RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-15_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.66 18.8010 0.659929 2 to 25 15.69 27.8478 0.953252 3 to 26 15.86 21.3417 0.788623 4 to 27 15.64 15.4659 0.438037 5 to 28 15.65 25.1407 0.908396 6 to 29 15.45 32.3120 0.986241 7 to 30 15.79 6.6783 0.012655 8 to 31 15.74 17.7243 0.593567 9 to 32 16.04 19.0459 0.674098 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.084999 Tough bday spacings test for dh-ranFile-2015-08-15_14:31: 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 4 44 76 88 93 87 53 26 19 7 3 (O-E)^2/E 2.9 1.5 0.1 1.0 0.2 1.0 0.0 0.5 1.1 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 8.609, p= 0.430 RESULTS OF GCD FOR dh-ranFile-2015-08-15_14:31 Euclid's algorithm: p-value, steps to gcd: 0.519716 p-value, dist. of gcd's: 0.914553 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-15_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.999 0.100 0.390 0.207 0.929 0.153 0.434 0.718 Bits 8 to 15---> 0.284 0.490 0.880 0.653 0.497 0.494 0.585 0.274 Bits 16 to 23---> 0.728 0.357 0.883 0.450 0.922 0.399 0.725 0.407 Bits 24 to 31---> 0.698 0.680 0.895 0.695 0.902 0.526 0.562 0.218 KS test for the above 32 p values: 0.801 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-15_14:31, p-values for 5 runs: 0.4516, 0.6961, 0.5203, 0.7038, 0.9941 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-15_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 198 211.4 0.852 0.852 r= 29 5185 5134.0 0.506 1.358 r= 30 23036 23103.0 0.195 1.553 r= 31 11581 11551.5 0.075 1.628 chi-square = 1.628 with df = 3; p-value = 0.347 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-15_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 224 211.4 0.749 0.749 r= 30 5134 5134.0 0.000 0.749 r= 31 23125 23103.0 0.021 0.770 r= 32 11517 11551.5 0.103 0.873 chi-square = 0.873 with df = 3; p-value = 0.168 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-15_14:31 b-rank test for bits 1 to 8, p=0.11754 b-rank test for bits 2 to 9, p=0.39668 b-rank test for bits 3 to 10, p=0.18566 b-rank test for bits 4 to 11, p=0.67542 b-rank test for bits 5 to 12, p=0.87628 b-rank test for bits 6 to 13, p=0.79404 b-rank test for bits 7 to 14, p=0.51947 b-rank test for bits 8 to 15, p=0.96344 b-rank test for bits 9 to 16, p=0.56288 b-rank test for bits 10 to 17, p=0.18377 b-rank test for bits 11 to 18, p=0.73677 b-rank test for bits 12 to 19, p=0.36732 b-rank test for bits 13 to 20, p=0.37817 b-rank test for bits 14 to 21, p=0.62969 b-rank test for bits 15 to 22, p=0.45065 b-rank test for bits 16 to 23, p=0.35488 b-rank test for bits 17 to 24, p=0.45489 b-rank test for bits 18 to 25, p=0.77806 b-rank test for bits 19 to 26, p=0.28204 b-rank test for bits 20 to 27, p=0.59676 b-rank test for bits 21 to 28, p=0.72548 b-rank test for bits 22 to 29, p=0.95325 b-rank test for bits 23 to 30, p=0.68851 b-rank test for bits 24 to 31, p=0.54224 b-rank test for bits 25 to 32, p=0.64761 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 = 0.317508 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-15_14:31 (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 141587 -0.75 0.225693 2 141792 -0.27 0.391990 3 142125 0.50 0.692835 4 141649 -0.61 0.271512 5 142705 1.86 0.968489 6 140995 -2.14 0.016328 7 142816 2.12 0.982929 8 141783 -0.30 0.383935 9 141955 0.11 0.542489 10 141866 -0.10 0.459681 11 141864 -0.11 0.457826 12 142225 0.74 0.769605 13 141568 -0.80 0.212580 14 142038 0.30 0.618152 15 141573 -0.79 0.215987 16 142515 1.42 0.921483 17 141709 -0.47 0.319871 18 142134 0.52 0.700184 19 141724 -0.43 0.332502 20 141770 -0.33 0.372387 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-15_14:31 Bits used No. missing words z-score p-value 23 to 32 141822 -0.3011 0.381655 22 to 31 142282 1.2851 0.900616 21 to 30 142561 2.2471 0.987684 20 to 29 142077 0.5782 0.718426 19 to 28 141588 -1.1080 0.133923 18 to 27 142249 1.1713 0.879256 17 to 26 142305 1.3644 0.913776 16 to 25 141691 -0.7529 0.225766 15 to 24 141931 0.0747 0.529783 14 to 23 142204 1.0161 0.845210 13 to 22 142614 2.4299 0.992448 12 to 21 142501 2.0402 0.979337 11 to 20 141806 -0.3563 0.360804 10 to 19 142172 0.9058 0.817468 9 to 18 141932 0.0782 0.531155 8 to 17 141922 0.0437 0.517424 7 to 16 141852 -0.1977 0.421644 6 to 15 142280 1.2782 0.899406 5 to 14 142257 1.1989 0.884709 4 to 13 141725 -0.6356 0.262512 3 to 12 141723 -0.6425 0.260269 2 to 11 141540 -1.2736 0.101411 1 to 10 141625 -0.9804 0.163432 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-15_14:31 Bits used No. missing words z-score p-value 28 to 32 142197 0.9752 0.835258 27 to 31 142051 0.4802 0.684471 26 to 30 142045 0.4599 0.677205 25 to 29 142130 0.7480 0.772780 24 to 28 141979 0.2362 0.593349 23 to 27 141975 0.2226 0.588081 22 to 26 141580 -1.1164 0.132131 21 to 25 141766 -0.4859 0.313532 20 to 24 141399 -1.7299 0.041821 19 to 23 141829 -0.2723 0.392694 18 to 22 141916 0.0226 0.509019 17 to 21 142098 0.6396 0.738770 16 to 20 142186 0.9379 0.825843 15 to 19 141734 -0.5943 0.276143 14 to 18 142105 0.6633 0.746427 13 to 17 142095 0.6294 0.735453 12 to 16 142261 1.1921 0.883389 11 to 15 142166 0.8701 0.807868 10 to 14 141635 -0.9299 0.176203 9 to 13 142558 2.1989 0.986057 8 to 12 141154 -2.5604 0.005227 7 to 11 141716 -0.6554 0.256119 6 to 10 141967 0.1955 0.577496 5 to 9 142118 0.7074 0.760327 4 to 8 142152 0.8226 0.794635 3 to 7 141655 -0.8621 0.194306 2 to 6 142340 1.4599 0.927841 1 to 5 141858 -0.1740 0.430933 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-15_14:31 Bits used No. missing words z-score p-value 31 to 32 141786 -0.3638 0.358002 30 to 31 142137 0.6716 0.749079 29 to 30 141936 0.0787 0.531354 28 to 29 141875 -0.1013 0.459669 27 to 28 141501 -1.2045 0.114196 26 to 27 141876 -0.0983 0.460840 25 to 26 141696 -0.6293 0.264579 24 to 25 142295 1.1377 0.872371 23 to 24 142319 1.2085 0.886566 22 to 23 141807 -0.3019 0.381380 21 to 22 142345 1.2852 0.900632 20 to 21 142125 0.6362 0.737675 19 to 20 142367 1.3501 0.911501 18 to 19 141873 -0.1072 0.457328 17 to 18 141432 -1.4081 0.079558 16 to 17 142304 1.1642 0.877832 15 to 16 142330 1.2409 0.892681 14 to 15 142696 2.3206 0.989845 13 to 14 141963 0.1583 0.562897 12 to 13 142680 2.2734 0.988498 11 to 12 142407 1.4681 0.928955 10 to 11 141751 -0.4671 0.320232 9 to 10 142418 1.5005 0.933258 8 to 9 142138 0.6745 0.750017 7 to 8 141771 -0.4081 0.341617 6 to 7 142354 1.3117 0.905191 5 to 6 142467 1.6450 0.950020 4 to 5 141732 -0.5231 0.300453 3 to 4 142035 0.3707 0.644573 2 to 3 141826 -0.2458 0.402914 1 to 2 141868 -0.1219 0.451482 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-15_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2576.16 1.077 0.859274 Test results for specific bytes for dh-ranFile-2015-08-15_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2504.26 0.060 0.524010 2 to 9 2460.07 -0.565 0.286131 3 to 10 2519.33 0.273 0.607691 4 to 11 2495.92 -0.058 0.476984 5 to 12 2571.12 1.006 0.842731 6 to 13 2560.05 0.849 0.802138 7 to 14 2484.44 -0.220 0.412900 8 to 15 2475.27 -0.350 0.363293 9 to 16 2525.70 0.363 0.641845 10 to 17 2535.98 0.509 0.694547 11 to 18 2548.80 0.690 0.754963 12 to 19 2515.43 0.218 0.586346 13 to 20 2514.84 0.210 0.583092 14 to 21 2420.02 -1.131 0.129002 15 to 22 2521.60 0.305 0.619981 16 to 23 2592.34 1.306 0.904216 17 to 24 2523.21 0.328 0.628651 18 to 25 2511.20 0.158 0.562928 19 to 26 2466.78 -0.470 0.319253 20 to 27 2437.61 -0.882 0.188789 21 to 28 2433.73 -0.937 0.174344 22 to 29 2462.76 -0.527 0.299202 23 to 30 2529.95 0.424 0.664064 24 to 31 2564.78 0.916 0.820201 25 to 32 2534.36 0.486 0.686498 CDPARK for dh-ranFile-2015-08-15_14:31: 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 3505 -0.8219 0.205562 3535 0.5479 0.708135 3511 -0.5479 0.291865 3518 -0.2283 0.409702 3512 -0.5023 0.307734 3536 0.5936 0.723613 3523 0.0000 0.500000 3491 -1.4612 0.071982 3520 -0.1370 0.445521 3517 -0.2740 0.392053 Square side=100, avg. no. parked=3516.80 sample std.=12.69 p-value of the KSTEST for those 10 p-values: 0.307356 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-15_14:31 0.6598,0.0026,0.7359,0.8943,0.6745,0.3360,0.4920,0.0866,0.4572,0.3070, The KS test for those 10 p-values: 0.751907 The 3DSPHERES test for dh-ranFile-2015-08-15_14:31 sample no r^3 equiv. uni. 1 25.767 0.576368 2 43.938 0.768829 3 18.846 0.466457 4 27.802 0.604149 5 20.895 0.501674 6 24.556 0.558923 7 65.170 0.886087 8 58.241 0.856491 9 17.504 0.442035 10 4.827 0.148618 11 10.474 0.294711 12 2.237 0.071851 13 35.128 0.689924 14 66.224 0.890023 15 48.453 0.801129 16 14.477 0.382798 17 26.396 0.585161 18 60.453 0.866694 19 10.477 0.294767 20 7.346 0.217184 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.603928 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-15_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 1.3 -1.9 0.3 -0.6 -0.9 -0.7 0.5 0.5 -1.8 -0.3 -1.3 1.8 1.3 -0.5 0.7 0.9 0.4 -0.1 -0.2 -0.6 -0.7 -1.1 -0.3 -0.9 1.9 1.2 -0.8 0.0 -0.8 1.6 0.4 -0.1 -1.7 -0.7 0.0 -0.4 -0.8 -1.3 0.9 -1.0 -0.1 Chi-square with 42 degrees of freedom:39.737404 z-score=-0.246869, p-value=0.429245 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-15_14:31 Test no p-value 1 0.578895 2 0.358626 3 0.034025 4 0.047079 5 0.461544 6 0.005723 7 0.100036 8 0.219335 9 0.714670 10 0.441364 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.027132 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-15_14:31: (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 66555 0.19 66923 0.99 3 25000.00 25071 0.20 24800 1.60 4 6666.67 6720 0.43 6612 0.45 5 1388.89 1371 0.23 1400 0.09 6 238.10 237 0.01 228 0.43 7 34.72 38 0.31 29 0.94 8 4.96 7 0.84 7 0.84 p=0.09955 p=0.49803 Number of rngs required: 688822, p-value: 0.685 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-15_14:31 No. of wins: Observed Expected 98856 98585.9 z-score= 1.208, pvalue=0.88652 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66629 66666.7 0.021 0.021 2 37377 37654.3 2.042 2.064 3 27032 26954.7 0.221 2.285 4 19415 19313.5 0.534 2.819 5 13980 13851.4 1.194 4.013 6 9905 9943.5 0.149 4.162 7 7101 7145.0 0.271 4.433 8 5197 5139.1 0.653 5.086 9 3776 3699.9 1.567 6.653 10 2685 2666.3 0.131 6.784 11 1947 1923.3 0.291 7.075 12 1344 1388.7 1.441 8.517 13 1012 1003.7 0.068 8.585 14 742 726.1 0.346 8.932 15 535 525.8 0.160 9.091 16 358 381.2 1.406 10.497 17 276 276.5 0.001 10.499 18 198 200.8 0.040 10.538 19 127 146.0 2.469 13.007 20 117 106.2 1.095 14.102 21 247 287.1 5.605 19.707 Chisq= 19.71 for 20 degrees of freedom, p= 0.52360 SUMMARY of craptest p-value for no. of wins: 0.886521 p-value for throws/game: 0.523597 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-15_14:31 No. of wins: Observed Expected 98571 98585.9 z-score=-0.066, pvalue=0.47351 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66411 66666.7 0.980 0.980 2 37745 37654.3 0.218 1.199 3 26862 26954.7 0.319 1.518 4 19340 19313.5 0.036 1.554 5 13918 13851.4 0.320 1.874 6 10067 9943.5 1.533 3.407 7 7139 7145.0 0.005 3.412 8 5086 5139.1 0.548 3.960 9 3658 3699.9 0.474 4.434 10 2665 2666.3 0.001 4.435 11 1982 1923.3 1.790 6.224 12 1470 1388.7 4.755 10.979 13 997 1003.7 0.045 11.024 14 728 726.1 0.005 11.029 15 539 525.8 0.330 11.358 16 375 381.2 0.099 11.458 17 278 276.5 0.008 11.465 18 179 200.8 2.373 13.838 19 144 146.0 0.027 13.865 20 105 106.2 0.014 13.879 21 312 287.1 2.157 16.036 Chisq= 16.04 for 20 degrees of freedom, p= 0.28563 SUMMARY of craptest p-value for no. of wins: 0.473507 p-value for throws/game: 0.285625 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0026,0.0052,0.0057,0.0127,0.0163,0.0271,0.0340,0.0418,0.0471,0.0719, 0.0720,0.0796,0.0850,0.0866,0.0996,0.0999,0.1000,0.1014,0.1142,0.1175, 0.1290,0.1321,0.1339,0.1486,0.1533,0.1634,0.1680,0.1743,0.1762,0.1838, 0.1857,0.1888,0.1943,0.2056,0.2068,0.2126,0.2160,0.2172,0.2177,0.2193, 0.2257,0.2258,0.2561,0.2603,0.2625,0.2646,0.2715,0.2739,0.2761,0.2820, 0.2836,0.2856,0.2861,0.2919,0.2947,0.2948,0.2992,0.3005,0.3070,0.3074, 0.3077,0.3135,0.3175,0.3193,0.3199,0.3202,0.3325,0.3360,0.3416,0.3469, 0.3549,0.3569,0.3580,0.3586,0.3608,0.3633,0.3673,0.3724,0.3782,0.3814, 0.3817,0.3828,0.3839,0.3901,0.3920,0.3921,0.3927,0.3967,0.3987,0.4029, 0.4072,0.4097,0.4129,0.4216,0.4292,0.4305,0.4309,0.4340,0.4380,0.4414, 0.4420,0.4455,0.4503,0.4507,0.4515,0.4516,0.4549,0.4572,0.4573,0.4578, 0.4597,0.4597,0.4608,0.4615,0.4665,0.4735,0.4770,0.4902,0.4920,0.4944, 0.4966,0.4980,0.5000,0.5017,0.5090,0.5174,0.5195,0.5197,0.5203,0.5236, 0.5240,0.5259,0.5298,0.5312,0.5314,0.5422,0.5425,0.5589,0.5620,0.5629, 0.5629,0.5629,0.5764,0.5775,0.5789,0.5831,0.5846,0.5852,0.5863,0.5881, 0.5933,0.5936,0.5968,0.6039,0.6041,0.6077,0.6182,0.6200,0.6287,0.6297, 0.6418,0.6446,0.6476,0.6529,0.6598,0.6599,0.6641,0.6741,0.6745,0.6754, 0.6772,0.6804,0.6845,0.6854,0.6865,0.6885,0.6899,0.6928,0.6945,0.6953, 0.6961,0.6978,0.7002,0.7038,0.7081,0.7147,0.7178,0.7184,0.7236,0.7249, 0.7255,0.7281,0.7355,0.7359,0.7368,0.7377,0.7388,0.7464,0.7491,0.7500, 0.7519,0.7550,0.7603,0.7688,0.7696,0.7728,0.7781,0.7886,0.7940,0.7946, 0.8011,0.8011,0.8021,0.8079,0.8175,0.8202,0.8258,0.8353,0.8427,0.8452, 0.8565,0.8593,0.8667,0.8724,0.8763,0.8778,0.8793,0.8800,0.8833,0.8834, 0.8847,0.8861,0.8865,0.8866,0.8900,0.8927,0.8943,0.8949,0.8994,0.9006, 0.9006,0.9025,0.9042,0.9052,0.9084,0.9115,0.9138,0.9146,0.9215,0.9216, 0.9278,0.9286,0.9290,0.9333,0.9500,0.9532,0.9533,0.9634,0.9685,0.9793, 0.9829,0.9861,0.9862,0.9877,0.9885,0.9898,0.9924,0.9941,0.9994, Overall p-value after applying KStest on 269 p-values = 0.008684 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.