RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-07-09_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 15.65 16.9215 0.540305 2 to 25 15.45 17.7460 0.594967 3 to 26 15.63 14.3295 0.356344 4 to 27 15.72 28.7015 0.962620 5 to 28 16.06 8.5924 0.047812 6 to 29 15.86 17.2960 0.565509 7 to 30 15.79 12.3870 0.223843 8 to 31 15.99 18.8042 0.660117 9 to 32 15.81 12.8286 0.252418 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.890215 Tough bday spacings test for dh-ranFile-2016-07-09_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 11 38 77 100 89 81 52 32 13 5 2 (O-E)^2/E 0.4 0.1 0.2 0.1 0.8 0.1 0.0 0.2 0.2 0.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 3.394, p= 0.029 RESULTS OF GCD FOR dh-ranFile-2016-07-09_04:31 Euclid's algorithm: p-value, steps to gcd: 0.407866 p-value, dist. of gcd's: 0.067526 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-07-09_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.177 0.274 0.402 0.232 0.902 0.774 0.640 0.170 Bits 8 to 15---> 0.428 0.222 0.388 0.016 0.445 0.731 0.964 0.522 Bits 16 to 23---> 0.066 0.073 0.052 0.681 0.852 0.270 0.906 0.852 Bits 24 to 31---> 0.808 0.036 0.483 0.555 0.527 0.803 0.441 0.375 KS test for the above 32 p values: 0.103 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-07-09_04:31, p-values for 5 runs: 0.3674, 0.6493, 0.6137, 0.9895, 0.0927 Rank test for binary matrices (31x31) for dh-ranFile-2016-07-09_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 198 211.4 0.852 0.852 r= 29 5257 5134.0 2.946 3.798 r= 30 22935 23103.0 1.222 5.020 r= 31 11610 11551.5 0.296 5.316 chi-square = 5.316 with df = 3; p-value = 0.850 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-07-09_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 211 211.4 0.001 0.001 r= 30 5290 5134.0 4.740 4.740 r= 31 23086 23103.0 0.013 4.753 r= 32 11413 11551.5 1.661 6.414 chi-square = 6.414 with df = 3; p-value = 0.907 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-07-09_04:31 b-rank test for bits 1 to 8, p=0.10792 b-rank test for bits 2 to 9, p=0.82207 b-rank test for bits 3 to 10, p=0.39307 b-rank test for bits 4 to 11, p=0.28326 b-rank test for bits 5 to 12, p=0.43865 b-rank test for bits 6 to 13, p=0.36910 b-rank test for bits 7 to 14, p=0.72457 b-rank test for bits 8 to 15, p=0.53746 b-rank test for bits 9 to 16, p=0.90910 b-rank test for bits 10 to 17, p=0.54048 b-rank test for bits 11 to 18, p=0.99224 b-rank test for bits 12 to 19, p=0.97743 b-rank test for bits 13 to 20, p=0.46974 b-rank test for bits 14 to 21, p=0.73122 b-rank test for bits 15 to 22, p=0.44151 b-rank test for bits 16 to 23, p=0.36734 b-rank test for bits 17 to 24, p=0.11483 b-rank test for bits 18 to 25, p=0.11279 b-rank test for bits 19 to 26, p=0.77288 b-rank test for bits 20 to 27, p=0.96409 b-rank test for bits 21 to 28, p=0.89003 b-rank test for bits 22 to 29, p=0.80966 b-rank test for bits 23 to 30, p=0.06184 b-rank test for bits 24 to 31, p=0.64743 b-rank test for bits 25 to 32, p=0.12533 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 = 0.614351 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-07-09_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 142576 1.56 0.940341 2 141620 -0.68 0.249519 3 141825 -0.20 0.421901 4 141018 -2.08 0.018646 5 141498 -0.96 0.168263 6 142347 1.02 0.846750 7 141790 -0.28 0.390196 8 142192 0.66 0.745516 9 141881 -0.07 0.473613 10 141246 -1.55 0.060590 11 142246 0.79 0.784246 12 141377 -1.24 0.106794 13 142310 0.94 0.825401 14 141931 0.05 0.520190 15 141871 -0.09 0.464320 16 141835 -0.17 0.431063 17 141620 -0.68 0.249519 18 141868 -0.10 0.461536 19 141219 -1.61 0.053381 20 141603 -0.72 0.237081 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-07-09_04:31 Bits used No. missing words z-score p-value 23 to 32 141880 -0.1011 0.459721 22 to 31 141430 -1.6529 0.049179 21 to 30 141827 -0.2839 0.388245 20 to 29 142101 0.6609 0.745672 19 to 28 141999 0.3092 0.621418 18 to 27 141815 -0.3253 0.372486 17 to 26 142174 0.9127 0.819288 16 to 25 141491 -1.4425 0.074578 15 to 24 141481 -1.4770 0.069838 14 to 23 141628 -0.9701 0.165998 13 to 22 142284 1.2920 0.901815 12 to 21 142503 2.0471 0.979678 11 to 20 141874 -0.1218 0.451518 10 to 19 141547 -1.2494 0.105757 9 to 18 141821 -0.3046 0.380341 8 to 17 141196 -2.4598 0.006952 7 to 16 142027 0.4058 0.657540 6 to 15 142312 1.3885 0.917510 5 to 14 141634 -0.9494 0.171205 4 to 13 142011 0.3506 0.637051 3 to 12 142130 0.7609 0.776651 2 to 11 141837 -0.2494 0.401520 1 to 10 141728 -0.6253 0.265895 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-07-09_04:31 Bits used No. missing words z-score p-value 28 to 32 141707 -0.6859 0.246399 27 to 31 141764 -0.4926 0.311132 26 to 30 142336 1.4463 0.925959 25 to 29 141929 0.0667 0.526581 24 to 28 141570 -1.1503 0.125016 23 to 27 142000 0.3074 0.620714 22 to 26 141829 -0.2723 0.392694 21 to 25 141844 -0.2215 0.412368 20 to 24 141518 -1.3265 0.092330 19 to 23 141739 -0.5774 0.281838 18 to 22 142233 1.0972 0.863720 17 to 21 142632 2.4497 0.992852 16 to 20 141858 -0.1740 0.430933 15 to 19 141221 -2.3333 0.009816 14 to 18 141924 0.0497 0.519831 13 to 17 141750 -0.5401 0.294564 12 to 16 142451 1.8362 0.966834 11 to 15 142116 0.7006 0.758216 10 to 14 141850 -0.2011 0.420303 9 to 13 142047 0.4667 0.679635 8 to 12 142000 0.3074 0.620714 7 to 11 142156 0.8362 0.798470 6 to 10 141803 -0.3604 0.359259 5 to 9 141976 0.2260 0.589399 4 to 8 142406 1.6836 0.953873 3 to 7 142014 0.3548 0.638635 2 to 6 140953 -3.2418 0.000594 1 to 5 141945 0.1209 0.548121 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-07-09_04:31 Bits used No. missing words z-score p-value 31 to 32 141601 -0.9095 0.181536 30 to 31 142162 0.7453 0.771967 29 to 30 141846 -0.1868 0.425903 28 to 29 141925 0.0462 0.518434 27 to 28 142243 0.9843 0.837510 26 to 27 141785 -0.3668 0.356901 25 to 26 141667 -0.7148 0.237355 24 to 25 141251 -1.9420 0.026070 23 to 24 142279 1.0905 0.862247 22 to 23 142071 0.4769 0.683284 21 to 22 141422 -1.4376 0.075281 20 to 21 141626 -0.8358 0.201639 19 to 20 142181 0.8014 0.788546 18 to 19 141551 -1.0570 0.145251 17 to 18 141147 -2.2488 0.012264 16 to 17 141790 -0.3520 0.362417 15 to 16 141734 -0.5172 0.302509 14 to 15 141788 -0.3579 0.360207 13 to 14 141674 -0.6942 0.243782 12 to 13 142247 0.9961 0.840394 11 to 12 141436 -1.3963 0.081319 10 to 11 141928 0.0551 0.521960 9 to 10 142277 1.0846 0.860944 8 to 9 142177 0.7896 0.785116 7 to 8 141851 -0.1721 0.431693 6 to 7 141912 0.0079 0.503142 5 to 6 141596 -0.9243 0.177671 4 to 5 141978 0.2026 0.580263 3 to 4 142470 1.6539 0.950925 2 to 3 141629 -0.8269 0.204138 1 to 2 141613 -0.8741 0.191024 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-07-09_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2509.13 0.129 0.551391 Test results for specific bytes for dh-ranFile-2016-07-09_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2457.12 -0.606 0.272142 2 to 9 2639.39 1.971 0.975654 3 to 10 2530.47 0.431 0.666712 4 to 11 2487.20 -0.181 0.428164 5 to 12 2305.27 -2.754 0.002945 6 to 13 2428.71 -1.008 0.156692 7 to 14 2599.37 1.405 0.920028 8 to 15 2513.60 0.192 0.576234 9 to 16 2562.01 0.877 0.809758 10 to 17 2573.80 1.044 0.851691 11 to 18 2409.15 -1.285 0.099417 12 to 19 2532.42 0.458 0.676680 13 to 20 2464.11 -0.508 0.305891 14 to 21 2576.45 1.081 0.860200 15 to 22 2562.23 0.880 0.810575 16 to 23 2506.52 0.092 0.536734 17 to 24 2577.74 1.099 0.864203 18 to 25 2439.93 -0.850 0.197800 19 to 26 2370.94 -1.825 0.033983 20 to 27 2530.94 0.438 0.669138 21 to 28 2630.13 1.840 0.967136 22 to 29 2501.23 0.017 0.506928 23 to 30 2486.16 -0.196 0.422432 24 to 31 2551.62 0.730 0.767293 25 to 32 2385.43 -1.620 0.052595 CDPARK for dh-ranFile-2016-07-09_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 3565 1.9178 0.972432 3497 -1.1872 0.117571 3549 1.1872 0.882429 3552 1.3242 0.907282 3488 -1.5982 0.055002 3577 2.4658 0.993164 3532 0.4110 0.659449 3516 -0.3196 0.374623 3535 0.5479 0.708135 3515 -0.3653 0.357445 Square side=100, avg. no. parked=3532.60 sample std.=27.41 p-value of the KSTEST for those 10 p-values: 0.199987 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-07-09_04:31 0.6398,0.0647,0.5873,0.1697,0.8500,0.9196,0.8756,0.2195,0.3845,0.1529, The KS test for those 10 p-values: 0.920683 The 3DSPHERES test for dh-ranFile-2016-07-09_04:31 sample no r^3 equiv. uni. 1 96.872 0.960405 2 24.343 0.555778 3 14.241 0.377926 4 68.310 0.897408 5 31.780 0.653316 6 30.458 0.637692 7 10.118 0.286272 8 113.706 0.977409 9 27.927 0.605797 10 3.875 0.121167 11 11.011 0.307221 12 42.157 0.754691 13 53.285 0.830712 14 2.729 0.086940 15 15.478 0.403066 16 5.957 0.180090 17 96.936 0.960490 18 11.938 0.328285 19 7.311 0.216268 20 5.654 0.171773 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.821638 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-07-09_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 -0.4 -0.1 -1.2 0.7 -0.6 0.8 0.4 -0.1 0.4 -1.4 0.3 -0.6 -0.1 -0.2 1.8 0.3 -0.7 0.9 -0.7 -0.8 0.8 0.3 -2.1 -0.3 2.0 -0.4 1.1 -0.9 0.4 0.4 -0.5 0.0 -1.9 0.4 -0.5 1.8 0.1 -1.8 0.9 0.0 -1.1 Chi-square with 42 degrees of freedom:37.068674 z-score=-0.538052, p-value=0.313085 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-07-09_04:31 Test no p-value 1 0.561606 2 0.398064 3 0.064236 4 0.341315 5 0.408993 6 0.038615 7 0.004910 8 0.149832 9 0.268007 10 0.769119 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.038381 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-07-09_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 66748 0.10 66787 0.22 3 25000.00 24966 0.05 24937 0.16 4 6666.67 6617 0.37 6637 0.13 5 1388.89 1381 0.04 1371 0.23 6 238.10 244 0.15 221 1.23 7 34.72 37 0.15 36 0.05 8 4.96 6 0.22 10 5.12 p=0.01737 p=0.69140 Number of rngs required: 687436, p-value: 0.131 RESULTS OF CRAPS TEST for dh-ranFile-2016-07-09_04:31 No. of wins: Observed Expected 98585 98585.9 z-score=-0.004, pvalue=0.49847 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66345 66666.7 1.552 1.552 2 37674 37654.3 0.010 1.562 3 27353 26954.7 5.885 7.447 4 19371 19313.5 0.171 7.618 5 13926 13851.4 0.402 8.020 6 9758 9943.5 3.462 11.482 7 7179 7145.0 0.162 11.644 8 5053 5139.1 1.442 13.085 9 3683 3699.9 0.077 13.162 10 2691 2666.3 0.229 13.391 11 1919 1923.3 0.010 13.401 12 1439 1388.7 1.819 15.220 13 990 1003.7 0.187 15.407 14 742 726.1 0.346 15.753 15 502 525.8 1.080 16.834 16 368 381.2 0.454 17.288 17 258 276.5 1.243 18.530 18 200 200.8 0.003 18.534 19 149 146.0 0.062 18.596 20 118 106.2 1.308 19.904 21 282 287.1 0.091 19.995 Chisq= 19.99 for 20 degrees of freedom, p= 0.54175 SUMMARY of craptest p-value for no. of wins: 0.498468 p-value for throws/game: 0.541747 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-07-09_04:31 No. of wins: Observed Expected 98622 98585.9 z-score= 0.162, pvalue=0.56421 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66679 66666.7 0.002 0.002 2 37856 37654.3 1.080 1.082 3 26845 26954.7 0.447 1.529 4 19314 19313.5 0.000 1.529 5 13720 13851.4 1.247 2.776 6 10009 9943.5 0.431 3.207 7 7050 7145.0 1.264 4.471 8 5142 5139.1 0.002 4.472 9 3726 3699.9 0.185 4.657 10 2677 2666.3 0.043 4.700 11 1909 1923.3 0.107 4.807 12 1416 1388.7 0.535 5.342 13 931 1003.7 5.268 10.610 14 745 726.1 0.490 11.100 15 532 525.8 0.072 11.172 16 397 381.2 0.659 11.831 17 267 276.5 0.329 12.160 18 225 200.8 2.909 15.069 19 143 146.0 0.061 15.130 20 104 106.2 0.046 15.176 21 313 287.1 2.334 17.510 Chisq= 17.51 for 20 degrees of freedom, p= 0.38035 SUMMARY of craptest p-value for no. of wins: 0.564207 p-value for throws/game: 0.380347 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0006,0.0029,0.0049,0.0070,0.0098,0.0123,0.0157,0.0174,0.0186,0.0261, 0.0294,0.0340,0.0360,0.0384,0.0386,0.0478,0.0492,0.0521,0.0526,0.0534, 0.0550,0.0606,0.0618,0.0642,0.0647,0.0661,0.0675,0.0698,0.0734,0.0746, 0.0753,0.0813,0.0869,0.0923,0.0927,0.0994,0.1034,0.1058,0.1068,0.1079, 0.1128,0.1148,0.1176,0.1212,0.1250,0.1253,0.1308,0.1453,0.1498,0.1529, 0.1567,0.1660,0.1683,0.1697,0.1705,0.1712,0.1718,0.1767,0.1777,0.1801, 0.1815,0.1910,0.1978,0.2000,0.2016,0.2041,0.2163,0.2195,0.2218,0.2238, 0.2318,0.2371,0.2374,0.2438,0.2464,0.2495,0.2495,0.2524,0.2659,0.2680, 0.2702,0.2721,0.2741,0.2818,0.2833,0.2863,0.2946,0.3025,0.3059,0.3072, 0.3111,0.3131,0.3283,0.3413,0.3563,0.3569,0.3574,0.3593,0.3602,0.3624, 0.3673,0.3674,0.3691,0.3725,0.3746,0.3748,0.3779,0.3803,0.3803,0.3845, 0.3879,0.3882,0.3902,0.3927,0.3931,0.3981,0.4015,0.4018,0.4031,0.4079, 0.4090,0.4124,0.4203,0.4219,0.4224,0.4259,0.4279,0.4282,0.4309,0.4311, 0.4317,0.4387,0.4408,0.4415,0.4447,0.4515,0.4597,0.4615,0.4643,0.4697, 0.4736,0.4831,0.4985,0.5031,0.5069,0.5184,0.5198,0.5202,0.5218,0.5220, 0.5266,0.5271,0.5367,0.5375,0.5403,0.5405,0.5417,0.5481,0.5514,0.5549, 0.5558,0.5616,0.5642,0.5655,0.5762,0.5803,0.5873,0.5894,0.5950,0.6058, 0.6137,0.6144,0.6207,0.6207,0.6214,0.6371,0.6377,0.6386,0.6398,0.6403, 0.6474,0.6493,0.6533,0.6575,0.6594,0.6601,0.6667,0.6691,0.6767,0.6796, 0.6808,0.6833,0.6914,0.7081,0.7246,0.7307,0.7312,0.7455,0.7457,0.7547, 0.7582,0.7673,0.7691,0.7720,0.7729,0.7735,0.7767,0.7842,0.7851,0.7885, 0.7985,0.8030,0.8084,0.8097,0.8098,0.8106,0.8193,0.8216,0.8221,0.8254, 0.8307,0.8375,0.8404,0.8467,0.8500,0.8500,0.8516,0.8517,0.8517,0.8602, 0.8609,0.8622,0.8637,0.8642,0.8756,0.8824,0.8900,0.8902,0.8974,0.9018, 0.9018,0.9057,0.9069,0.9073,0.9091,0.9175,0.9196,0.9200,0.9207,0.9260, 0.9403,0.9509,0.9539,0.9604,0.9605,0.9626,0.9637,0.9641,0.9668,0.9671, 0.9724,0.9757,0.9774,0.9774,0.9797,0.9895,0.9922,0.9929,0.9932, Overall p-value after applying KStest on 269 p-values = 0.261176 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.