RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-05_02:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.12 21.4416 0.792843
2 to 25 15.64 13.0070 0.264282
3 to 26 16.12 9.9397 0.093881
4 to 27 15.65 18.0655 0.615280
5 to 28 15.69 15.7396 0.457633
6 to 29 15.89 21.3591 0.789364
7 to 30 15.90 8.7365 0.051833
8 to 31 15.93 20.1627 0.734007
9 to 32 15.67 22.8299 0.845129
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.835488
Tough bday spacings test for dh-ranFile-2015-07-05_02:31: 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 14 35 71 105 98 69 50 27 22 7 2
(O-E)^2/E 2.6 0.1 0.1 0.5 0.0 1.1 0.1 0.3 3.4 0.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 9.138, p= 0.481
RESULTS OF GCD FOR dh-ranFile-2015-07-05_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.069423
p-value, dist. of gcd's: 0.029316
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-05_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.015 0.888 0.799 0.650 0.372 0.294 0.118 0.306
Bits 8 to 15---> 0.865 0.836 0.143 0.943 0.691 0.943 0.207 0.676
Bits 16 to 23---> 0.761 0.662 0.434 0.988 0.998 0.155 0.549 0.024
Bits 24 to 31---> 0.123 0.582 0.626 0.005 0.935 0.055 0.447 0.911
KS test for the above 32 p values: 0.719
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-05_02:31,
p-values for 5 runs: 0.5021, 0.7627, 0.2697, 0.8998, 0.8794
Rank test for binary matrices (31x31) for dh-ranFile-2015-07-05_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 218 211.4 0.205 0.205
r= 29 5120 5134.0 0.038 0.243
r= 30 23027 23103.0 0.250 0.493
r= 31 11635 11551.5 0.603 1.097
chi-square = 1.097 with df = 3; p-value = 0.222
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2015-07-05_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 197 211.4 0.983 0.983
r= 30 5121 5134.0 0.033 1.016
r= 31 23142 23103.0 0.066 1.082
r= 32 11540 11551.5 0.011 1.093
chi-square = 1.093 with df = 3; p-value = 0.221
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2015-07-05_02:31
b-rank test for bits 1 to 8, p=0.75560
b-rank test for bits 2 to 9, p=0.68866
b-rank test for bits 3 to 10, p=0.50735
b-rank test for bits 4 to 11, p=0.28660
b-rank test for bits 5 to 12, p=0.00798
b-rank test for bits 6 to 13, p=0.45063
b-rank test for bits 7 to 14, p=0.73066
b-rank test for bits 8 to 15, p=0.69608
b-rank test for bits 9 to 16, p=0.11699
b-rank test for bits 10 to 17, p=0.28564
b-rank test for bits 11 to 18, p=0.05449
b-rank test for bits 12 to 19, p=0.38719
b-rank test for bits 13 to 20, p=0.02045
b-rank test for bits 14 to 21, p=0.82207
b-rank test for bits 15 to 22, p=0.13372
b-rank test for bits 16 to 23, p=0.88822
b-rank test for bits 17 to 24, p=0.64086
b-rank test for bits 18 to 25, p=0.51190
b-rank test for bits 19 to 26, p=0.73895
b-rank test for bits 20 to 27, p=0.78062
b-rank test for bits 21 to 28, p=0.85133
b-rank test for bits 22 to 29, p=0.89922
b-rank test for bits 23 to 30, p=0.29982
b-rank test for bits 24 to 31, p=0.59438
b-rank test for bits 25 to 32, p=0.89879
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 = 0.675669
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-05_02:31
(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 141625 -0.66 0.253242
2 142372 1.08 0.860153
3 141869 -0.09 0.462464
4 142052 0.33 0.630562
5 141181 -1.70 0.044405
6 141432 -1.12 0.132370
7 142579 1.56 0.941167
8 141717 -0.45 0.326583
9 141845 -0.15 0.440263
10 141959 0.12 0.546194
11 141743 -0.39 0.348778
12 142310 0.94 0.825401
13 142258 0.81 0.792364
14 141797 -0.26 0.396486
15 142006 0.23 0.589347
16 142047 0.32 0.626144
17 141645 -0.62 0.268422
18 141743 -0.39 0.348778
19 142041 0.31 0.620822
20 142471 1.31 0.905293
----------------------------------------------------------------
OPSO test for dh-ranFile-2015-07-05_02:31
Bits used No. missing words z-score p-value
23 to 32 141779 -0.4494 0.326567
22 to 31 141975 0.2264 0.589574
21 to 30 142072 0.5609 0.712578
20 to 29 141971 0.2127 0.584202
19 to 28 142295 1.3299 0.908224
18 to 27 142527 2.1299 0.983410
17 to 26 142125 0.7437 0.771468
16 to 25 142092 0.6299 0.735619
15 to 24 141742 -0.5770 0.281970
14 to 23 142126 0.7471 0.772510
13 to 22 142076 0.5747 0.717261
12 to 21 141768 -0.4873 0.313007
11 to 20 141875 -0.1184 0.452884
10 to 19 142029 0.4127 0.660070
9 to 18 141548 -1.2460 0.106389
8 to 17 141467 -1.5253 0.063595
7 to 16 141890 -0.0667 0.473428
6 to 15 141838 -0.2460 0.402855
5 to 14 141924 0.0506 0.520172
4 to 13 142040 0.4506 0.673856
3 to 12 142163 0.8747 0.809138
2 to 11 141422 -1.6804 0.046435
1 to 10 142061 0.5230 0.699513
-----------------------------------------------------------------
OQSO test for dh-ranFile-2015-07-05_02:31
Bits used No. missing words z-score p-value
28 to 32 141949 0.1345 0.553486
27 to 31 142172 0.8904 0.813376
26 to 30 141810 -0.3367 0.368167
25 to 29 142150 0.8158 0.792702
24 to 28 141435 -1.6079 0.053929
23 to 27 142176 0.9040 0.816993
22 to 26 141643 -0.9028 0.183312
21 to 25 141900 -0.0316 0.487385
20 to 24 142090 0.6124 0.729877
19 to 23 142036 0.4294 0.666180
18 to 22 142035 0.4260 0.664946
17 to 21 141741 -0.5706 0.284132
16 to 20 141806 -0.3503 0.363068
15 to 19 141893 -0.0554 0.477928
14 to 18 141616 -0.9943 0.160029
13 to 17 142298 1.3175 0.906169
12 to 16 142279 1.2531 0.894919
11 to 15 141586 -1.0960 0.136532
10 to 14 141848 -0.2079 0.417654
9 to 13 142224 1.0667 0.856941
8 to 12 141619 -0.9842 0.162516
7 to 11 142243 1.1311 0.870990
6 to 10 141838 -0.2418 0.404469
5 to 9 142239 1.1175 0.868115
4 to 8 142475 1.9175 0.972414
3 to 7 141823 -0.2926 0.384897
2 to 6 141566 -1.1638 0.122246
1 to 5 141583 -1.1062 0.134319
-----------------------------------------------------------------
DNA test for dh-ranFile-2015-07-05_02:31
Bits used No. missing words z-score p-value
31 to 32 141662 -0.7296 0.232821
30 to 31 142441 1.5683 0.941600
29 to 30 141963 0.1583 0.562897
28 to 29 141708 -0.5939 0.276292
27 to 28 141887 -0.0659 0.473741
26 to 27 141692 -0.6411 0.260732
25 to 26 141970 0.1790 0.571018
24 to 25 141931 0.0639 0.525484
23 to 24 141962 0.1554 0.561735
22 to 23 141870 -0.1160 0.453819
21 to 22 142073 0.4828 0.685382
20 to 21 141342 -1.6735 0.047111
19 to 20 142300 1.1524 0.875426
18 to 19 141723 -0.5496 0.291281
17 to 18 141626 -0.8358 0.201639
16 to 17 141851 -0.1721 0.431693
15 to 16 141886 -0.0688 0.472566
14 to 15 141788 -0.3579 0.360207
13 to 14 141668 -0.7119 0.238267
12 to 13 141789 -0.3550 0.361311
11 to 12 142036 0.3737 0.645671
10 to 11 142120 0.6214 0.732847
9 to 10 141866 -0.1278 0.449147
8 to 9 142071 0.4769 0.683284
7 to 8 141935 0.0757 0.530180
6 to 7 142413 1.4858 0.931328
5 to 6 141508 -1.1839 0.118233
4 to 5 142469 1.6509 0.950625
3 to 4 142349 1.2970 0.902678
2 to 3 141833 -0.2252 0.410927
1 to 2 142237 0.9666 0.833123
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-05_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2530.26 0.428 0.665645
Test results for specific bytes for dh-ranFile-2015-07-05_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2548.37 0.684 0.753045
2 to 9 2506.60 0.093 0.537194
3 to 10 2450.71 -0.697 0.242874
4 to 11 2444.77 -0.781 0.217391
5 to 12 2359.91 -1.981 0.023788
6 to 13 2524.52 0.347 0.635606
7 to 14 2393.38 -1.508 0.065797
8 to 15 2602.91 1.455 0.927211
9 to 16 2464.54 -0.501 0.308025
10 to 17 2640.24 1.983 0.976336
11 to 18 2505.70 0.081 0.532127
12 to 19 2500.34 0.005 0.501907
13 to 20 2700.89 2.841 0.997752
14 to 21 2600.43 1.420 0.922243
15 to 22 2425.62 -1.052 0.146422
16 to 23 2510.55 0.149 0.559279
17 to 24 2539.98 0.565 0.714121
18 to 25 2487.29 -0.180 0.428660
19 to 26 2584.57 1.196 0.884157
20 to 27 2458.02 -0.594 0.276345
21 to 28 2657.68 2.230 0.987124
22 to 29 2364.51 -1.916 0.027678
23 to 30 2478.18 -0.309 0.378817
24 to 31 2569.15 0.978 0.835962
25 to 32 2378.70 -1.715 0.043139
CDPARK for dh-ranFile-2015-07-05_02:31: 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
3530 0.3196 0.625377
3489 -1.5525 0.060270
3498 -1.1416 0.126820
3540 0.7763 0.781201
3524 0.0457 0.518210
3540 0.7763 0.781201
3549 1.1872 0.882429
3524 0.0457 0.518210
Square side=100, avg. no. parked=3523.60 sample std.=21.33
p-value of the KSTEST for those 10 p-values: 0.711514
Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-05_02:31
0.6218,0.8580,0.1816,0.3985,0.1795,0.7677,0.5054,0.1229,0.2133,0.1043,
The KS test for those 10 p-values: 0.371357
The 3DSPHERES test for dh-ranFile-2015-07-05_02:31
sample no r^3 equiv. uni.
1 26.244 0.583051
2 18.381 0.458112
3 61.829 0.872669
4 1.021 0.033447
5 51.528 0.820504
6 0.327 0.010854
7 19.173 0.472232
8 69.020 0.899807
9 52.725 0.827525
10 33.816 0.676058
11 4.453 0.137940
12 14.070 0.374376
13 2.486 0.079528
14 37.983 0.718073
15 35.469 0.693428
16 32.184 0.657949
17 7.605 0.223924
18 24.229 0.554093
19 11.729 0.323594
20 17.503 0.442017
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.905312
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-05_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 1.8 0.8 -0.1 0.5 -0.6
1.0 0.4 -0.7 0.2 -1.4 -0.2
0.6 0.4 1.0 -0.5 1.4 -1.1
-0.5 0.1 -0.9 1.0 0.6 -0.4
1.0 -0.6 0.9 -1.5 -0.9 1.4
-1.3 -0.4 -1.3 -1.1 -1.2 2.0
-0.7 -0.1 -1.2 -0.7 0.1 -1.0
-0.1
Chi-square with 42 degrees of freedom:40.547444
z-score=-0.158487, p-value=0.465209
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2015-07-05_02:31
Test no p-value
1 0.331014
2 0.239172
3 0.806253
4 0.057885
5 0.828730
6 0.177216
7 0.023890
8 0.222004
9 0.974096
10 0.616747
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.490775
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-05_02:31:
(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 66668 0.00 66524 0.31
3 25000.00 24898 0.42 25282 3.18
4 6666.67 6759 1.28 6546 2.18
5 1388.89 1396 0.04 1359 0.64
6 238.10 234 0.07 243 0.10
7 34.72 38 0.31 39 0.53
8 4.96 6 0.22 6 0.22
p=0.11298 p=0.69373
Number of rngs required: 687748, p-value: 0.225
RESULTS OF CRAPS TEST for dh-ranFile-2015-07-05_02:31
No. of wins: Observed Expected
98856 98585.9
z-score= 1.208, pvalue=0.88652
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66587 66666.7 0.095 0.095
2 37458 37654.3 1.024 1.119
3 27085 26954.7 0.630 1.748
4 19181 19313.5 0.908 2.657
5 13816 13851.4 0.091 2.747
6 10078 9943.5 1.818 4.566
7 7191 7145.0 0.296 4.861
8 5215 5139.1 1.122 5.983
9 3712 3699.9 0.040 6.023
10 2733 2666.3 1.669 7.692
11 1921 1923.3 0.003 7.694
12 1421 1388.7 0.749 8.444
13 1038 1003.7 1.171 9.615
14 680 726.1 2.932 12.547
15 521 525.8 0.044 12.591
16 354 381.2 1.934 14.525
17 280 276.5 0.043 14.569
18 205 200.8 0.087 14.655
19 138 146.0 0.437 15.092
20 100 106.2 0.364 15.456
21 286 287.1 0.004 15.460
Chisq= 15.46 for 20 degrees of freedom, p= 0.25049
SUMMARY of craptest
p-value for no. of wins: 0.886521
p-value for throws/game: 0.250487
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-05_02:31
No. of wins: Observed Expected
98583 98585.9
z-score=-0.013, pvalue=0.49490
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67060 66666.7 2.321 2.321
2 37721 37654.3 0.118 2.439
3 27226 26954.7 2.730 5.169
4 19151 19313.5 1.367 6.535
5 13615 13851.4 4.035 10.571
6 9896 9943.5 0.227 10.798
7 7017 7145.0 2.294 13.092
8 5115 5139.1 0.113 13.205
9 3625 3699.9 1.515 14.720
10 2745 2666.3 2.323 17.043
11 1877 1923.3 1.116 18.159
12 1387 1388.7 0.002 18.161
13 981 1003.7 0.514 18.675
14 700 726.1 0.941 19.616
15 477 525.8 4.536 24.151
16 380 381.2 0.003 24.155
17 269 276.5 0.206 24.360
18 205 200.8 0.087 24.447
19 156 146.0 0.687 25.134
20 119 106.2 1.539 26.673
21 278 287.1 0.289 26.962
Chisq= 26.96 for 20 degrees of freedom, p= 0.86367
SUMMARY of craptest
p-value for no. of wins: 0.494900
p-value for throws/game: 0.863674
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0049,0.0080,0.0109,0.0146,0.0205,0.0238,0.0238,0.0239,0.0277,0.0293,
0.0334,0.0431,0.0444,0.0464,0.0471,0.0518,0.0539,0.0545,0.0553,0.0579,
0.0603,0.0636,0.0658,0.0694,0.0795,0.0927,0.0939,0.1043,0.1064,0.1130,
0.1170,0.1175,0.1182,0.1222,0.1227,0.1229,0.1268,0.1324,0.1337,0.1343,
0.1365,0.1379,0.1431,0.1464,0.1553,0.1600,0.1625,0.1772,0.1795,0.1816,
0.1833,0.2016,0.2073,0.2133,0.2174,0.2213,0.2220,0.2221,0.2239,0.2246,
0.2328,0.2383,0.2392,0.2429,0.2505,0.2532,0.2607,0.2643,0.2684,0.2697,
0.2763,0.2763,0.2820,0.2841,0.2856,0.2866,0.2913,0.2944,0.2998,0.3055,
0.3080,0.3130,0.3236,0.3266,0.3266,0.3310,0.3488,0.3488,0.3602,0.3613,
0.3631,0.3682,0.3714,0.3719,0.3744,0.3788,0.3849,0.3872,0.3965,0.3985,
0.4029,0.4045,0.4109,0.4177,0.4287,0.4317,0.4335,0.4403,0.4420,0.4474,
0.4491,0.4506,0.4529,0.4538,0.4576,0.4581,0.4625,0.4652,0.4722,0.4726,
0.4734,0.4737,0.4779,0.4809,0.4874,0.4908,0.4949,0.5019,0.5021,0.5054,
0.5074,0.5119,0.5182,0.5182,0.5202,0.5255,0.5302,0.5321,0.5372,0.5462,
0.5490,0.5535,0.5541,0.5593,0.5617,0.5629,0.5710,0.5816,0.5831,0.5842,
0.5893,0.5896,0.5944,0.6153,0.6167,0.6208,0.6218,0.6254,0.6258,0.6261,
0.6306,0.6356,0.6409,0.6457,0.6505,0.6579,0.6601,0.6617,0.6649,0.6656,
0.6662,0.6739,0.6756,0.6757,0.6761,0.6833,0.6854,0.6887,0.6906,0.6934,
0.6937,0.6961,0.6995,0.7115,0.7126,0.7141,0.7173,0.7181,0.7188,0.7299,
0.7307,0.7328,0.7340,0.7356,0.7390,0.7530,0.7556,0.7615,0.7627,0.7677,
0.7715,0.7725,0.7806,0.7812,0.7812,0.7894,0.7924,0.7927,0.7928,0.7990,
0.8063,0.8091,0.8134,0.8170,0.8205,0.8221,0.8254,0.8275,0.8287,0.8331,
0.8355,0.8355,0.8360,0.8451,0.8513,0.8569,0.8580,0.8602,0.8637,0.8649,
0.8681,0.8710,0.8727,0.8732,0.8754,0.8794,0.8824,0.8842,0.8865,0.8882,
0.8883,0.8949,0.8988,0.8992,0.8998,0.8998,0.9027,0.9053,0.9053,0.9062,
0.9082,0.9111,0.9222,0.9272,0.9313,0.9346,0.9412,0.9416,0.9428,0.9435,
0.9506,0.9724,0.9741,0.9763,0.9834,0.9871,0.9881,0.9978,0.9979,
Overall p-value after applying KStest on 269 p-values = 0.578424
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.