RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-07_04:31
(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 11.3228 0.160702
2 to 25 15.66 24.1550 0.884716
3 to 26 15.98 15.4595 0.437579
4 to 27 15.91 5.2303 0.002958
5 to 28 15.65 11.0000 0.143437
6 to 29 15.72 15.2652 0.423611
7 to 30 16.00 14.8457 0.393402
8 to 31 15.95 14.4096 0.362077
9 to 32 15.84 19.6677 0.708423
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.333084
Tough bday spacings test for dh-ranFile-2015-12-07_04:31: 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 5 33 92 103 106 75 43 25 13 3 2
(O-E)^2/E 1.9 0.4 4.8 0.3 0.7 0.1 1.6 0.8 0.2 2.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 13.782, p= 0.817
RESULTS OF GCD FOR dh-ranFile-2015-12-07_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.098320
p-value, dist. of gcd's: 0.973773
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-07_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.131 0.061 0.094 0.006 0.774 0.043 0.614 0.599
Bits 8 to 15---> 0.394 0.040 0.424 0.671 0.226 0.225 0.552 0.632
Bits 16 to 23---> 0.555 0.535 0.806 0.838 0.430 0.115 0.324 0.236
Bits 24 to 31---> 0.962 0.087 0.183 0.119 0.955 0.929 0.157 0.361
KS test for the above 32 p values: 0.899
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-07_04:31,
p-values for 5 runs: 0.6241, 0.8449, 0.3013, 0.9566, 0.6794
Rank test for binary matrices (31x31) for dh-ranFile-2015-12-07_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 196 211.4 1.124 1.124
r= 29 5158 5134.0 0.112 1.236
r= 30 23148 23103.0 0.087 1.324
r= 31 11498 11551.5 0.248 1.572
chi-square = 1.572 with df = 3; p-value = 0.334
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2015-12-07_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 206 211.4 0.139 0.139
r= 30 5056 5134.0 1.185 1.324
r= 31 23228 23103.0 0.676 2.000
r= 32 11510 11551.5 0.149 2.149
chi-square = 2.149 with df = 3; p-value = 0.458
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2015-12-07_04:31
b-rank test for bits 1 to 8, p=0.85592
b-rank test for bits 2 to 9, p=0.49371
b-rank test for bits 3 to 10, p=0.48587
b-rank test for bits 4 to 11, p=0.69530
b-rank test for bits 5 to 12, p=0.83305
b-rank test for bits 6 to 13, p=0.77765
b-rank test for bits 7 to 14, p=0.28478
b-rank test for bits 8 to 15, p=0.11221
b-rank test for bits 9 to 16, p=0.87084
b-rank test for bits 10 to 17, p=0.48100
b-rank test for bits 11 to 18, p=0.71960
b-rank test for bits 12 to 19, p=0.08585
b-rank test for bits 13 to 20, p=0.64751
b-rank test for bits 14 to 21, p=0.64825
b-rank test for bits 15 to 22, p=0.34187
b-rank test for bits 16 to 23, p=0.39931
b-rank test for bits 17 to 24, p=0.67629
b-rank test for bits 18 to 25, p=0.84702
b-rank test for bits 19 to 26, p=0.57970
b-rank test for bits 20 to 27, p=0.06751
b-rank test for bits 21 to 28, p=0.57418
b-rank test for bits 22 to 29, p=0.03066
b-rank test for bits 23 to 30, p=0.54708
b-rank test for bits 24 to 31, p=0.01211
b-rank test for bits 25 to 32, p=0.05805
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 = 0.522409
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-07_04:31
(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 142099 0.44 0.671173
2 141342 -1.33 0.092497
3 142358 1.05 0.852749
4 142153 0.57 0.715431
5 141707 -0.47 0.318202
6 141846 -0.15 0.441184
7 141310 -1.40 0.080711
8 141128 -1.83 0.033960
9 142311 0.94 0.826001
10 141818 -0.21 0.415512
11 141807 -0.24 0.405518
12 141500 -0.96 0.169441
13 142164 0.60 0.724086
14 141789 -0.28 0.389300
15 143265 3.17 0.999231
16 141802 -0.25 0.400996
17 141918 0.02 0.508081
18 141808 -0.24 0.406425
19 141955 0.11 0.542489
20 141528 -0.89 0.186476
----------------------------------------------------------------
OPSO test for dh-ranFile-2015-12-07_04:31
Bits used No. missing words z-score p-value
23 to 32 141691 -0.7529 0.225766
22 to 31 141581 -1.1322 0.128781
21 to 30 141976 0.2299 0.590914
20 to 29 141640 -0.9287 0.176516
19 to 28 141465 -1.5322 0.062740
18 to 27 141713 -0.6770 0.249203
17 to 26 142176 0.9196 0.821097
16 to 25 141853 -0.1942 0.422994
15 to 24 142066 0.5402 0.705485
14 to 23 141869 -0.1391 0.444698
13 to 22 142105 0.6747 0.750075
12 to 21 141575 -1.1529 0.124484
11 to 20 141681 -0.7873 0.215540
10 to 19 141830 -0.2736 0.392215
9 to 18 141912 0.0092 0.503673
8 to 17 141574 -1.1563 0.123777
7 to 16 141765 -0.4977 0.309351
6 to 15 142150 0.8299 0.796701
5 to 14 141820 -0.3080 0.379028
4 to 13 141437 -1.6287 0.051686
3 to 12 141994 0.2920 0.614844
2 to 11 141510 -1.3770 0.084256
1 to 10 141892 -0.0598 0.476174
-----------------------------------------------------------------
OQSO test for dh-ranFile-2015-12-07_04:31
Bits used No. missing words z-score p-value
28 to 32 141754 -0.5265 0.299256
27 to 31 142004 0.3209 0.625863
26 to 30 142206 1.0057 0.842711
25 to 29 141301 -2.0621 0.019597
24 to 28 141598 -1.0554 0.145631
23 to 27 141494 -1.4079 0.079581
22 to 26 141922 0.0429 0.517129
21 to 25 142097 0.6362 0.737667
20 to 24 142222 1.0599 0.855405
19 to 23 141929 0.0667 0.526581
18 to 22 141726 -0.6215 0.267149
17 to 21 142214 1.0328 0.849147
16 to 20 142146 0.8023 0.788802
15 to 19 141732 -0.6011 0.273881
14 to 18 141985 0.2565 0.601221
13 to 17 141935 0.0870 0.534671
12 to 16 141971 0.2091 0.582796
11 to 15 141240 -2.2689 0.011637
10 to 14 141572 -1.1435 0.126417
9 to 13 141497 -1.3977 0.081097
8 to 12 142275 1.2396 0.892431
7 to 11 141916 0.0226 0.509019
6 to 10 141897 -0.0418 0.483330
5 to 9 142289 1.2870 0.900956
4 to 8 141387 -1.7706 0.038313
3 to 7 141844 -0.2215 0.412368
2 to 6 141875 -0.1164 0.453679
1 to 5 142026 0.3955 0.653760
-----------------------------------------------------------------
DNA test for dh-ranFile-2015-12-07_04:31
Bits used No. missing words z-score p-value
31 to 32 142183 0.8073 0.790249
30 to 31 142211 0.8899 0.813235
29 to 30 142391 1.4209 0.922321
28 to 29 142203 0.8663 0.806833
27 to 28 142015 0.3117 0.622370
26 to 27 142093 0.5418 0.706022
25 to 26 142539 1.8574 0.968375
24 to 25 141809 -0.2960 0.383631
23 to 24 141952 0.1259 0.550083
22 to 23 142254 1.0167 0.845358
21 to 22 142079 0.5005 0.691639
20 to 21 141913 0.0108 0.504319
19 to 20 142293 1.1318 0.871134
18 to 19 142239 0.9725 0.834594
17 to 18 142008 0.2911 0.614498
16 to 17 142379 1.3855 0.917044
15 to 16 141972 0.1849 0.573333
14 to 15 141908 -0.0039 0.498435
13 to 14 142213 0.8958 0.814815
12 to 13 142258 1.0285 0.848149
11 to 12 142428 1.5300 0.936992
10 to 11 142227 0.9371 0.825641
9 to 10 141925 0.0462 0.518434
8 to 9 142380 1.3884 0.917493
7 to 8 141957 0.1406 0.555915
6 to 7 141515 -1.1632 0.122371
5 to 6 141938 0.0846 0.533699
4 to 5 142350 1.2999 0.903184
3 to 4 141438 -1.3904 0.082211
2 to 3 141899 -0.0305 0.487845
1 to 2 141725 -0.5437 0.293308
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-07_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2545.15 0.638 0.738421
Test results for specific bytes for dh-ranFile-2015-12-07_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2459.74 -0.569 0.284534
2 to 9 2559.19 0.837 0.798705
3 to 10 2525.69 0.363 0.641801
4 to 11 2598.23 1.389 0.917615
5 to 12 2545.21 0.639 0.738706
6 to 13 2490.45 -0.135 0.446289
7 to 14 2373.87 -1.784 0.037232
8 to 15 2434.55 -0.926 0.177322
9 to 16 2567.88 0.960 0.831462
10 to 17 2568.15 0.964 0.832431
11 to 18 2528.23 0.399 0.655161
12 to 19 2469.34 -0.434 0.332298
13 to 20 2428.94 -1.005 0.157453
14 to 21 2555.89 0.790 0.785372
15 to 22 2504.06 0.057 0.522908
16 to 23 2600.45 1.421 0.922277
17 to 24 2535.43 0.501 0.691859
18 to 25 2692.24 2.719 0.996723
19 to 26 2502.27 0.032 0.512833
20 to 27 2557.06 0.807 0.790171
21 to 28 2359.34 -1.989 0.023339
22 to 29 2478.65 -0.302 0.381334
23 to 30 2561.13 0.865 0.806363
24 to 31 2643.89 2.035 0.979067
25 to 32 2498.86 -0.016 0.493589
CDPARK for dh-ranFile-2015-12-07_04:31: 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
3514 -0.4110 0.340551
3512 -0.5023 0.307734
3509 -0.6393 0.261324
3575 2.3744 0.991212
3569 2.1005 0.982156
3529 0.2740 0.607947
3541 0.8219 0.794438
3528 0.2283 0.590298
3549 1.1872 0.882429
3532 0.4110 0.659449
Square side=100, avg. no. parked=3535.80 sample std.=21.73
p-value of the KSTEST for those 10 p-values: 0.138777
Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-07_04:31
0.7000,0.5635,0.1325,0.8742,0.6073,0.7423,0.8099,0.1213,0.5909,0.9042,
The KS test for those 10 p-values: 0.319017
The 3DSPHERES test for dh-ranFile-2015-12-07_04:31
sample no r^3 equiv. uni.
1 30.990 0.644060
2 19.485 0.477691
3 28.988 0.619501
4 28.756 0.616544
5 20.466 0.494504
6 27.689 0.602660
7 63.137 0.878103
8 69.769 0.902280
9 21.760 0.515845
10 4.023 0.125489
11 41.371 0.748177
12 83.924 0.939036
13 66.276 0.890210
14 56.113 0.845945
15 9.812 0.278956
16 51.282 0.819023
17 24.267 0.554651
18 33.545 0.673117
19 23.087 0.536789
20 78.700 0.927439
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.019427
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-07_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 -0.7 -0.1 -1.9 1.5 -0.7
0.3 1.0 -0.2 0.7 -1.5 -0.7
0.5 1.2 0.2 0.8 -0.9 -0.2
0.9 0.3 0.1 0.5 0.9 -1.9
0.7 -0.1 -0.6 -1.7 0.1 -0.9
-2.1 -1.1 -0.4 -1.1 -0.6 -0.3
0.5 0.8 -0.4 -0.7 0.9 0.0
-0.1
Chi-square with 42 degrees of freedom:38.159434
z-score=-0.419040, p-value=0.359741
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2015-12-07_04:31
Test no p-value
1 0.012626
2 0.033483
3 0.188303
4 0.441284
5 0.098294
6 0.511169
7 0.024412
8 0.167755
9 0.262760
10 0.124273
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000474
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-07_04:31:
(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 66586 0.10 66605 0.06
3 25000.00 25110 0.48 25081 0.26
4 6666.67 6622 0.30 6629 0.21
5 1388.89 1418 0.61 1402 0.12
6 238.10 232 0.16 245 0.20
7 34.72 26 2.19 34 0.01
8 4.96 5 0.00 3 0.77
p=0.30134 p=0.05077
Number of rngs required: 687736, p-value: 0.220
RESULTS OF CRAPS TEST for dh-ranFile-2015-12-07_04:31
No. of wins: Observed Expected
98438 98585.9
z-score=-0.661, pvalue=0.25421
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66292 66666.7 2.106 2.106
2 37836 37654.3 0.877 2.982
3 27026 26954.7 0.188 3.171
4 19433 19313.5 0.740 3.911
5 13880 13851.4 0.059 3.969
6 9806 9943.5 1.903 5.872
7 7170 7145.0 0.087 5.959
8 5158 5139.1 0.070 6.029
9 3674 3699.9 0.181 6.210
10 2703 2666.3 0.505 6.715
11 1906 1923.3 0.156 6.871
12 1397 1388.7 0.049 6.920
13 953 1003.7 2.562 9.483
14 736 726.1 0.134 9.617
15 555 525.8 1.618 11.234
16 394 381.2 0.433 11.667
17 312 276.5 4.547 16.214
18 209 200.8 0.332 16.547
19 168 146.0 3.320 19.867
20 113 106.2 0.433 20.300
21 279 287.1 0.229 20.530
Chisq= 20.53 for 20 degrees of freedom, p= 0.57474
SUMMARY of craptest
p-value for no. of wins: 0.254207
p-value for throws/game: 0.574736
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-07_04:31
No. of wins: Observed Expected
98620 98585.9
z-score= 0.153, pvalue=0.56068
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66487 66666.7 0.484 0.484
2 37850 37654.3 1.017 1.501
3 27155 26954.7 1.488 2.989
4 19124 19313.5 1.859 4.848
5 13883 13851.4 0.072 4.920
6 9966 9943.5 0.051 4.970
7 7146 7145.0 0.000 4.970
8 5093 5139.1 0.413 5.384
9 3599 3699.9 2.750 8.133
10 2710 2666.3 0.716 8.850
11 1955 1923.3 0.522 9.371
12 1407 1388.7 0.240 9.611
13 1034 1003.7 0.914 10.525
14 718 726.1 0.091 10.616
15 522 525.8 0.028 10.644
16 338 381.2 4.885 15.529
17 257 276.5 1.381 16.910
18 201 200.8 0.000 16.910
19 153 146.0 0.337 17.247
20 115 106.2 0.727 17.974
21 287 287.1 0.000 17.974
Chisq= 17.97 for 20 degrees of freedom, p= 0.41087
SUMMARY of craptest
p-value for no. of wins: 0.560683
p-value for throws/game: 0.410871
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0030,0.0063,0.0116,0.0121,0.0126,0.0194,0.0196,0.0233,0.0244,
0.0307,0.0335,0.0340,0.0372,0.0383,0.0404,0.0434,0.0508,0.0517,0.0580,
0.0607,0.0627,0.0675,0.0796,0.0807,0.0811,0.0822,0.0843,0.0858,0.0866,
0.0925,0.0936,0.0983,0.0983,0.1122,0.1152,0.1186,0.1213,0.1224,0.1238,
0.1243,0.1245,0.1255,0.1264,0.1288,0.1315,0.1325,0.1388,0.1434,0.1456,
0.1566,0.1575,0.1607,0.1678,0.1694,0.1765,0.1773,0.1828,0.1865,0.1883,
0.2155,0.2205,0.2247,0.2258,0.2265,0.2364,0.2492,0.2542,0.2613,0.2628,
0.2671,0.2739,0.2790,0.2845,0.2848,0.2933,0.2993,0.3013,0.3013,0.3077,
0.3094,0.3182,0.3190,0.3241,0.3323,0.3331,0.3342,0.3406,0.3419,0.3597,
0.3605,0.3621,0.3790,0.3813,0.3836,0.3893,0.3922,0.3934,0.3938,0.3993,
0.4010,0.4055,0.4064,0.4109,0.4124,0.4155,0.4230,0.4236,0.4245,0.4299,
0.4376,0.4412,0.4413,0.4447,0.4463,0.4537,0.4580,0.4762,0.4777,0.4810,
0.4833,0.4859,0.4878,0.4936,0.4937,0.4945,0.4984,0.5037,0.5043,0.5081,
0.5090,0.5112,0.5128,0.5158,0.5171,0.5184,0.5224,0.5229,0.5266,0.5337,
0.5347,0.5352,0.5368,0.5425,0.5471,0.5501,0.5515,0.5547,0.5553,0.5559,
0.5607,0.5635,0.5733,0.5742,0.5747,0.5797,0.5828,0.5903,0.5909,0.5909,
0.5994,0.6012,0.6027,0.6073,0.6079,0.6140,0.6145,0.6148,0.6165,0.6195,
0.6224,0.6241,0.6259,0.6319,0.6418,0.6441,0.6475,0.6483,0.6538,0.6552,
0.6594,0.6712,0.6714,0.6731,0.6763,0.6794,0.6916,0.6919,0.6953,0.7000,
0.7055,0.7060,0.7084,0.7154,0.7196,0.7241,0.7377,0.7384,0.7387,0.7423,
0.7482,0.7501,0.7738,0.7777,0.7854,0.7888,0.7902,0.7902,0.7944,0.7967,
0.7987,0.8062,0.8064,0.8068,0.8099,0.8132,0.8148,0.8168,0.8190,0.8211,
0.8256,0.8260,0.8315,0.8324,0.8331,0.8346,0.8382,0.8427,0.8449,0.8454,
0.8459,0.8470,0.8481,0.8491,0.8527,0.8554,0.8559,0.8708,0.8711,0.8742,
0.8781,0.8824,0.8847,0.8902,0.8924,0.8992,0.9010,0.9023,0.9032,0.9042,
0.9170,0.9175,0.9176,0.9223,0.9223,0.9274,0.9290,0.9370,0.9390,0.9554,
0.9566,0.9617,0.9684,0.9738,0.9791,0.9822,0.9912,0.9967,0.9992,
Overall p-value after applying KStest on 269 p-values = 0.575884
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.