RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-12_07:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.73 14.2054 0.347488
2 to 25 15.81 20.7143 0.760669
3 to 26 15.64 30.2813 0.975614
4 to 27 15.54 23.7340 0.873157
5 to 28 15.67 20.2666 0.739180
6 to 29 15.90 36.9090 0.996538
7 to 30 16.04 11.9058 0.194193
8 to 31 15.56 32.2095 0.985829
9 to 32 15.85 19.2889 0.687794
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.008027
Tough bday spacings test for dh-ranFile-2018-07-12_07:31: 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 8 31 75 109 78 83 60 36 15 4 1
(O-E)^2/E 0.1 0.9 0.0 1.3 4.0 0.3 1.2 1.3 0.0 1.0 2.3
Birthday Spacings: Sum(O-E)^2/E= 12.481, p= 0.746
RESULTS OF GCD FOR dh-ranFile-2018-07-12_07:31
Euclid's algorithm:
p-value, steps to gcd: 0.756083
p-value, dist. of gcd's: 0.539311
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-12_07:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.247 0.934 0.718 0.851 0.792 0.045 0.428 0.965
Bits 8 to 15---> 0.853 0.108 0.238 0.868 0.203 0.188 0.735 0.935
Bits 16 to 23---> 0.707 0.044 0.741 0.959 0.967 0.632 0.484 0.077
Bits 24 to 31---> 0.388 0.047 0.727 0.505 0.690 0.537 0.449 0.266
KS test for the above 32 p values: 0.499
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-12_07:31,
p-values for 5 runs: 0.4488, 0.1705, 0.7600, 0.2464, 0.3565
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-12_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 216 211.4 0.099 0.099
r= 29 5165 5134.0 0.187 0.286
r= 30 23132 23103.0 0.036 0.323
r= 31 11487 11551.5 0.360 0.683
chi-square = 0.683 with df = 3; p-value = 0.123
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-12_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 202 211.4 0.420 0.420
r= 30 5064 5134.0 0.955 1.374
r= 31 23105 23103.0 0.000 1.374
r= 32 11629 11551.5 0.520 1.894
chi-square = 1.894 with df = 3; p-value = 0.405
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-12_07:31
b-rank test for bits 1 to 8, p=0.73595
b-rank test for bits 2 to 9, p=0.31341
b-rank test for bits 3 to 10, p=0.66948
b-rank test for bits 4 to 11, p=0.64020
b-rank test for bits 5 to 12, p=0.93358
b-rank test for bits 6 to 13, p=0.22266
b-rank test for bits 7 to 14, p=0.77912
b-rank test for bits 8 to 15, p=0.51542
b-rank test for bits 9 to 16, p=0.86306
b-rank test for bits 10 to 17, p=0.48543
b-rank test for bits 11 to 18, p=0.82731
b-rank test for bits 12 to 19, p=0.54126
b-rank test for bits 13 to 20, p=0.67113
b-rank test for bits 14 to 21, p=0.43636
b-rank test for bits 15 to 22, p=0.39324
b-rank test for bits 16 to 23, p=0.64284
b-rank test for bits 17 to 24, p=0.92792
b-rank test for bits 18 to 25, p=0.87676
b-rank test for bits 19 to 26, p=0.64425
b-rank test for bits 20 to 27, p=0.74708
b-rank test for bits 21 to 28, p=0.28423
b-rank test for bits 22 to 29, p=0.74331
b-rank test for bits 23 to 30, p=0.10069
b-rank test for bits 24 to 31, p=0.60200
b-rank test for bits 25 to 32, p=0.39697
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 = 0.080563
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-12_07:31
(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 141965 0.13 0.551745
2 141460 -1.05 0.146897
3 141761 -0.35 0.364459
4 142327 0.98 0.835434
5 142090 0.42 0.663534
6 141350 -1.31 0.095633
7 141887 -0.05 0.479196
8 142284 0.88 0.809321
9 141903 -0.01 0.494100
10 140987 -2.15 0.015582
11 141498 -0.96 0.168263
12 142174 0.62 0.731840
13 141500 -0.96 0.169441
14 142143 0.55 0.707453
15 142339 1.00 0.842287
16 141915 0.01 0.505285
17 142614 1.65 0.950162
18 141939 0.07 0.527634
19 141665 -0.57 0.284046
20 142207 0.70 0.756626
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-12_07:31
Bits used No. missing words z-score p-value
23 to 32 142178 0.9264 0.822894
22 to 31 141520 -1.3425 0.089714
21 to 30 141907 -0.0080 0.496795
20 to 29 141787 -0.4218 0.336575
19 to 28 141692 -0.7494 0.226804
18 to 27 141306 -2.0804 0.018742
17 to 26 142028 0.4092 0.658806
16 to 25 141719 -0.6563 0.255812
15 to 24 141914 0.0161 0.506424
14 to 23 142008 0.3402 0.633163
13 to 22 142146 0.8161 0.792780
12 to 21 142672 2.6299 0.995729
11 to 20 141562 -1.1977 0.115519
10 to 19 142279 1.2747 0.898797
9 to 18 141828 -0.2804 0.389567
8 to 17 141348 -1.9356 0.026457
7 to 16 141833 -0.2632 0.396196
6 to 15 141968 0.2023 0.580163
5 to 14 141749 -0.5529 0.290179
4 to 13 141950 0.1402 0.555765
3 to 12 141683 -0.7804 0.217564
2 to 11 141936 0.0920 0.536637
1 to 10 141852 -0.1977 0.421644
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-12_07:31
Bits used No. missing words z-score p-value
28 to 32 142133 0.7582 0.775835
27 to 31 142322 1.3989 0.919076
26 to 30 141956 0.1582 0.562852
25 to 29 141982 0.2463 0.597290
24 to 28 142162 0.8565 0.804142
23 to 27 142550 2.1718 0.985063
22 to 26 142190 0.9514 0.829305
21 to 25 141925 0.0531 0.521181
20 to 24 142076 0.5650 0.713957
19 to 23 142284 1.2701 0.897970
18 to 22 141938 0.0972 0.538711
17 to 21 141753 -0.5299 0.298080
16 to 20 142442 1.8057 0.964514
15 to 19 141888 -0.0723 0.471180
14 to 18 141918 0.0294 0.511723
13 to 17 141630 -0.9469 0.171850
12 to 16 141978 0.2328 0.592034
11 to 15 141627 -0.9571 0.169271
10 to 14 141368 -1.8350 0.033252
9 to 13 141546 -1.2316 0.109044
8 to 12 141757 -0.5164 0.302797
7 to 11 141879 -0.1028 0.459056
6 to 10 141711 -0.6723 0.250695
5 to 9 142150 0.8158 0.792702
4 to 8 142112 0.6870 0.753964
3 to 7 142199 0.9819 0.836933
2 to 6 142130 0.7480 0.772780
1 to 5 141902 -0.0248 0.490088
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-12_07:31
Bits used No. missing words z-score p-value
31 to 32 141317 -1.7473 0.040294
30 to 31 141538 -1.0954 0.136678
29 to 30 141596 -0.9243 0.177671
28 to 29 141995 0.2527 0.599755
27 to 28 142398 1.4415 0.925279
26 to 27 142433 1.5447 0.938797
25 to 26 141817 -0.2724 0.392673
24 to 25 142305 1.1672 0.878429
23 to 24 142006 0.2852 0.612240
22 to 23 142018 0.3206 0.625728
21 to 22 141252 -1.9390 0.026249
20 to 21 141782 -0.3756 0.353605
19 to 20 142005 0.2822 0.611110
18 to 19 142102 0.5683 0.715101
17 to 18 142287 1.1141 0.867376
16 to 17 142031 0.3589 0.640168
15 to 16 141716 -0.5703 0.284239
14 to 15 142078 0.4976 0.690600
13 to 14 142211 0.8899 0.813235
12 to 13 141478 -1.2724 0.101623
11 to 12 141575 -0.9862 0.162012
10 to 11 141818 -0.2694 0.393807
9 to 10 141841 -0.2016 0.420129
8 to 9 141626 -0.8358 0.201639
7 to 8 141967 0.1701 0.567541
6 to 7 142697 2.3235 0.989924
5 to 6 141667 -0.7148 0.237355
4 to 5 141856 -0.1573 0.437498
3 to 4 141784 -0.3697 0.355801
2 to 3 141611 -0.8800 0.189422
1 to 2 142430 1.5359 0.937719
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-12_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2466.73 -0.470 0.319008
Test results for specific bytes for dh-ranFile-2018-07-12_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2448.84 -0.724 0.234681
2 to 9 2495.91 -0.058 0.476941
3 to 10 2502.27 0.032 0.512805
4 to 11 2408.02 -1.301 0.096657
5 to 12 2491.61 -0.119 0.452749
6 to 13 2552.47 0.742 0.770967
7 to 14 2499.24 -0.011 0.495689
8 to 15 2524.61 0.348 0.636090
9 to 16 2512.14 0.172 0.568175
10 to 17 2430.05 -0.989 0.161287
11 to 18 2580.23 1.135 0.871736
12 to 19 2415.32 -1.198 0.115547
13 to 20 2437.38 -0.886 0.187934
14 to 21 2524.82 0.351 0.637197
15 to 22 2370.22 -1.835 0.033226
16 to 23 2469.96 -0.425 0.335473
17 to 24 2390.18 -1.553 0.060193
18 to 25 2653.38 2.169 0.984963
19 to 26 2464.37 -0.504 0.307167
20 to 27 2487.28 -0.180 0.428634
21 to 28 2582.15 1.162 0.877335
22 to 29 2343.20 -2.218 0.013293
23 to 30 2484.65 -0.217 0.414088
24 to 31 2598.20 1.389 0.917555
25 to 32 2310.96 -2.673 0.003754
CDPARK for dh-ranFile-2018-07-12_07:31: 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
3535 0.5479 0.708135
3507 -0.7306 0.232514
3530 0.3196 0.625377
3502 -0.9589 0.168804
3505 -0.8219 0.205562
3470 -2.4201 0.007758
3496 -1.2329 0.108811
3540 0.7763 0.781201
3521 -0.0913 0.463617
3530 0.3196 0.625377
Square side=100, avg. no. parked=3513.60 sample std.=20.52
p-value of the KSTEST for those 10 p-values: 0.349222
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-12_07:31
0.5713,0.2292,0.0259,0.2147,0.1718,0.7300,0.1247,0.4667,0.1547,0.4605,
The KS test for those 10 p-values: 0.065822
The 3DSPHERES test for dh-ranFile-2018-07-12_07:31
sample no r^3 equiv. uni.
1 2.319 0.074381
2 10.093 0.285687
3 2.655 0.084707
4 105.866 0.970662
5 8.811 0.254495
6 85.757 0.942649
7 22.386 0.525841
8 65.447 0.887137
9 21.541 0.512294
10 6.765 0.201888
11 17.810 0.447698
12 16.994 0.432471
13 23.060 0.536371
14 5.387 0.164364
15 9.994 0.283330
16 20.314 0.491930
17 9.058 0.260604
18 10.242 0.289222
19 36.510 0.703887
20 36.486 0.703646
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.553562
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-12_07:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.5 -0.8 -1.6 1.6 -0.4
-1.2 1.7 -0.0 0.3 2.7 -2.4
1.1 -0.8 -0.4 -1.3 -0.6 1.8
0.3 -0.3 -0.8 -0.8 0.6 1.6
0.9 -0.5 0.2 -1.4 -0.6 -1.3
2.5 -1.1 0.2 1.1 0.6 -0.1
0.7 0.5 -2.0 0.4 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:55.897432
z-score=1.516334, p-value=0.925971
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-12_07:31
Test no p-value
1 0.116200
2 0.067757
3 0.955188
4 0.814700
5 0.958295
6 0.339068
7 0.004324
8 0.098850
9 0.034303
10 0.020204
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.005562
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-12_07:31:
(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 66715 0.04 66731 0.06
3 25000.00 24913 0.30 25086 0.30
4 6666.67 6730 0.60 6531 2.76
5 1388.89 1368 0.31 1366 0.38
6 238.10 239 0.00 252 0.81
7 34.72 26 2.19 29 0.94
8 4.96 8 1.86 4 0.19
p=0.49533 p=0.51081
Number of rngs required: 688119, p-value: 0.372
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-12_07:31
No. of wins: Observed Expected
98485 98585.9
z-score=-0.451, pvalue=0.32596
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66485 66666.7 0.495 0.495
2 37652 37654.3 0.000 0.495
3 27019 26954.7 0.153 0.648
4 19257 19313.5 0.165 0.813
5 13844 13851.4 0.004 0.817
6 9817 9943.5 1.610 2.428
7 7213 7145.0 0.647 3.075
8 5198 5139.1 0.676 3.750
9 3779 3699.9 1.693 5.443
10 2739 2666.3 1.982 7.425
11 1868 1923.3 1.592 9.017
12 1373 1388.7 0.178 9.195
13 969 1003.7 1.201 10.396
14 792 726.1 5.973 16.369
15 538 525.8 0.281 16.651
16 404 381.2 1.370 18.020
17 312 276.5 4.547 22.568
18 197 200.8 0.073 22.641
19 122 146.0 3.940 26.581
20 112 106.2 0.315 26.896
21 310 287.1 1.824 28.720
Chisq= 28.72 for 20 degrees of freedom, p= 0.90659
SUMMARY of craptest
p-value for no. of wins: 0.325959
p-value for throws/game: 0.906587
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-12_07:31
No. of wins: Observed Expected
98671 98585.9
z-score= 0.381, pvalue=0.64832
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66634 66666.7 0.016 0.016
2 37815 37654.3 0.686 0.702
3 26682 26954.7 2.760 3.461
4 19222 19313.5 0.433 3.894
5 13839 13851.4 0.011 3.905
6 9992 9943.5 0.236 4.142
7 7227 7145.0 0.940 5.082
8 5224 5139.1 1.404 6.486
9 3701 3699.9 0.000 6.486
10 2640 2666.3 0.259 6.745
11 1900 1923.3 0.283 7.028
12 1383 1388.7 0.024 7.052
13 1009 1003.7 0.028 7.080
14 742 726.1 0.346 7.426
15 537 525.8 0.237 7.663
16 394 381.2 0.433 8.096
17 301 276.5 2.164 10.260
18 183 200.8 1.583 11.843
19 156 146.0 0.687 12.530
20 100 106.2 0.364 12.894
21 319 287.1 3.541 16.435
Chisq= 16.43 for 20 degrees of freedom, p= 0.31070
SUMMARY of craptest
p-value for no. of wins: 0.648325
p-value for throws/game: 0.310702
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0038,0.0043,0.0056,0.0078,0.0080,0.0133,0.0156,0.0187,0.0202,0.0259,
0.0262,0.0265,0.0332,0.0333,0.0343,0.0403,0.0445,0.0450,0.0473,0.0602,
0.0658,0.0678,0.0744,0.0769,0.0806,0.0847,0.0897,0.0956,0.0967,0.0988,
0.1007,0.1016,0.1082,0.1088,0.1090,0.1155,0.1155,0.1162,0.1228,0.1247,
0.1367,0.1469,0.1547,0.1613,0.1620,0.1644,0.1683,0.1688,0.1693,0.1694,
0.1705,0.1718,0.1718,0.1777,0.1878,0.1879,0.1894,0.1942,0.2016,0.2019,
0.2029,0.2056,0.2147,0.2176,0.2227,0.2268,0.2292,0.2325,0.2347,0.2374,
0.2376,0.2464,0.2472,0.2507,0.2545,0.2558,0.2606,0.2663,0.2833,0.2840,
0.2842,0.2842,0.2857,0.2892,0.2902,0.2981,0.3028,0.3072,0.3107,0.3134,
0.3190,0.3260,0.3355,0.3366,0.3391,0.3475,0.3492,0.3536,0.3558,0.3565,
0.3645,0.3719,0.3881,0.3896,0.3927,0.3932,0.3938,0.3962,0.3970,0.4053,
0.4141,0.4201,0.4216,0.4281,0.4286,0.4325,0.4364,0.4375,0.4477,0.4488,
0.4493,0.4527,0.4591,0.4605,0.4636,0.4667,0.4712,0.4769,0.4792,0.4840,
0.4854,0.4901,0.4919,0.4941,0.4953,0.4957,0.4968,0.4994,0.5050,0.5053,
0.5064,0.5108,0.5117,0.5123,0.5128,0.5154,0.5212,0.5258,0.5276,0.5364,
0.5366,0.5370,0.5387,0.5393,0.5413,0.5517,0.5536,0.5558,0.5629,0.5675,
0.5682,0.5713,0.5802,0.5920,0.5973,0.5998,0.6020,0.6111,0.6122,0.6254,
0.6254,0.6257,0.6317,0.6332,0.6361,0.6372,0.6402,0.6402,0.6428,0.6442,
0.6483,0.6588,0.6635,0.6695,0.6711,0.6878,0.6898,0.6906,0.7036,0.7039,
0.7072,0.7075,0.7081,0.7140,0.7151,0.7176,0.7271,0.7300,0.7318,0.7352,
0.7359,0.7392,0.7410,0.7433,0.7459,0.7471,0.7540,0.7561,0.7566,0.7600,
0.7607,0.7710,0.7728,0.7758,0.7791,0.7812,0.7921,0.7927,0.7928,0.8041,
0.8093,0.8132,0.8147,0.8229,0.8273,0.8293,0.8354,0.8369,0.8423,0.8509,
0.8532,0.8631,0.8674,0.8677,0.8717,0.8732,0.8768,0.8773,0.8784,0.8871,
0.8980,0.8988,0.9066,0.9176,0.9191,0.9253,0.9260,0.9279,0.9336,0.9337,
0.9345,0.9377,0.9388,0.9426,0.9502,0.9552,0.9583,0.9586,0.9645,0.9649,
0.9674,0.9707,0.9756,0.9850,0.9851,0.9858,0.9899,0.9957,0.9965,
Overall p-value after applying KStest on 269 p-values = 0.859258
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.