RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-04-30_23:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.84 20.7293 0.761366
2 to 25 16.02 20.6442 0.757388
3 to 26 16.01 21.2306 0.783853
4 to 27 15.88 17.9005 0.604859
5 to 28 15.89 18.3527 0.633074
6 to 29 15.94 26.1993 0.929095
7 to 30 15.69 23.7149 0.872610
8 to 31 16.20 23.0322 0.851794
9 to 32 15.82 18.2714 0.628082
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.007826
Tough bday spacings test for dh-ranFile-2017-04-30_23:31: 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 9 39 70 86 94 78 62 34 17 7 4
(O-E)^2/E 0.0 0.2 0.1 1.4 0.1 0.0 1.9 0.6 0.3 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 4.645, p= 0.086
RESULTS OF GCD FOR dh-ranFile-2017-04-30_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.290020
p-value, dist. of gcd's: 0.257085
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-04-30_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.832 0.353 0.146 0.599 0.825 0.598 0.025 0.500
Bits 8 to 15---> 0.186 0.739 0.889 0.962 0.418 0.755 0.045 0.029
Bits 16 to 23---> 0.697 0.556 0.724 0.677 0.695 0.001 0.057 0.117
Bits 24 to 31---> 0.176 0.507 0.619 0.785 0.558 0.556 0.219 0.766
KS test for the above 32 p values: 0.589
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-04-30_23:31,
p-values for 5 runs: 0.2142, 0.7938, 0.7781, 0.7966, 0.9033
Rank test for binary matrices (31x31) for dh-ranFile-2017-04-30_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 213 211.4 0.012 0.012
r= 29 5035 5134.0 1.909 1.921
r= 30 23133 23103.0 0.039 1.960
r= 31 11619 11551.5 0.394 2.354
chi-square = 2.354 with df = 3; p-value = 0.498
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2017-04-30_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 222 211.4 0.530 0.530
r= 30 5060 5134.0 1.067 1.597
r= 31 23077 23103.0 0.029 1.626
r= 32 11641 11551.5 0.693 2.319
chi-square = 2.319 with df = 3; p-value = 0.491
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2017-04-30_23:31
b-rank test for bits 1 to 8, p=0.10019
b-rank test for bits 2 to 9, p=0.61982
b-rank test for bits 3 to 10, p=0.98711
b-rank test for bits 4 to 11, p=0.60361
b-rank test for bits 5 to 12, p=0.06184
b-rank test for bits 6 to 13, p=0.78164
b-rank test for bits 7 to 14, p=0.47732
b-rank test for bits 8 to 15, p=0.82469
b-rank test for bits 9 to 16, p=0.10952
b-rank test for bits 10 to 17, p=0.21552
b-rank test for bits 11 to 18, p=0.88560
b-rank test for bits 12 to 19, p=0.63979
b-rank test for bits 13 to 20, p=0.14411
b-rank test for bits 14 to 21, p=0.44626
b-rank test for bits 15 to 22, p=0.81885
b-rank test for bits 16 to 23, p=0.74262
b-rank test for bits 17 to 24, p=0.75387
b-rank test for bits 18 to 25, p=0.30516
b-rank test for bits 19 to 26, p=0.59401
b-rank test for bits 20 to 27, p=0.09645
b-rank test for bits 21 to 28, p=0.68389
b-rank test for bits 22 to 29, p=0.71659
b-rank test for bits 23 to 30, p=0.89369
b-rank test for bits 24 to 31, p=0.19700
b-rank test for bits 25 to 32, p=0.58596
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 = 0.679370
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-04-30_23:31
(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 141582 -0.76 0.222198
2 142338 1.00 0.841723
3 141436 -1.11 0.134382
4 141805 -0.24 0.403708
5 142114 0.48 0.683746
6 141755 -0.36 0.359205
7 141985 0.18 0.570167
8 142175 0.62 0.732610
9 142321 0.96 0.831936
10 142066 0.37 0.642837
11 142450 1.26 0.896750
12 141406 -1.18 0.119797
13 141628 -0.66 0.255490
14 141374 -1.25 0.105509
15 142009 0.23 0.592070
16 141714 -0.46 0.324059
17 142156 0.58 0.717805
18 142044 0.31 0.623486
19 142328 0.98 0.836013
20 142510 1.40 0.919756
----------------------------------------------------------------
OPSO test for dh-ranFile-2017-04-30_23:31
Bits used No. missing words z-score p-value
23 to 32 142129 0.7575 0.775620
22 to 31 142671 2.6264 0.995686
21 to 30 142334 1.4644 0.928455
20 to 29 142083 0.5989 0.725368
19 to 28 141823 -0.2977 0.382970
18 to 27 141865 -0.1529 0.439254
17 to 26 142065 0.5368 0.704295
16 to 25 141953 0.1506 0.559849
15 to 24 141574 -1.1563 0.123777
14 to 23 141339 -1.9667 0.024611
13 to 22 141662 -0.8529 0.196868
12 to 21 141557 -1.2149 0.112196
11 to 20 141524 -1.3287 0.091970
10 to 19 142200 1.0023 0.841903
9 to 18 141647 -0.9046 0.182842
8 to 17 142016 0.3678 0.643499
7 to 16 142132 0.7678 0.778705
6 to 15 142063 0.5299 0.701908
5 to 14 142238 1.1333 0.871465
4 to 13 141834 -0.2598 0.397525
3 to 12 141816 -0.3218 0.373792
2 to 11 141806 -0.3563 0.360804
1 to 10 142075 0.5713 0.716094
-----------------------------------------------------------------
OQSO test for dh-ranFile-2017-04-30_23:31
Bits used No. missing words z-score p-value
28 to 32 141738 -0.5808 0.280695
27 to 31 141698 -0.7164 0.236881
26 to 30 142604 2.3548 0.990734
25 to 29 142042 0.4497 0.673547
24 to 28 141663 -0.8350 0.201854
23 to 27 141788 -0.4113 0.340431
22 to 26 141584 -1.1028 0.135054
21 to 25 141969 0.2023 0.580148
20 to 24 142120 0.7141 0.762428
19 to 23 142247 1.1446 0.873822
18 to 22 142145 0.7989 0.787820
17 to 21 142227 1.0768 0.859226
16 to 20 142032 0.4158 0.661233
15 to 19 142098 0.6396 0.738770
14 to 18 142104 0.6599 0.745341
13 to 17 141952 0.1446 0.557504
12 to 16 142091 0.6158 0.730997
11 to 15 141300 -2.0655 0.019437
10 to 14 141929 0.0667 0.526581
9 to 13 141784 -0.4248 0.335474
8 to 12 142217 1.0429 0.851514
7 to 11 142230 1.0870 0.861485
6 to 10 142303 1.3345 0.908976
5 to 9 141447 -1.5672 0.058532
4 to 8 141529 -1.2893 0.098655
3 to 7 141835 -0.2520 0.400534
2 to 6 141714 -0.6621 0.253942
1 to 5 141784 -0.4248 0.335474
-----------------------------------------------------------------
DNA test for dh-ranFile-2017-04-30_23:31
Bits used No. missing words z-score p-value
31 to 32 141549 -1.0629 0.143909
30 to 31 141393 -1.5231 0.063867
29 to 30 142009 0.2940 0.615626
28 to 29 142306 1.1701 0.879023
27 to 28 141477 -1.2753 0.101100
26 to 27 142035 0.3707 0.644573
25 to 26 141843 -0.1957 0.422437
24 to 25 141599 -0.9154 0.179984
23 to 24 141971 0.1819 0.572176
22 to 23 141911 0.0049 0.501965
21 to 22 141607 -0.8918 0.186242
20 to 21 142096 0.5506 0.709063
19 to 20 141738 -0.5054 0.306640
18 to 19 141983 0.2173 0.586019
17 to 18 141534 -1.1072 0.134111
16 to 17 141859 -0.1485 0.440988
15 to 16 140987 -2.7207 0.003257
14 to 15 141561 -1.0275 0.152087
13 to 14 141782 -0.3756 0.353605
12 to 13 141938 0.0846 0.533699
11 to 12 141620 -0.8535 0.196696
10 to 11 141995 0.2527 0.599755
9 to 10 141889 -0.0600 0.476090
8 to 9 142176 0.7866 0.784253
7 to 8 142140 0.6804 0.751888
6 to 7 142114 0.6037 0.726994
5 to 6 141873 -0.1072 0.457328
4 to 5 141672 -0.7001 0.241936
3 to 4 142079 0.5005 0.691639
2 to 3 141194 -2.1101 0.017424
1 to 2 141773 -0.4022 0.343786
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2017-04-30_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2429.11 -1.002 0.158057
Test results for specific bytes for dh-ranFile-2017-04-30_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2546.97 0.664 0.746759
2 to 9 2395.89 -1.472 0.070459
3 to 10 2683.50 2.595 0.995273
4 to 11 2444.87 -0.780 0.217807
5 to 12 2732.51 3.288 0.999496
6 to 13 2545.99 0.650 0.742289
7 to 14 2470.99 -0.410 0.340824
8 to 15 2398.44 -1.436 0.075468
9 to 16 2440.50 -0.841 0.200057
10 to 17 2515.14 0.214 0.584794
11 to 18 2568.20 0.964 0.832594
12 to 19 2534.39 0.486 0.686631
13 to 20 2554.44 0.770 0.779336
14 to 21 2299.98 -2.829 0.002337
15 to 22 2524.47 0.346 0.635370
16 to 23 2439.56 -0.855 0.196350
17 to 24 2417.26 -1.170 0.120986
18 to 25 2404.12 -1.356 0.087556
19 to 26 2466.86 -0.469 0.319664
20 to 27 2599.26 1.404 0.919808
21 to 28 2591.84 1.299 0.902999
22 to 29 2372.31 -1.806 0.035477
23 to 30 2402.88 -1.373 0.084807
24 to 31 2538.35 0.542 0.706219
25 to 32 2629.25 1.828 0.966215
CDPARK for dh-ranFile-2017-04-30_23:31: 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
3552 1.3242 0.907282
3538 0.6849 0.753306
3501 -1.0046 0.157553
3513 -0.4566 0.323972
3518 -0.2283 0.409702
3527 0.1826 0.572463
3531 0.3653 0.642555
3513 -0.4566 0.323972
3503 -0.9132 0.180558
3516 -0.3196 0.374623
Square side=100, avg. no. parked=3521.20 sample std.=15.07
p-value of the KSTEST for those 10 p-values: 0.757749
Results for the MINIMUM DISTANCE test for dh-ranFile-2017-04-30_23:31
0.1104,0.4715,0.4600,0.5452,0.0630,0.7343,0.1354,0.2259,0.4814,0.2390,
The KS test for those 10 p-values: 0.137647
The 3DSPHERES test for dh-ranFile-2017-04-30_23:31
sample no r^3 equiv. uni.
1 37.211 0.710724
2 7.016 0.208540
3 30.450 0.637595
4 62.462 0.875328
5 16.088 0.415064
6 75.909 0.920364
7 14.806 0.389531
8 46.422 0.787200
9 48.513 0.801524
10 21.582 0.512957
11 23.525 0.543506
12 7.325 0.216640
13 4.641 0.143320
14 27.020 0.593707
15 10.417 0.293367
16 13.124 0.354332
17 14.524 0.383767
18 16.322 0.419615
19 76.016 0.920647
20 33.933 0.677326
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.558902
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-04-30_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.5 -0.6 -0.8 -0.5 0.7
-0.1 1.5 0.2 -0.2 0.2 -0.4
1.3 -0.0 -1.0 -2.0 -1.1 1.5
-0.9 0.0 -0.1 -0.3 1.8 1.2
-0.4 0.3 0.2 0.2 -0.4 -0.4
-0.2 1.9 -0.0 -1.0 2.4 1.0
1.4 -1.3 3.0 -0.7 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:46.919891
z-score=0.536804, p-value=0.722173
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2017-04-30_23:31
Test no p-value
1 0.011585
2 0.595520
3 0.828911
4 0.548720
5 0.647765
6 0.104941
7 0.193254
8 0.104962
9 0.467885
10 0.013240
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.083683
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-04-30_23:31:
(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 66699 0.02 66461 0.63
3 25000.00 24942 0.13 25098 0.38
4 6666.67 6617 0.37 6722 0.46
5 1388.89 1416 0.53 1440 1.88
6 238.10 283 8.47 234 0.07
7 34.72 37 0.15 37 0.15
8 4.96 5 0.00 7 0.84
p=0.86068 p=0.37968
Number of rngs required: 690441, p-value: 0.992
RESULTS OF CRAPS TEST for dh-ranFile-2017-04-30_23:31
No. of wins: Observed Expected
98466 98585.9
z-score=-0.536, pvalue=0.29595
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66451 66666.7 0.698 0.698
2 38091 37654.3 5.064 5.762
3 26740 26954.7 1.711 7.473
4 19198 19313.5 0.690 8.163
5 13928 13851.4 0.423 8.586
6 9944 9943.5 0.000 8.586
7 7137 7145.0 0.009 8.595
8 5109 5139.1 0.176 8.771
9 3749 3699.9 0.653 9.424
10 2663 2666.3 0.004 9.428
11 1912 1923.3 0.067 9.495
12 1389 1388.7 0.000 9.495
13 1030 1003.7 0.688 10.183
14 710 726.1 0.359 10.542
15 558 525.8 1.967 12.509
16 354 381.2 1.934 14.443
17 271 276.5 0.111 14.554
18 198 200.8 0.040 14.594
19 162 146.0 1.757 16.351
20 111 106.2 0.216 16.567
21 295 287.1 0.217 16.783
Chisq= 16.78 for 20 degrees of freedom, p= 0.33299
SUMMARY of craptest
p-value for no. of wins: 0.295952
p-value for throws/game: 0.332992
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2017-04-30_23:31
No. of wins: Observed Expected
98407 98585.9
z-score=-0.800, pvalue=0.21187
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66710 66666.7 0.028 0.028
2 37718 37654.3 0.108 0.136
3 27024 26954.7 0.178 0.314
4 19209 19313.5 0.565 0.879
5 13750 13851.4 0.743 1.621
6 9858 9943.5 0.736 2.357
7 7168 7145.0 0.074 2.431
8 5193 5139.1 0.566 2.997
9 3683 3699.9 0.077 3.074
10 2564 2666.3 3.925 6.999
11 2050 1923.3 8.343 15.341
12 1414 1388.7 0.459 15.801
13 996 1003.7 0.059 15.860
14 737 726.1 0.162 16.023
15 495 525.8 1.808 17.831
16 373 381.2 0.174 18.005
17 280 276.5 0.043 18.048
18 199 200.8 0.017 18.065
19 153 146.0 0.337 18.402
20 118 106.2 1.308 19.710
21 308 287.1 1.519 21.229
Chisq= 21.23 for 20 degrees of freedom, p= 0.61624
SUMMARY of craptest
p-value for no. of wins: 0.211867
p-value for throws/game: 0.616243
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0008,0.0023,0.0033,0.0078,0.0116,0.0132,0.0174,0.0194,0.0246,0.0247,
0.0294,0.0355,0.0452,0.0572,0.0585,0.0618,0.0630,0.0639,0.0705,0.0755,
0.0837,0.0848,0.0864,0.0876,0.0920,0.0965,0.0987,0.1002,0.1011,0.1049,
0.1050,0.1055,0.1095,0.1104,0.1122,0.1174,0.1198,0.1210,0.1238,0.1341,
0.1344,0.1351,0.1354,0.1376,0.1433,0.1439,0.1441,0.1461,0.1521,0.1576,
0.1581,0.1760,0.1800,0.1806,0.1828,0.1862,0.1864,0.1933,0.1963,0.1967,
0.1969,0.1970,0.2001,0.2019,0.2085,0.2119,0.2142,0.2155,0.2166,0.2178,
0.2187,0.2222,0.2259,0.2369,0.2390,0.2419,0.2539,0.2555,0.2571,0.2807,
0.2900,0.2934,0.2960,0.3052,0.3066,0.3197,0.3240,0.3240,0.3241,0.3330,
0.3355,0.3355,0.3404,0.3408,0.3438,0.3532,0.3536,0.3543,0.3592,0.3608,
0.3738,0.3746,0.3797,0.3830,0.3838,0.3895,0.3975,0.4005,0.4037,0.4097,
0.4151,0.4176,0.4196,0.4224,0.4393,0.4410,0.4463,0.4573,0.4600,0.4679,
0.4715,0.4761,0.4773,0.4814,0.4911,0.4978,0.5004,0.5020,0.5075,0.5130,
0.5266,0.5337,0.5435,0.5452,0.5487,0.5556,0.5560,0.5575,0.5584,0.5589,
0.5598,0.5702,0.5722,0.5725,0.5801,0.5848,0.5860,0.5860,0.5894,0.5921,
0.5937,0.5940,0.5955,0.5976,0.5994,0.5998,0.6036,0.6049,0.6156,0.6162,
0.6186,0.6198,0.6235,0.6281,0.6331,0.6354,0.6376,0.6398,0.6426,0.6428,
0.6435,0.6446,0.6478,0.6612,0.6735,0.6773,0.6774,0.6794,0.6837,0.6839,
0.6866,0.6916,0.6952,0.6967,0.7019,0.7043,0.7062,0.7091,0.7107,0.7161,
0.7166,0.7178,0.7222,0.7244,0.7254,0.7270,0.7310,0.7326,0.7343,0.7388,
0.7392,0.7423,0.7426,0.7453,0.7468,0.7519,0.7533,0.7539,0.7552,0.7574,
0.7577,0.7614,0.7624,0.7660,0.7756,0.7781,0.7787,0.7793,0.7816,0.7839,
0.7843,0.7853,0.7872,0.7878,0.7938,0.7966,0.8015,0.8189,0.8247,0.8249,
0.8289,0.8319,0.8320,0.8326,0.8360,0.8417,0.8419,0.8515,0.8518,0.8592,
0.8607,0.8615,0.8715,0.8726,0.8738,0.8753,0.8790,0.8856,0.8889,0.8937,
0.8967,0.9030,0.9033,0.9073,0.9090,0.9198,0.9198,0.9204,0.9206,0.9285,
0.9291,0.9618,0.9662,0.9871,0.9907,0.9924,0.9953,0.9957,0.9995,
Overall p-value after applying KStest on 269 p-values = 0.295456
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.