RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-25_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.03 13.3003 0.284139 2 to 25 15.69 15.1860 0.417916 3 to 26 15.79 19.0167 0.672426 4 to 27 15.83 12.4402 0.227219 5 to 28 15.84 13.3603 0.288251 6 to 29 16.20 14.5440 0.371710 7 to 30 15.47 31.3646 0.981974 8 to 31 15.79 9.0159 0.060239 9 to 32 15.75 18.0536 0.614534 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.641719 Tough bday spacings test for dh-ranFile-2015-07-25_08:31: 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 12 28 72 104 107 67 60 25 16 5 4 (O-E)^2/E 0.9 2.0 0.0 0.4 0.9 1.6 1.2 0.8 0.1 0.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 8.267, p= 0.397 RESULTS OF GCD FOR dh-ranFile-2015-07-25_08:31 Euclid's algorithm: p-value, steps to gcd: 0.604587 p-value, dist. of gcd's: 0.561396 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-25_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.562 0.760 0.093 0.554 0.903 0.073 0.751 0.901 Bits 8 to 15---> 0.610 0.859 0.893 0.238 0.530 0.118 0.850 0.777 Bits 16 to 23---> 0.760 0.957 0.903 0.701 0.843 0.400 0.821 0.310 Bits 24 to 31---> 0.909 0.374 0.879 0.463 0.501 0.933 0.973 0.138 KS test for the above 32 p values: 0.992 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-25_08:31, p-values for 5 runs: 0.2802, 0.7948, 0.1878, 0.2099, 0.1338 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-25_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 228 211.4 1.301 1.301 r= 29 5065 5134.0 0.928 2.228 r= 30 23330 23103.0 2.229 4.458 r= 31 11377 11551.5 2.637 7.094 chi-square = 7.094 with df = 3; p-value = 0.931 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-25_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 241 211.4 4.139 4.139 r= 30 5159 5134.0 0.122 4.261 r= 31 23171 23103.0 0.200 4.461 r= 32 11429 11551.5 1.300 5.760 chi-square = 5.760 with df = 3; p-value = 0.876 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-25_08:31 b-rank test for bits 1 to 8, p=0.09758 b-rank test for bits 2 to 9, p=0.22986 b-rank test for bits 3 to 10, p=0.06338 b-rank test for bits 4 to 11, p=0.46054 b-rank test for bits 5 to 12, p=0.88499 b-rank test for bits 6 to 13, p=0.57504 b-rank test for bits 7 to 14, p=0.67736 b-rank test for bits 8 to 15, p=0.92419 b-rank test for bits 9 to 16, p=0.27702 b-rank test for bits 10 to 17, p=0.56202 b-rank test for bits 11 to 18, p=0.54226 b-rank test for bits 12 to 19, p=0.92352 b-rank test for bits 13 to 20, p=0.27275 b-rank test for bits 14 to 21, p=0.13240 b-rank test for bits 15 to 22, p=0.83212 b-rank test for bits 16 to 23, p=0.61294 b-rank test for bits 17 to 24, p=0.27273 b-rank test for bits 18 to 25, p=0.01300 b-rank test for bits 19 to 26, p=0.30399 b-rank test for bits 20 to 27, p=0.71690 b-rank test for bits 21 to 28, p=0.62062 b-rank test for bits 22 to 29, p=0.97640 b-rank test for bits 23 to 30, p=0.09244 b-rank test for bits 24 to 31, p=0.92627 b-rank test for bits 25 to 32, p=0.67894 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 = 0.934750 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-25_08:31 (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 141904 -0.01 0.495032 2 141808 -0.24 0.406425 3 142220 0.73 0.766039 4 142501 1.38 0.916577 5 142264 0.83 0.796354 6 141500 -0.96 0.169441 7 141642 -0.62 0.266116 8 141812 -0.23 0.410054 9 141810 -0.23 0.408238 10 142448 1.26 0.895908 11 141788 -0.28 0.388404 12 141482 -1.00 0.159034 13 141868 -0.10 0.461536 14 142247 0.79 0.784929 15 141675 -0.55 0.292018 16 141102 -1.89 0.029628 17 142098 0.44 0.670328 18 141543 -0.86 0.196023 19 141851 -0.14 0.445798 20 141738 -0.40 0.344466 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-25_08:31 Bits used No. missing words z-score p-value 23 to 32 142283 1.2885 0.901217 22 to 31 142186 0.9540 0.829967 21 to 30 142581 2.3161 0.989724 20 to 29 141656 -0.8736 0.191181 19 to 28 141843 -0.2287 0.409542 18 to 27 141733 -0.6080 0.271582 17 to 26 141851 -0.2011 0.420295 16 to 25 142214 1.0506 0.853276 15 to 24 142142 0.8023 0.788813 14 to 23 142103 0.6678 0.747878 13 to 22 142065 0.5368 0.704295 12 to 21 141916 0.0230 0.509175 11 to 20 141891 -0.0632 0.474801 10 to 19 142047 0.4747 0.682508 9 to 18 141761 -0.5115 0.304507 8 to 17 142448 1.8575 0.968379 7 to 16 141813 -0.3322 0.369880 6 to 15 142394 1.6713 0.952666 5 to 14 141468 -1.5218 0.064026 4 to 13 142304 1.3609 0.913232 3 to 12 142258 1.2023 0.885378 2 to 11 141424 -1.6736 0.047109 1 to 10 141777 -0.4563 0.324083 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-25_08:31 Bits used No. missing words z-score p-value 28 to 32 141736 -0.5876 0.278414 27 to 31 142284 1.2701 0.897970 26 to 30 141762 -0.4994 0.308741 25 to 29 141892 -0.0587 0.476577 24 to 28 141992 0.2802 0.610352 23 to 27 141553 -1.2079 0.113543 22 to 26 141933 0.0802 0.531976 21 to 25 141653 -0.8689 0.192447 20 to 24 142375 1.5785 0.942779 19 to 23 141916 0.0226 0.509019 18 to 22 141836 -0.2486 0.401844 17 to 21 141906 -0.0113 0.495497 16 to 20 141800 -0.3706 0.355464 15 to 19 141627 -0.9571 0.169271 14 to 18 142265 1.2057 0.886026 13 to 17 142614 2.3887 0.991546 12 to 16 141899 -0.0350 0.486033 11 to 15 142254 1.1684 0.878672 10 to 14 141576 -1.1299 0.129252 9 to 13 141575 -1.1333 0.128540 8 to 12 141252 -2.2282 0.012932 7 to 11 141705 -0.6926 0.244267 6 to 10 142290 1.2904 0.901545 5 to 9 141667 -0.8215 0.205693 4 to 8 142220 1.0531 0.853857 3 to 7 142239 1.1175 0.868115 2 to 6 141872 -0.1265 0.449651 1 to 5 142407 1.6870 0.954200 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-25_08:31 Bits used No. missing words z-score p-value 31 to 32 142112 0.5978 0.725029 30 to 31 142226 0.9341 0.824882 29 to 30 141807 -0.3019 0.381380 28 to 29 142311 1.1849 0.881965 27 to 28 142245 0.9902 0.838956 26 to 27 141321 -1.7355 0.041327 25 to 26 141792 -0.3461 0.364632 24 to 25 141907 -0.0069 0.497258 23 to 24 141850 -0.1750 0.430534 22 to 23 141385 -1.5467 0.060968 21 to 22 141735 -0.5142 0.303539 20 to 21 141649 -0.7679 0.221263 19 to 20 141742 -0.4936 0.310795 18 to 19 141847 -0.1839 0.427060 17 to 18 141935 0.0757 0.530180 16 to 17 142151 0.7129 0.762043 15 to 16 141897 -0.0364 0.485493 14 to 15 141847 -0.1839 0.427060 13 to 14 141781 -0.3786 0.352509 12 to 13 141971 0.1819 0.572176 11 to 12 141889 -0.0600 0.476090 10 to 11 141063 -2.4965 0.006270 9 to 10 142154 0.7217 0.764773 8 to 9 141588 -0.9479 0.171596 7 to 8 142170 0.7689 0.779035 6 to 7 142094 0.5447 0.707037 5 to 6 142547 1.8810 0.970016 4 to 5 141991 0.2409 0.595189 3 to 4 141574 -0.9892 0.161289 2 to 3 141528 -1.1249 0.130323 1 to 2 141944 0.1023 0.540729 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-25_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2560.13 0.850 0.802449 Test results for specific bytes for dh-ranFile-2015-07-25_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2458.74 -0.584 0.279765 2 to 9 2449.11 -0.720 0.235849 3 to 10 2494.04 -0.084 0.466410 4 to 11 2593.97 1.329 0.908055 5 to 12 2522.23 0.314 0.623387 6 to 13 2359.87 -1.982 0.023752 7 to 14 2565.09 0.921 0.821349 8 to 15 2576.89 1.087 0.861568 9 to 16 2506.26 0.089 0.535285 10 to 17 2483.19 -0.238 0.406068 11 to 18 2659.89 2.261 0.988126 12 to 19 2532.31 0.457 0.676157 13 to 20 2434.96 -0.920 0.178851 14 to 21 2425.00 -1.061 0.144438 15 to 22 2337.30 -2.301 0.010697 16 to 23 2476.25 -0.336 0.368487 17 to 24 2573.98 1.046 0.852279 18 to 25 2536.01 0.509 0.694694 19 to 26 2552.29 0.740 0.770205 20 to 27 2460.89 -0.553 0.290110 21 to 28 2611.12 1.571 0.941965 22 to 29 2624.35 1.759 0.960673 23 to 30 2520.04 0.283 0.611542 24 to 31 2600.79 1.425 0.922981 25 to 32 2374.23 -1.779 0.037642 CDPARK for dh-ranFile-2015-07-25_08:31: 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 3522 -0.0457 0.481790 3497 -1.1872 0.117571 3528 0.2283 0.590298 3504 -0.8676 0.192812 3487 -1.6438 0.050105 3544 0.9589 0.831196 3517 -0.2740 0.392053 3517 -0.2740 0.392053 3487 -1.6438 0.050105 3495 -1.2785 0.100530 Square side=100, avg. no. parked=3509.80 sample std.=17.92 p-value of the KSTEST for those 10 p-values: 0.069009 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-25_08:31 0.8302,0.7083,0.7976,0.0232,0.5209,0.7476,0.1036,0.1304,0.9011,0.1827, The KS test for those 10 p-values: 0.639066 The 3DSPHERES test for dh-ranFile-2015-07-25_08:31 sample no r^3 equiv. uni. 1 22.261 0.523855 2 14.106 0.375128 3 26.220 0.582716 4 7.007 0.208300 5 21.931 0.518588 6 36.881 0.707518 7 68.556 0.898247 8 139.133 0.990321 9 22.402 0.526082 10 35.759 0.696374 11 7.770 0.228169 12 57.134 0.851100 13 6.793 0.202638 14 34.170 0.679864 15 11.554 0.319644 16 2.775 0.088344 17 48.822 0.803558 18 23.257 0.539408 19 35.418 0.692902 20 3.972 0.124019 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.832998 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-25_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -2.0 -1.1 -1.3 1.1 0.7 0.5 -0.7 0.9 0.1 0.4 0.4 -0.2 -0.3 0.2 -0.9 -0.2 0.7 -0.0 -0.3 0.0 -0.7 0.2 0.4 -1.2 1.6 -1.7 0.6 0.6 1.3 0.1 0.2 0.6 -0.2 -0.2 -0.1 -1.4 -0.1 -0.4 -0.7 -1.3 -1.0 3.7 Chi-square with 42 degrees of freedom:43.318008 z-score=0.143807, p-value=0.585102 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-25_08:31 Test no p-value 1 0.187457 2 0.363731 3 0.136285 4 0.012949 5 0.456530 6 0.099513 7 0.017548 8 0.155574 9 0.050243 10 0.079188 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000089 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-25_08:31: (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 66579 0.12 66718 0.04 3 25000.00 25015 0.01 24966 0.05 4 6666.67 6671 0.00 6652 0.03 5 1388.89 1444 2.19 1374 0.16 6 238.10 251 0.70 252 0.81 7 34.72 31 0.40 28 1.30 8 4.96 8 1.86 9 3.29 p=0.49095 p=0.54015 Number of rngs required: 688736, p-value: 0.649 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-25_08:31 No. of wins: Observed Expected 98475 98585.9 z-score=-0.496, pvalue=0.31001 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66743 66666.7 0.087 0.087 2 37579 37654.3 0.151 0.238 3 26950 26954.7 0.001 0.239 4 19391 19313.5 0.311 0.550 5 13996 13851.4 1.509 2.059 6 9949 9943.5 0.003 2.062 7 7050 7145.0 1.264 3.326 8 5165 5139.1 0.131 3.457 9 3668 3699.9 0.274 3.731 10 2595 2666.3 1.907 5.638 11 1898 1923.3 0.334 5.971 12 1362 1388.7 0.515 6.486 13 986 1003.7 0.313 6.799 14 761 726.1 1.673 8.472 15 550 525.8 1.110 9.583 16 355 381.2 1.794 11.377 17 266 276.5 0.402 11.779 18 192 200.8 0.388 12.167 19 144 146.0 0.027 12.194 20 111 106.2 0.216 12.409 21 289 287.1 0.012 12.422 Chisq= 12.42 for 20 degrees of freedom, p= 0.09921 SUMMARY of craptest p-value for no. of wins: 0.310009 p-value for throws/game: 0.099209 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-25_08:31 No. of wins: Observed Expected 98488 98585.9 z-score=-0.438, pvalue=0.33081 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67081 66666.7 2.575 2.575 2 37587 37654.3 0.120 2.695 3 26588 26954.7 4.990 7.685 4 19321 19313.5 0.003 7.688 5 13741 13851.4 0.880 8.568 6 10009 9943.5 0.431 8.999 7 7211 7145.0 0.609 9.608 8 5095 5139.1 0.378 9.986 9 3695 3699.9 0.006 9.993 10 2668 2666.3 0.001 9.994 11 1920 1923.3 0.006 9.999 12 1408 1388.7 0.267 10.267 13 959 1003.7 1.992 12.259 14 748 726.1 0.658 12.917 15 530 525.8 0.033 12.950 16 364 381.2 0.772 13.721 17 292 276.5 0.864 14.586 18 211 200.8 0.515 15.101 19 153 146.0 0.337 15.438 20 103 106.2 0.097 15.535 21 316 287.1 2.906 18.441 Chisq= 18.44 for 20 degrees of freedom, p= 0.44164 SUMMARY of craptest p-value for no. of wins: 0.330809 p-value for throws/game: 0.441643 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0063,0.0107,0.0129,0.0129,0.0130,0.0175,0.0232,0.0238,0.0296, 0.0376,0.0413,0.0471,0.0501,0.0501,0.0502,0.0602,0.0610,0.0634,0.0640, 0.0690,0.0731,0.0792,0.0883,0.0924,0.0933,0.0976,0.0992,0.0995,0.1005, 0.1036,0.1135,0.1176,0.1184,0.1240,0.1285,0.1293,0.1303,0.1304,0.1324, 0.1338,0.1363,0.1384,0.1444,0.1556,0.1590,0.1613,0.1693,0.1694,0.1716, 0.1789,0.1827,0.1875,0.1878,0.1912,0.1924,0.1928,0.1960,0.2026,0.2057, 0.2083,0.2099,0.2213,0.2272,0.2282,0.2299,0.2358,0.2375,0.2443,0.2661, 0.2716,0.2727,0.2727,0.2770,0.2784,0.2798,0.2802,0.2841,0.2883,0.2901, 0.2920,0.3035,0.3040,0.3045,0.3087,0.3100,0.3100,0.3108,0.3196,0.3241, 0.3308,0.3445,0.3525,0.3555,0.3637,0.3646,0.3685,0.3699,0.3717,0.3736, 0.3751,0.3814,0.3884,0.3921,0.3921,0.3972,0.4003,0.4018,0.4061,0.4064, 0.4082,0.4095,0.4101,0.4179,0.4203,0.4271,0.4271,0.4305,0.4416,0.4458, 0.4497,0.4565,0.4605,0.4615,0.4628,0.4664,0.4748,0.4761,0.4766,0.4818, 0.4855,0.4860,0.4910,0.4950,0.4955,0.4973,0.5007,0.5090,0.5092,0.5186, 0.5209,0.5239,0.5261,0.5300,0.5302,0.5320,0.5353,0.5394,0.5401,0.5407, 0.5423,0.5542,0.5614,0.5618,0.5620,0.5722,0.5750,0.5827,0.5851,0.5903, 0.5952,0.6046,0.6097,0.6104,0.6115,0.6129,0.6145,0.6206,0.6234,0.6391, 0.6417,0.6493,0.6703,0.6724,0.6762,0.6774,0.6789,0.6799,0.6825,0.6929, 0.6947,0.6964,0.7013,0.7043,0.7070,0.7075,0.7083,0.7169,0.7250,0.7476, 0.7479,0.7508,0.7599,0.7602,0.7620,0.7648,0.7660,0.7702,0.7773,0.7790, 0.7849,0.7888,0.7948,0.7964,0.7976,0.8024,0.8036,0.8205,0.8213,0.8249, 0.8300,0.8302,0.8312,0.8321,0.8330,0.8390,0.8426,0.8502,0.8511,0.8523, 0.8533,0.8539,0.8589,0.8616,0.8681,0.8761,0.8785,0.8787,0.8820,0.8850, 0.8854,0.8860,0.8928,0.8959,0.8980,0.8982,0.9010,0.9011,0.9012,0.9015, 0.9025,0.9034,0.9081,0.9087,0.9132,0.9166,0.9230,0.9235,0.9242,0.9263, 0.9311,0.9325,0.9347,0.9420,0.9428,0.9527,0.9542,0.9567,0.9607,0.9684, 0.9700,0.9732,0.9764,0.9820,0.9881,0.9897,0.9903,0.9915,0.9919, Overall p-value after applying KStest on 269 p-values = 0.647782 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.