RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-18_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.32 26.5985 0.935775 2 to 25 15.93 14.3961 0.361104 3 to 26 15.94 10.0214 0.097288 4 to 27 15.85 24.3130 0.888823 5 to 28 15.73 23.1952 0.856998 6 to 29 15.79 13.6780 0.310247 7 to 30 15.72 13.3219 0.285616 8 to 31 15.65 20.2490 0.738311 9 to 32 15.71 14.1309 0.342186 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.740894 Tough bday spacings test for dh-ranFile-2015-09-18_11:31: 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 34 66 97 106 80 54 25 18 3 5 (O-E)^2/E 0.9 0.2 0.7 0.0 0.7 0.0 0.1 0.8 0.7 2.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 6.224, p= 0.204 RESULTS OF GCD FOR dh-ranFile-2015-09-18_11:31 Euclid's algorithm: p-value, steps to gcd: 0.093116 p-value, dist. of gcd's: 0.790413 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-18_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.207 0.384 0.922 0.592 0.081 0.677 0.904 0.976 Bits 8 to 15---> 0.837 0.725 0.172 0.856 0.368 0.566 0.636 0.201 Bits 16 to 23---> 0.248 0.583 0.536 0.216 0.672 0.181 0.290 0.072 Bits 24 to 31---> 0.625 0.565 0.926 0.835 0.438 0.046 0.666 0.805 KS test for the above 32 p values: 0.106 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-18_11:31, p-values for 5 runs: 0.7634, 0.0684, 0.5174, 0.0004, 0.6169 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-18_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 196 211.4 1.124 1.124 r= 29 5050 5134.0 1.375 2.499 r= 30 23031 23103.0 0.225 2.724 r= 31 11723 11551.5 2.545 5.269 chi-square = 5.269 with df = 3; p-value = 0.847 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-18_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5168 5134.0 0.225 0.485 r= 31 23083 23103.0 0.017 0.503 r= 32 11545 11551.5 0.004 0.506 chi-square = 0.506 with df = 3; p-value = 0.083 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-18_11:31 b-rank test for bits 1 to 8, p=0.36878 b-rank test for bits 2 to 9, p=0.04466 b-rank test for bits 3 to 10, p=0.63972 b-rank test for bits 4 to 11, p=0.63007 b-rank test for bits 5 to 12, p=0.11322 b-rank test for bits 6 to 13, p=0.00192 b-rank test for bits 7 to 14, p=0.97533 b-rank test for bits 8 to 15, p=0.14884 b-rank test for bits 9 to 16, p=0.89247 b-rank test for bits 10 to 17, p=0.85536 b-rank test for bits 11 to 18, p=0.91463 b-rank test for bits 12 to 19, p=0.48645 b-rank test for bits 13 to 20, p=0.58289 b-rank test for bits 14 to 21, p=0.92877 b-rank test for bits 15 to 22, p=0.01163 b-rank test for bits 16 to 23, p=0.53467 b-rank test for bits 17 to 24, p=0.00051 b-rank test for bits 18 to 25, p=0.94033 b-rank test for bits 19 to 26, p=0.48457 b-rank test for bits 20 to 27, p=0.54193 b-rank test for bits 21 to 28, p=0.23515 b-rank test for bits 22 to 29, p=0.26882 b-rank test for bits 23 to 30, p=0.60961 b-rank test for bits 24 to 31, p=0.31602 b-rank test for bits 25 to 32, p=0.17037 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 = 0.241444 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-18_11:31 (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 142402 1.15 0.875154 2 141582 -0.76 0.222198 3 142078 0.39 0.653242 4 142479 1.33 0.908406 5 141969 0.14 0.555439 6 142227 0.74 0.771023 7 141831 -0.18 0.427394 8 142357 1.05 0.852210 9 141604 -0.71 0.237803 10 142021 0.26 0.602920 11 142152 0.57 0.714638 12 141999 0.21 0.582975 13 142463 1.29 0.902102 14 141566 -0.80 0.211227 15 142020 0.26 0.602018 16 141792 -0.27 0.391990 17 141741 -0.39 0.347051 18 142509 1.40 0.919408 19 141615 -0.69 0.245825 20 141709 -0.47 0.319871 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-18_11:31 Bits used No. missing words z-score p-value 23 to 32 142163 0.8747 0.809138 22 to 31 141788 -0.4184 0.337835 21 to 30 141873 -0.1253 0.450153 20 to 29 141902 -0.0253 0.489918 19 to 28 141936 0.0920 0.536637 18 to 27 141856 -0.1839 0.427047 17 to 26 141846 -0.2184 0.413567 16 to 25 141142 -2.6460 0.004073 15 to 24 141825 -0.2908 0.385605 14 to 23 141725 -0.6356 0.262512 13 to 22 141896 -0.0460 0.481669 12 to 21 142142 0.8023 0.788813 11 to 20 141704 -0.7080 0.239462 10 to 19 142125 0.7437 0.771468 9 to 18 142328 1.4437 0.925587 8 to 17 141945 0.1230 0.548947 7 to 16 141716 -0.6667 0.252496 6 to 15 141473 -1.5046 0.066215 5 to 14 141870 -0.1356 0.446061 4 to 13 142127 0.7506 0.773549 3 to 12 142171 0.9023 0.816554 2 to 11 141822 -0.3011 0.381655 1 to 10 141668 -0.8322 0.202656 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-18_11:31 Bits used No. missing words z-score p-value 28 to 32 141918 0.0294 0.511723 27 to 31 142077 0.5684 0.715109 26 to 30 141885 -0.0825 0.467135 25 to 29 141636 -0.9265 0.177082 24 to 28 141995 0.2904 0.614248 23 to 27 141847 -0.2113 0.416331 22 to 26 141492 -1.4147 0.078581 21 to 25 141652 -0.8723 0.191521 20 to 24 141487 -1.4316 0.076125 19 to 23 141627 -0.9571 0.169271 18 to 22 142349 1.4904 0.931941 17 to 21 141666 -0.8248 0.204729 16 to 20 142250 1.1548 0.875917 15 to 19 142229 1.0836 0.860735 14 to 18 141369 -1.8316 0.033504 13 to 17 142239 1.1175 0.868115 12 to 16 142036 0.4294 0.666180 11 to 15 141926 0.0565 0.522532 10 to 14 141772 -0.4655 0.320778 9 to 13 142076 0.5650 0.713957 8 to 12 141336 -1.9435 0.025978 7 to 11 142216 1.0396 0.850728 6 to 10 141587 -1.0926 0.137275 5 to 9 142422 1.7379 0.958883 4 to 8 142233 1.0972 0.863720 3 to 7 141849 -0.2045 0.418978 2 to 6 141666 -0.8248 0.204729 1 to 5 142033 0.4192 0.662473 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-18_11:31 Bits used No. missing words z-score p-value 31 to 32 141784 -0.3697 0.355801 30 to 31 142112 0.5978 0.725029 29 to 30 141543 -1.0806 0.139933 28 to 29 141723 -0.5496 0.291281 27 to 28 141642 -0.7886 0.215178 26 to 27 141983 0.2173 0.586019 25 to 26 141770 -0.4110 0.340535 24 to 25 141510 -1.1780 0.119405 23 to 24 141382 -1.5555 0.059908 22 to 23 141978 0.2026 0.580263 21 to 22 142075 0.4887 0.687474 20 to 21 141245 -1.9597 0.025017 19 to 20 142153 0.7188 0.763865 18 to 19 142047 0.4061 0.657668 17 to 18 142118 0.6155 0.730903 16 to 17 141636 -0.8063 0.210040 15 to 16 142389 1.4150 0.921459 14 to 15 141814 -0.2812 0.389275 13 to 14 142128 0.6450 0.740551 12 to 13 142047 0.4061 0.657668 11 to 12 142343 1.2793 0.899598 10 to 11 141529 -1.1219 0.130949 9 to 10 142535 1.8456 0.967527 8 to 9 141791 -0.3491 0.363524 7 to 8 141593 -0.9331 0.175377 6 to 7 141372 -1.5850 0.056478 5 to 6 142077 0.4946 0.689559 4 to 5 141788 -0.3579 0.360207 3 to 4 142269 1.0610 0.855649 2 to 3 141585 -0.9567 0.169353 1 to 2 141751 -0.4671 0.320232 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-18_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2479.14 -0.295 0.384017 Test results for specific bytes for dh-ranFile-2015-09-18_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2531.70 0.448 0.673027 2 to 9 2501.05 0.015 0.505944 3 to 10 2604.19 1.474 0.929694 4 to 11 2507.78 0.110 0.543819 5 to 12 2616.25 1.644 0.949913 6 to 13 2543.39 0.614 0.730267 7 to 14 2654.35 2.183 0.985476 8 to 15 2552.70 0.745 0.771973 9 to 16 2389.10 -1.568 0.058398 10 to 17 2435.83 -0.908 0.182064 11 to 18 2447.00 -0.750 0.226751 12 to 19 2504.78 0.068 0.526946 13 to 20 2419.35 -1.141 0.127013 14 to 21 2430.03 -0.990 0.161193 15 to 22 2529.00 0.410 0.659132 16 to 23 2435.66 -0.910 0.181429 17 to 24 2503.00 0.042 0.516895 18 to 25 2385.01 -1.626 0.051959 19 to 26 2456.26 -0.619 0.268104 20 to 27 2564.04 0.906 0.817438 21 to 28 2473.89 -0.369 0.355988 22 to 29 2395.18 -1.482 0.069126 23 to 30 2339.99 -2.263 0.011822 24 to 31 2389.89 -1.557 0.059721 25 to 32 2368.09 -1.865 0.031058 CDPARK for dh-ranFile-2015-09-18_11:31: 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 3529 0.2740 0.607947 3536 0.5936 0.723613 3478 -2.0548 0.019949 3574 2.3288 0.990064 3488 -1.5982 0.055002 3542 0.8676 0.807188 3533 0.4566 0.676028 3502 -0.9589 0.168804 3560 1.6895 0.954438 3481 -1.9178 0.027568 Square side=100, avg. no. parked=3522.30 sample std.=31.76 p-value of the KSTEST for those 10 p-values: 0.188947 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-18_11:31 0.0013,0.6701,0.8647,0.3560,0.0063,0.2776,0.4511,0.4903,0.2870,0.4816, The KS test for those 10 p-values: 0.122855 The 3DSPHERES test for dh-ranFile-2015-09-18_11:31 sample no r^3 equiv. uni. 1 42.703 0.759115 2 51.859 0.822472 3 3.806 0.119137 4 16.238 0.417980 5 36.286 0.701662 6 8.137 0.237558 7 47.453 0.794391 8 0.707 0.023285 9 40.007 0.736461 10 9.759 0.277683 11 16.926 0.431190 12 25.203 0.568337 13 8.145 0.237767 14 8.024 0.234694 15 0.825 0.027124 16 40.531 0.741030 17 77.524 0.924539 18 37.392 0.712458 19 29.591 0.627076 20 54.658 0.838285 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.746035 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-18_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 -0.3 -0.4 0.2 -1.3 0.7 0.2 -1.8 0.5 1.8 -2.0 0.3 0.7 -2.3 1.6 0.9 -0.7 0.2 -1.5 0.5 0.5 1.4 -1.0 1.1 -1.2 0.1 0.3 -1.1 -0.1 0.9 0.9 -0.9 0.8 1.2 -0.2 -0.3 1.2 -0.1 -1.2 -0.1 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:45.982274 z-score=0.434502, p-value=0.689258 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-18_11:31 Test no p-value 1 0.129111 2 0.004015 3 0.957258 4 0.978549 5 0.762478 6 0.316373 7 0.058213 8 0.003367 9 0.711701 10 0.693440 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.074502 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-18_11:31: (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 66723 0.05 66647 0.01 3 25000.00 24966 0.05 25056 0.13 4 6666.67 6661 0.00 6656 0.02 5 1388.89 1387 0.00 1367 0.35 6 238.10 222 1.09 237 0.01 7 34.72 33 0.09 31 0.40 8 4.96 7 0.84 5 0.00 p=0.09103 p=0.01079 Number of rngs required: 689289, p-value: 0.848 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-18_11:31 No. of wins: Observed Expected 98517 98585.9 z-score=-0.308, pvalue=0.37905 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66835 66666.7 0.425 0.425 2 37613 37654.3 0.045 0.470 3 26825 26954.7 0.624 1.095 4 19247 19313.5 0.229 1.323 5 13802 13851.4 0.176 1.500 6 9943 9943.5 0.000 1.500 7 7175 7145.0 0.126 1.626 8 5283 5139.1 4.031 5.657 9 3727 3699.9 0.199 5.856 10 2668 2666.3 0.001 5.857 11 1857 1923.3 2.287 8.144 12 1365 1388.7 0.406 8.550 13 1002 1003.7 0.003 8.553 14 701 726.1 0.870 9.423 15 557 525.8 1.847 11.270 16 330 381.2 6.864 18.135 17 304 276.5 2.727 20.862 18 196 200.8 0.116 20.978 19 148 146.0 0.028 21.006 20 99 106.2 0.490 21.496 21 323 287.1 4.485 25.981 Chisq= 25.98 for 20 degrees of freedom, p= 0.83356 SUMMARY of craptest p-value for no. of wins: 0.379050 p-value for throws/game: 0.833560 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-18_11:31 No. of wins: Observed Expected 98765 98585.9 z-score= 0.801, pvalue=0.78850 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66736 66666.7 0.072 0.072 2 37572 37654.3 0.180 0.252 3 26928 26954.7 0.027 0.279 4 19157 19313.5 1.268 1.546 5 13903 13851.4 0.192 1.738 6 10002 9943.5 0.344 2.082 7 7184 7145.0 0.213 2.294 8 5176 5139.1 0.265 2.560 9 3744 3699.9 0.526 3.086 10 2679 2666.3 0.061 3.147 11 1924 1923.3 0.000 3.147 12 1382 1388.7 0.033 3.180 13 968 1003.7 1.271 4.451 14 741 726.1 0.304 4.755 15 545 525.8 0.698 5.453 16 370 381.2 0.326 5.779 17 259 276.5 1.112 6.892 18 190 200.8 0.584 7.476 19 152 146.0 0.248 7.724 20 125 106.2 3.322 11.046 21 263 287.1 2.025 13.071 Chisq= 13.07 for 20 degrees of freedom, p= 0.12569 SUMMARY of craptest p-value for no. of wins: 0.788499 p-value for throws/game: 0.125689 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0005,0.0013,0.0019,0.0034,0.0040,0.0041,0.0063,0.0108,0.0116, 0.0118,0.0199,0.0233,0.0250,0.0260,0.0271,0.0276,0.0311,0.0335,0.0447, 0.0462,0.0520,0.0550,0.0565,0.0582,0.0584,0.0597,0.0599,0.0662,0.0684, 0.0691,0.0724,0.0745,0.0761,0.0786,0.0810,0.0825,0.0910,0.0931,0.0973, 0.1064,0.1132,0.1191,0.1194,0.1229,0.1257,0.1270,0.1291,0.1309,0.1373, 0.1399,0.1488,0.1612,0.1688,0.1693,0.1694,0.1704,0.1717,0.1754,0.1771, 0.1809,0.1814,0.1821,0.1889,0.1915,0.2015,0.2027,0.2039,0.2047,0.2047, 0.2066,0.2100,0.2112,0.2152,0.2162,0.2222,0.2268,0.2347,0.2352,0.2376, 0.2378,0.2378,0.2395,0.2414,0.2458,0.2478,0.2525,0.2625,0.2681,0.2688, 0.2776,0.2777,0.2856,0.2870,0.2901,0.2913,0.3102,0.3160,0.3164,0.3199, 0.3202,0.3208,0.3378,0.3405,0.3422,0.3471,0.3558,0.3560,0.3560,0.3602, 0.3611,0.3635,0.3675,0.3688,0.3791,0.3817,0.3836,0.3840,0.3856,0.3893, 0.3920,0.4136,0.4163,0.4180,0.4190,0.4270,0.4274,0.4312,0.4379,0.4461, 0.4502,0.4511,0.4671,0.4816,0.4817,0.4846,0.4865,0.4899,0.4903,0.5059, 0.5117,0.5169,0.5174,0.5225,0.5269,0.5347,0.5360,0.5366,0.5419,0.5438, 0.5489,0.5554,0.5653,0.5656,0.5683,0.5803,0.5826,0.5829,0.5830,0.5860, 0.5920,0.6020,0.6029,0.6079,0.6096,0.6142,0.6169,0.6253,0.6271,0.6301, 0.6359,0.6397,0.6532,0.6577,0.6577,0.6591,0.6625,0.6657,0.6662,0.6701, 0.6722,0.6730,0.6760,0.6774,0.6875,0.6893,0.6896,0.6934,0.7017,0.7117, 0.7125,0.7140,0.7146,0.7151,0.7236,0.7250,0.7252,0.7303,0.7309,0.7365, 0.7383,0.7406,0.7409,0.7410,0.7460,0.7591,0.7625,0.7634,0.7639,0.7710, 0.7715,0.7720,0.7735,0.7885,0.7888,0.7904,0.7944,0.8052,0.8072,0.8091, 0.8166,0.8174,0.8225,0.8336,0.8351,0.8370,0.8383,0.8469,0.8478,0.8507, 0.8522,0.8554,0.8556,0.8563,0.8570,0.8607,0.8637,0.8647,0.8681,0.8752, 0.8759,0.8888,0.8925,0.8996,0.9021,0.9045,0.9084,0.9146,0.9194,0.9215, 0.9221,0.9245,0.9256,0.9261,0.9288,0.9297,0.9319,0.9358,0.9403,0.9499, 0.9544,0.9573,0.9589,0.9675,0.9753,0.9759,0.9785,0.9855,0.9901, Overall p-value after applying KStest on 269 p-values = 0.054919 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.