RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-29_15:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.55 21.5127 0.795805 2 to 25 15.68 11.7911 0.187382 3 to 26 15.49 24.8064 0.900871 4 to 27 15.94 16.6632 0.522596 5 to 28 15.67 19.2923 0.687985 6 to 29 15.84 15.6738 0.452935 7 to 30 15.87 10.8124 0.133853 8 to 31 15.67 22.3659 0.828948 9 to 32 15.80 20.7837 0.763885 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.578321 Tough bday spacings test for dh-ranFile-2015-07-29_15:31: 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 36 67 104 92 88 50 27 14 9 2 (O-E)^2/E 0.4 0.0 0.5 0.4 0.3 1.2 0.1 0.3 0.1 0.9 1.0 Birthday Spacings: Sum(O-E)^2/E= 5.202, p= 0.123 RESULTS OF GCD FOR dh-ranFile-2015-07-29_15:31 Euclid's algorithm: p-value, steps to gcd: 0.864544 p-value, dist. of gcd's: 0.991803 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-29_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.475 0.927 0.192 0.784 0.128 0.066 0.949 0.341 Bits 8 to 15---> 0.131 0.140 0.186 0.124 0.174 0.268 0.606 0.987 Bits 16 to 23---> 0.226 0.915 0.364 0.812 0.021 0.671 0.788 0.307 Bits 24 to 31---> 0.996 0.657 0.350 0.515 0.538 0.215 0.381 0.226 KS test for the above 32 p values: 0.690 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-29_15:31, p-values for 5 runs: 0.3417, 0.9384, 0.2488, 0.2464, 0.3562 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-29_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 217 211.4 0.147 0.147 r= 29 5157 5134.0 0.103 0.250 r= 30 23076 23103.0 0.032 0.282 r= 31 11550 11551.5 0.000 0.282 chi-square = 0.282 with df = 3; p-value = 0.037 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-29_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 227 211.4 1.148 1.148 r= 30 5200 5134.0 0.848 1.997 r= 31 22909 23103.0 1.630 3.626 r= 32 11664 11551.5 1.095 4.722 chi-square = 4.722 with df = 3; p-value = 0.807 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-29_15:31 b-rank test for bits 1 to 8, p=0.62043 b-rank test for bits 2 to 9, p=0.75293 b-rank test for bits 3 to 10, p=0.89458 b-rank test for bits 4 to 11, p=0.64483 b-rank test for bits 5 to 12, p=0.99096 b-rank test for bits 6 to 13, p=0.55332 b-rank test for bits 7 to 14, p=0.75507 b-rank test for bits 8 to 15, p=0.51152 b-rank test for bits 9 to 16, p=0.73317 b-rank test for bits 10 to 17, p=0.39429 b-rank test for bits 11 to 18, p=0.60703 b-rank test for bits 12 to 19, p=0.22631 b-rank test for bits 13 to 20, p=0.35402 b-rank test for bits 14 to 21, p=0.86519 b-rank test for bits 15 to 22, p=0.85365 b-rank test for bits 16 to 23, p=0.97802 b-rank test for bits 17 to 24, p=0.97081 b-rank test for bits 18 to 25, p=0.75196 b-rank test for bits 19 to 26, p=0.93595 b-rank test for bits 20 to 27, p=0.30390 b-rank test for bits 21 to 28, p=0.68905 b-rank test for bits 22 to 29, p=0.98772 b-rank test for bits 23 to 30, p=0.23986 b-rank test for bits 24 to 31, p=0.85879 b-rank test for bits 25 to 32, p=0.55464 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 = 0.002274 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-29_15:31 (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 141765 -0.34 0.367976 2 142418 1.19 0.882678 3 141945 0.08 0.533210 4 141642 -0.62 0.266116 5 141648 -0.61 0.270738 6 141437 -1.10 0.134889 7 141683 -0.53 0.298469 8 142273 0.85 0.802253 9 141517 -0.92 0.179661 10 142404 1.16 0.876113 11 142162 0.59 0.722522 12 142567 1.54 0.937806 13 142218 0.72 0.764604 14 141049 -2.01 0.022209 15 142432 1.22 0.888993 16 141884 -0.06 0.476404 17 141264 -1.51 0.065805 18 142265 0.83 0.797015 19 141506 -0.94 0.173004 20 141720 -0.44 0.329114 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-29_15:31 Bits used No. missing words z-score p-value 23 to 32 142293 1.3230 0.907082 22 to 31 142338 1.4782 0.930319 21 to 30 141860 -0.1701 0.432464 20 to 29 142482 1.9747 0.975850 19 to 28 142322 1.4230 0.922632 18 to 27 142163 0.8747 0.809138 17 to 26 141625 -0.9804 0.163432 16 to 25 141711 -0.6839 0.247020 15 to 24 141967 0.1989 0.578815 14 to 23 142122 0.7333 0.768326 13 to 22 141765 -0.4977 0.309351 12 to 21 142095 0.6402 0.738992 11 to 20 141859 -0.1736 0.431109 10 to 19 141511 -1.3736 0.084790 9 to 18 141602 -1.0598 0.144627 8 to 17 141727 -0.6287 0.264765 7 to 16 141827 -0.2839 0.388245 6 to 15 141758 -0.5218 0.300895 5 to 14 141886 -0.0804 0.467940 4 to 13 141986 0.2644 0.604256 3 to 12 141837 -0.2494 0.401520 2 to 11 141411 -1.7184 0.042864 1 to 10 141574 -1.1563 0.123777 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-29_15:31 Bits used No. missing words z-score p-value 28 to 32 141910 0.0023 0.500906 27 to 31 141663 -0.8350 0.201854 26 to 30 142114 0.6938 0.756095 25 to 29 142132 0.7548 0.774820 24 to 28 141705 -0.6926 0.244267 23 to 27 142131 0.7514 0.773801 22 to 26 142311 1.3616 0.913337 21 to 25 141527 -1.2960 0.097482 20 to 24 141339 -1.9333 0.026598 19 to 23 141887 -0.0757 0.469831 18 to 22 141948 0.1311 0.552146 17 to 21 141281 -2.1299 0.016589 16 to 20 142068 0.5379 0.704665 15 to 19 141881 -0.0960 0.461747 14 to 18 141562 -1.1774 0.119520 13 to 17 141660 -0.8452 0.199003 12 to 16 142237 1.1107 0.866661 11 to 15 141886 -0.0791 0.468483 10 to 14 142312 1.3650 0.913871 9 to 13 141477 -1.4655 0.071389 8 to 12 141787 -0.4147 0.339189 7 to 11 141795 -0.3876 0.349171 6 to 10 142061 0.5141 0.696421 5 to 9 141653 -0.8689 0.192447 4 to 8 141860 -0.1672 0.433598 3 to 7 141450 -1.5571 0.059729 2 to 6 141557 -1.1943 0.116173 1 to 5 141945 0.1209 0.548121 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-29_15:31 Bits used No. missing words z-score p-value 31 to 32 141676 -0.6883 0.245635 30 to 31 141744 -0.4877 0.312882 29 to 30 141931 0.0639 0.525484 28 to 29 141297 -1.8063 0.035437 27 to 28 142136 0.6686 0.748138 26 to 27 142193 0.8368 0.798643 25 to 26 141765 -0.4258 0.335144 24 to 25 142265 1.0492 0.852951 23 to 24 142271 1.0669 0.856985 22 to 23 142106 0.5801 0.719092 21 to 22 142199 0.8545 0.803582 20 to 21 142084 0.5153 0.696811 19 to 20 142547 1.8810 0.970016 18 to 19 142828 2.7099 0.996635 17 to 18 141701 -0.6145 0.269428 16 to 17 141570 -1.0010 0.158420 15 to 16 141014 -2.6411 0.004132 14 to 15 142440 1.5654 0.941255 13 to 14 142448 1.5890 0.943969 12 to 13 141498 -1.2134 0.112496 11 to 12 142112 0.5978 0.725029 10 to 11 141830 -0.2340 0.407488 9 to 10 141526 -1.1308 0.129077 8 to 9 141551 -1.0570 0.145251 7 to 8 141609 -0.8859 0.187828 6 to 7 141833 -0.2252 0.410927 5 to 6 141819 -0.2665 0.394942 4 to 5 142057 0.4356 0.668438 3 to 4 142545 1.8751 0.969613 2 to 3 141717 -0.5673 0.285240 1 to 2 141685 -0.6617 0.254069 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-29_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2569.31 0.980 0.836498 Test results for specific bytes for dh-ranFile-2015-07-29_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2580.51 1.139 0.872553 2 to 9 2482.00 -0.255 0.399537 3 to 10 2381.66 -1.674 0.047102 4 to 11 2461.92 -0.538 0.295125 5 to 12 2452.99 -0.665 0.253065 6 to 13 2536.44 0.515 0.696833 7 to 14 2426.11 -1.045 0.148036 8 to 15 2470.31 -0.420 0.337295 9 to 16 2472.68 -0.386 0.349632 10 to 17 2548.61 0.687 0.754100 11 to 18 2517.91 0.253 0.599977 12 to 19 2656.08 2.207 0.986351 13 to 20 2415.81 -1.191 0.116892 14 to 21 2539.38 0.557 0.711201 15 to 22 2461.81 -0.540 0.294550 16 to 23 2608.94 1.541 0.938293 17 to 24 2484.84 -0.214 0.415097 18 to 25 2368.63 -1.858 0.031596 19 to 26 2577.32 1.093 0.862901 20 to 27 2478.87 -0.299 0.382550 21 to 28 2446.51 -0.756 0.224676 22 to 29 2419.72 -1.135 0.128110 23 to 30 2502.86 0.040 0.516110 24 to 31 2378.17 -1.723 0.042447 25 to 32 2494.29 -0.081 0.467837 CDPARK for dh-ranFile-2015-07-29_15:31: 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 3531 0.3653 0.642555 3529 0.2740 0.607947 3545 1.0046 0.842447 3518 -0.2283 0.409702 3541 0.8219 0.794438 3519 -0.1826 0.427537 3542 0.8676 0.807188 3515 -0.3653 0.357445 3546 1.0502 0.853193 3539 0.7306 0.767486 Square side=100, avg. no. parked=3532.50 sample std.=11.21 p-value of the KSTEST for those 10 p-values: 0.096568 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-29_15:31 0.1534,0.0382,0.5666,0.4181,0.3600,0.6167,0.9713,0.0517,0.5551,0.0783, The KS test for those 10 p-values: 0.237617 The 3DSPHERES test for dh-ranFile-2015-07-29_15:31 sample no r^3 equiv. uni. 1 27.160 0.595596 2 29.274 0.623105 3 14.732 0.388031 4 11.799 0.325163 5 14.456 0.382365 6 21.057 0.504352 7 3.905 0.122063 8 115.169 0.978484 9 11.197 0.311496 10 73.142 0.912671 11 31.251 0.647146 12 14.550 0.384302 13 45.986 0.784085 14 3.603 0.113175 15 9.843 0.279703 16 2.967 0.094161 17 13.953 0.371924 18 60.315 0.866080 19 61.356 0.870644 20 51.830 0.822300 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.895465 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-29_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.2 -1.6 -0.7 -0.3 0.3 0.5 -1.2 -0.8 0.1 1.0 -0.4 1.1 -1.0 1.8 -1.0 -0.6 -0.5 -1.8 0.1 2.5 -1.6 1.0 -0.3 1.7 0.1 -1.9 1.1 1.0 0.6 -0.4 -0.5 0.4 -0.8 0.6 -0.1 0.0 0.8 1.3 1.5 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:45.263930 z-score=0.356124, p-value=0.662633 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-29_15:31 Test no p-value 1 0.059340 2 0.494065 3 0.160622 4 0.003571 5 0.377654 6 0.524622 7 0.309247 8 0.032737 9 0.334978 10 0.380561 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.012410 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-29_15:31: (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 66471 0.57 66530 0.28 3 25000.00 25283 3.20 25179 1.28 4 6666.67 6632 0.18 6632 0.18 5 1388.89 1340 1.72 1365 0.41 6 238.10 238 0.00 247 0.33 7 34.72 31 0.40 39 0.53 8 4.96 4 0.19 7 0.84 p=0.60568 p=0.30340 Number of rngs required: 689296, p-value: 0.850 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-29_15:31 No. of wins: Observed Expected 98173 98585.9 z-score=-1.847, pvalue=0.03241 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66403 66666.7 1.043 1.043 2 37689 37654.3 0.032 1.075 3 27161 26954.7 1.578 2.653 4 19522 19313.5 2.252 4.905 5 13803 13851.4 0.169 5.074 6 9686 9943.5 6.671 11.745 7 7020 7145.0 2.188 13.932 8 5217 5139.1 1.182 15.114 9 3694 3699.9 0.009 15.123 10 2694 2666.3 0.288 15.411 11 1995 1923.3 2.671 18.082 12 1434 1388.7 1.475 19.557 13 1016 1003.7 0.150 19.707 14 743 726.1 0.391 20.099 15 517 525.8 0.148 20.247 16 386 381.2 0.062 20.309 17 303 276.5 2.532 22.841 18 189 200.8 0.697 23.538 19 151 146.0 0.172 23.710 20 108 106.2 0.030 23.740 21 269 287.1 1.143 24.883 Chisq= 24.88 for 20 degrees of freedom, p= 0.79405 SUMMARY of craptest p-value for no. of wins: 0.032407 p-value for throws/game: 0.794046 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-29_15:31 No. of wins: Observed Expected 98603 98585.9 z-score= 0.077, pvalue=0.53056 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66515 66666.7 0.345 0.345 2 37633 37654.3 0.012 0.357 3 27020 26954.7 0.158 0.515 4 19596 19313.5 4.133 4.648 5 13619 13851.4 3.900 8.548 6 9991 9943.5 0.226 8.775 7 7127 7145.0 0.045 8.820 8 5069 5139.1 0.955 9.776 9 3781 3699.9 1.779 11.555 10 2722 2666.3 1.164 12.719 11 1946 1923.3 0.267 12.986 12 1369 1388.7 0.281 13.266 13 1014 1003.7 0.105 13.372 14 717 726.1 0.115 13.487 15 514 525.8 0.266 13.753 16 377 381.2 0.045 13.799 17 256 276.5 1.526 15.324 18 194 200.8 0.232 15.556 19 158 146.0 0.989 16.545 20 101 106.2 0.256 16.801 21 281 287.1 0.130 16.932 Chisq= 16.93 for 20 degrees of freedom, p= 0.34259 SUMMARY of craptest p-value for no. of wins: 0.530556 p-value for throws/game: 0.342589 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0023,0.0036,0.0041,0.0124,0.0166,0.0209,0.0222,0.0266,0.0316,0.0324, 0.0327,0.0354,0.0367,0.0382,0.0424,0.0429,0.0471,0.0517,0.0593,0.0597, 0.0658,0.0662,0.0714,0.0783,0.0848,0.0942,0.0966,0.0975,0.1125,0.1132, 0.1162,0.1169,0.1195,0.1221,0.1227,0.1238,0.1238,0.1276,0.1281,0.1291, 0.1315,0.1339,0.1349,0.1404,0.1446,0.1453,0.1480,0.1534,0.1584,0.1606, 0.1634,0.1730,0.1737,0.1797,0.1858,0.1874,0.1878,0.1923,0.1924,0.1990, 0.2019,0.2149,0.2247,0.2257,0.2261,0.2263,0.2376,0.2399,0.2443,0.2456, 0.2464,0.2470,0.2488,0.2531,0.2541,0.2648,0.2661,0.2677,0.2694,0.2707, 0.2797,0.2852,0.2945,0.2951,0.2985,0.3009,0.3034,0.3039,0.3067,0.3092, 0.3094,0.3115,0.3129,0.3252,0.3291,0.3350,0.3351,0.3373,0.3392,0.3410, 0.3417,0.3426,0.3492,0.3495,0.3496,0.3540,0.3562,0.3574,0.3600,0.3641, 0.3680,0.3719,0.3777,0.3806,0.3808,0.3824,0.3825,0.3843,0.3880,0.3882, 0.3943,0.3949,0.3995,0.4015,0.4075,0.4097,0.4109,0.4151,0.4181,0.4275, 0.4311,0.4325,0.4336,0.4529,0.4617,0.4678,0.4679,0.4685,0.4698,0.4747, 0.4764,0.4941,0.5009,0.5044,0.5115,0.5153,0.5161,0.5226,0.5246,0.5255, 0.5306,0.5332,0.5380,0.5481,0.5521,0.5533,0.5546,0.5551,0.5666,0.5783, 0.5788,0.5956,0.6000,0.6043,0.6057,0.6058,0.6070,0.6079,0.6167,0.6204, 0.6231,0.6426,0.6448,0.6471,0.6566,0.6626,0.6684,0.6710,0.6880,0.6891, 0.6896,0.6964,0.6968,0.6968,0.7047,0.7112,0.7191,0.7225,0.7250,0.7332, 0.7390,0.7481,0.7520,0.7529,0.7541,0.7551,0.7561,0.7639,0.7646,0.7675, 0.7683,0.7738,0.7748,0.7839,0.7841,0.7883,0.7940,0.7944,0.7958,0.7970, 0.7986,0.8023,0.8036,0.8066,0.8072,0.8091,0.8123,0.8223,0.8289,0.8365, 0.8424,0.8497,0.8530,0.8532,0.8537,0.8570,0.8588,0.8629,0.8645,0.8652, 0.8661,0.8667,0.8706,0.8726,0.8761,0.8827,0.8890,0.8946,0.8955,0.9009, 0.9071,0.9127,0.9133,0.9139,0.9153,0.9226,0.9269,0.9303,0.9359,0.9378, 0.9383,0.9384,0.9413,0.9440,0.9495,0.9696,0.9700,0.9708,0.9713,0.9759, 0.9780,0.9785,0.9864,0.9875,0.9877,0.9910,0.9918,0.9956,0.9966, Overall p-value after applying KStest on 269 p-values = 0.426738 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.