5706 0.284132
24 to 28 141686 -0.7571 0.224510
23 to 27 142012 0.3480 0.636093
22 to 26 141532 -1.2791 0.100434
21 to 25 141130 -2.6418 0.004123
20 to 24 141819 -0.3062 0.379725
19 to 23 141890 -0.0655 0.473878
18 to 22 141937 0.0938 0.537365
17 to 21 141975 0.2226 0.588081
16 to 20 142289 1.2870 0.900956
15 to 19 141581 -1.1130 0.132858
14 to 18 141956 0.1582 0.562852
13 to 17 142126 0.7345 0.768670
12 to 16 141975 0.2226 0.588081
11 to 15 141586 -1.0960 0.136532
10 to 14 142456 1.8531 0.968067
9 to 13 142225 1.0701 0.857706
8 to 12 141805 -0.3537 0.361797
7 to 11 142304 1.3379 0.909530
6 to 10 141954 0.1514 0.560179
5 to 9 142488 1.9616 0.975095
4 to 8 141573 -1.1401 0.127122
3 to 7 141781 -0.4350 0.331775
2 to 6 141144 -2.5943 0.004739
1 to 5 141844 -0.2215 0.412368
-----------------------------------------------------------------
DNA test for dh-ranFile-2015-07-17_10:31
Bits used No. missing words z-score p-value
31 to 32 141797 -0.3314 0.370187
30 to 31 141937 0.0816 0.532527
29 to 30 141427 -1.4228 0.077397
28 to 29 141836 -0.2163 0.414372
27 to 28 141637 -0.8033 0.210891
26 to 27 142087 0.5241 0.699896
25 to 26 141430 -1.4140 0.078688
24 to 25 141855 -0.1603 0.436336
23 to 24 141770 -0.4110 0.340535
22 to 23 142139 0.6775 0.750953
21 to 22 142072 0.4799 0.684334
20 to 21 142117 0.6126 0.729928
19 to 20 141998 0.2616 0.603171
18 to 19 142068 0.4681 0.680127
17 to 18 141984 0.2203 0.587168
16 to 17 141733 -0.5201 0.301480
15 to 16 141991 0.2409 0.595189
14 to 15 141785 -0.3668 0.356901
13 to 14 141732 -0.5231 0.300453
12 to 13 142209 0.8840 0.811647
11 to 12 141697 -0.6263 0.265545
10 to 11 141776 -0.3933 0.347048
9 to 10 142049 0.4120 0.659832
8 to 9 141834 -0.2222 0.412074
7 to 8 141825 -0.2488 0.401773
6 to 7 141551 -1.0570 0.145251
5 to 6 141731 -0.5260 0.299428
4 to 5 141871 -0.1131 0.454988
3 to 4 141669 -0.7089 0.239182
2 to 3 142029 0.3530 0.637959
1 to 2 141907 -0.0069 0.497258
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-17_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2460.96 -0.552 0.290438
Test results for specific bytes for dh-ranFile-2015-07-17_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2462.34 -0.533 0.297149
2 to 9 2514.44 0.204 0.580917
3 to 10 2574.87 1.059 0.855149
4 to 11 2590.97 1.287 0.900879
5 to 12 2587.40 1.236 0.891771
6 to 13 2488.17 -0.167 0.433564
7 to 14 2465.88 -0.483 0.314711
8 to 15 2503.55 0.050 0.520025
9 to 16 2501.82 0.026 0.510271
10 to 17 2544.47 0.629 0.735290
11 to 18 2477.58 -0.317 0.375595
12 to 19 2516.15 0.228 0.590348
13 to 20 2528.04 0.397 0.654161
14 to 21 2455.44 -0.630 0.264289
15 to 22 2376.82 -1.742 0.040746
16 to 23 2494.36 -0.080 0.468215
17 to 24 2342.26 -2.231 0.012848
18 to 25 2506.07 0.086 0.534231
19 to 26 2655.71 2.202 0.986171
20 to 27 2492.23 -0.110 0.456260
21 to 28 2534.66 0.490 0.688014
22 to 29 2367.58 -1.873 0.030555
23 to 30 2565.92 0.932 0.824400
24 to 31 2553.88 0.762 0.776957
25 to 32 2576.95 1.088 0.861744
CDPARK for dh-ranFile-2015-07-17_10:31: result of 10 tests
(Of 12000 tries, the average no. of successes should be
3523.0 with sigma=21.9)
No. succeses z-score p-value
3548 1.1416 0.873180
3494 -1.3242 0.092718
3565 1.9178 0.972432
3516 -0.3196 0.374623
3540 0.7763 0.781201
3546 1.0502 0.853193
3498 -1.1416 0.126820
3541 0.8219 0.794438
3459 -2.9224 0.001737
3550 1.2329 0.891189
Square side=100, avg. no. parked=3525.70 sample std.=31.30
p-value of the KSTEST for those 10 p-values: 0.138482
Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-17_10:31
0.7211,0.2001,0.8975,0.7641,0.6048,0.4216,0.3055,0.1209,0.9757,0.6906,
The KS test for those 10 p-values: 0.806818
The 3DSPHERES test for dh-ranFile-2015-07-17_10:31
sample no r^3 equiv. uni.
1 9.924 0.281640
2 21.230 0.507206
3 1.752 0.056740
4 3.759 0.117760
5 6.120 0.184543
6 4.152 0.129262
7 43.519 0.765576
8 10.616 0.298020
9 6.806 0.202980
10 24.707 0.561131
11 6.536 0.195770
12 85.809 0.942747
13 35.018 0.688786
14 2.693 0.085849
15 1.751 0.056697
16 27.816 0.604344
17 60.419 0.866541
18 17.462 0.441252
19 10.887 0.304354
20 34.188 0.680058
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.189043
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-17_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.1 -0.6 0.3 0.4 0.2
-1.4 -1.1 0.4 -0.4 1.0 0.5
-0.9 -1.0 1.6 0.6 -2.2 -1.4
1.9 -0.0 -1.7 0.2 -0.4 -0.2
1.0 1.0 1.6 0.6 1.0 0.4
0.4 0.2 1.6 -0.3 -0.5 -0.1
-1.6 1.5 -0.8 1.5 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:44.224227
z-score=0.242683, p-value=0.622112
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2015-07-17_10:31
Test no p-value
1 0.080523
2 0.888854
3 0.062396
4 0.013363
5 0.011993
6 0.654630
7 0.519393
8 0.070052
9 0.731677
10 0.032829
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.003634
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-17_10:31:
(for k>=2, the prob. of a run of length k is 2*k/(k+1)!)
Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E
2 66666.67 66520 0.32 66613 0.04
3 25000.00 25196 1.54 25065 0.17
4 6666.67 6613 0.43 6665 0.00
5 1388.89 1393 0.01 1375 0.14
6 238.10 233 0.11 242 0.06
7 34.72 38 0.31 36 0.05
8 4.96 6 0.22 3 0.77
p=0.18373 p=0.02500
Number of rngs required: 687541, p-value: 0.159
RESULTS OF CRAPS TEST for dh-ranFile-2015-07-17_10:31
No. of wins: Observed Expected
98464 98585.9
z-score=-0.545, pvalue=0.29287
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66295 66666.7 2.072 2.072
2 38005 37654.3 3.266 5.338
3 27117 26954.7 0.977 6.315
4 19199 19313.5 0.678 6.993
5 13940 13851.4 0.566 7.560
6 9839 9943.5 1.099 8.659
7 7182 7145.0 0.191 8.850
8 5195 5139.1 0.609 9.459
9 3697 3699.9 0.002 9.461
10 2647 2666.3 0.140 9.601
11 1955 1923.3 0.522 10.122
12 1324 1388.7 3.018 13.140
13 1005 1003.7 0.002 13.142
14 692 726.1 1.605 14.747
15 527 525.8 0.003 14.750
16 370 381.2 0.326 15.076
17 280 276.5 0.043 15.119
18 204 200.8 0.050 15.169
19 143 146.0 0.061 15.230
20 86 106.2 3.847 19.078
21 298 287.1 0.413 19.490
Chisq= 19.49 for 20 degrees of freedom, p= 0.50981
SUMMARY of craptest
p-value for no. of wins: 0.292869
p-value for throws/game: 0.509812
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-17_10:31
No. of wins: Observed Expected
98724 98585.9
z-score= 0.618, pvalue=0.73166
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66801 66666.7 0.271 0.271
2 37498 37654.3 0.649 0.920
3 26814 26954.7 0.735 1.654
4 19339 19313.5 0.034 1.688
5 13923 13851.4 0.370 2.058
6 10029 9943.5 0.734 2.793
7 6967 7145.0 4.436 7.228
8 5249 5139.1 2.351 9.580
9 3767 3699.9 1.218 10.798
10 2685 2666.3 0.131 10.929
11 1866 1923.3 1.709 12.638
12 1391 1388.7 0.004 12.642
13 1025 1003.7 0.451 13.093
14 737 726.1 0.162 13.255
15 547 525.8 0.852 14.107
16 386 381.2 0.062 14.169
17 258 276.5 1.243 15.412
18 175 200.8 3.322 18.734
19 135 146.0 0.827 19.560
20 111 106.2 0.216 19.776
21 297 287.1 0.340 20.116
Chisq= 20.12 for 20 degrees of freedom, p= 0.54932
SUMMARY of craptest
p-value for no. of wins: 0.731663
p-value for throws/game: 0.549323
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0017,0.0036,0.0041,0.0047,0.0059,0.0120,0.0128,0.0134,0.0250,0.0306,
0.0326,0.0328,0.0394,0.0407,0.0422,0.0444,0.0450,0.0485,0.0492,0.0567,
0.0567,0.0590,0.0624,0.0701,0.0726,0.0774,0.0787,0.0805,0.0858,0.0891,
0.0927,0.1004,0.1178,0.1209,0.1247,0.1268,0.1271,0.1293,0.1329,0.1334,
0.1365,0.1385,0.1392,0.1453,0.1518,0.1551,0.1590,0.1592,0.1646,0.1651,
0.1671,0.1676,0.1712,0.1720,0.1729,0.1756,0.1837,0.1845,0.1890,0.1958,
0.2001,0.2005,0.2030,0.2035,0.2107,0.2109,0.2170,0.2245,0.2392,0.2488,
0.2555,0.2643,0.2655,0.2741,0.2775,0.2802,0.2816,0.2841,0.2862,0.2904,
0.2929,0.2946,0.2971,0.2980,0.2994,0.3005,0.3015,0.3044,0.3055,0.3147,
0.3213,0.3252,0.3318,0.3341,0.3358,0.3405,0.3470,0.3505,0.3569,0.3613,
0.3618,0.3640,0.3702,0.3716,0.3745,0.3746,0.3755,0.3756,0.3767,0.3797,
0.3803,0.3909,0.3912,0.4018,0.4029,0.4079,0.4121,0.4124,0.4144,0.4144,
0.4148,0.4216,0.4270,0.4336,0.4363,0.4413,0.4422,0.4458,0.4550,0.4563,
0.4682,0.4739,0.4822,0.4858,0.4973,0.5037,0.5072,0.5087,0.5098,0.5103,
0.5107,0.5194,0.5200,0.5266,0.5270,0.5293,0.5311,0.5312,0.5325,0.5342,
0.5374,0.5394,0.5479,0.5493,0.5588,0.5602,0.5611,0.5629,0.5748,0.5809,
0.5872,0.5881,0.5881,0.5903,0.5930,0.5952,0.6002,0.6032,0.6043,0.6048,
0.6162,0.6221,0.6259,0.6267,0.6332,0.6361,0.6380,0.6453,0.6498,0.6542,
0.6546,0.6587,0.6598,0.6619,0.6719,0.6721,0.6801,0.6801,0.6843,0.6844,
0.6874,0.6877,0.6880,0.6888,0.6906,0.6999,0.7194,0.7211,0.7266,0.7273,
0.7288,0.7299,0.7317,0.7317,0.7353,0.7364,0.7440,0.7510,0.7529,0.7533,
0.7584,0.7632,0.7632,0.7641,0.7656,0.7687,0.7725,0.7770,0.7797,0.7812,
0.7823,0.7902,0.7910,0.7944,0.8013,0.8068,0.8077,0.8100,0.8116,0.8244,
0.8260,0.8354,0.8360,0.8437,0.8485,0.8532,0.8551,0.8577,0.8617,0.8665,
0.8732,0.8771,0.8815,0.8889,0.8912,0.8917,0.8918,0.8975,0.9009,0.9010,
0.9095,0.9221,0.9223,0.9278,0.9320,0.9427,0.9453,0.9470,0.9546,0.9567,
0.9612,0.9681,0.9724,0.9751,0.9757,0.9762,0.9768,0.9836,0.9862,
Overall p-value after applying KStest on 269 p-values = 0.486230
In response to requests, we have provided a list of all the p-values
produced by the tests you have chosen for this run. The individual
p-values are supposed to be uniform in [0,1), but they are not necessarily
independent. So even though we have applied a KSTEST to the accumulated
p-values, the result is not necessarily---even if your file contains truly
random bits---uniform in [0,1). But it is probably pretty close, so take
that last p-value with a grain of salt. In particular, there may be some
values so close to 0 or 1 that the tests they came from should be applied
several more times, or new, related tests should be undertaken.