RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-03_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.95 18.9490 0.668535 2 to 25 15.89 10.0084 0.096741 3 to 26 15.74 13.3221 0.285629 4 to 27 15.37 46.6144 0.999861 5 to 28 15.71 14.6490 0.379251 6 to 29 16.02 15.4911 0.439845 7 to 30 15.83 11.0332 0.145169 8 to 31 16.00 22.7169 0.841303 9 to 32 15.67 23.2120 0.857526 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.486901 Tough bday spacings test for dh-ranFile-2015-06-03_10:31: 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 13 37 78 108 93 70 52 28 9 8 4 (O-E)^2/E 1.6 0.0 0.3 1.1 0.2 0.8 0.0 0.1 2.3 0.3 0.0 Birthday Spacings: Sum(O-E)^2/E= 6.808, p= 0.257 RESULTS OF GCD FOR dh-ranFile-2015-06-03_10:31 Euclid's algorithm: p-value, steps to gcd: 0.679902 p-value, dist. of gcd's: 0.196922 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-03_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.696 0.265 0.573 0.339 0.292 0.111 0.887 0.847 Bits 8 to 15---> 0.762 0.099 0.594 0.100 0.201 0.108 0.809 0.167 Bits 16 to 23---> 0.695 0.094 0.892 0.833 0.292 0.450 0.511 0.762 Bits 24 to 31---> 0.922 0.909 0.238 0.541 0.353 0.436 0.442 0.771 KS test for the above 32 p values: 0.121 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-03_10:31, p-values for 5 runs: 0.0817, 0.1375, 0.3128, 0.9295, 0.5815 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-03_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5165 5134.0 0.187 0.279 r= 30 23302 23103.0 1.713 1.993 r= 31 11326 11551.5 4.403 6.396 chi-square = 6.396 with df = 3; p-value = 0.906 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-03_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5103 5134.0 0.187 0.199 r= 31 23219 23103.0 0.582 0.781 r= 32 11465 11551.5 0.648 1.429 chi-square = 1.429 with df = 3; p-value = 0.301 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-03_10:31 b-rank test for bits 1 to 8, p=0.95443 b-rank test for bits 2 to 9, p=0.93190 b-rank test for bits 3 to 10, p=0.27832 b-rank test for bits 4 to 11, p=0.93028 b-rank test for bits 5 to 12, p=0.71969 b-rank test for bits 6 to 13, p=0.15508 b-rank test for bits 7 to 14, p=0.30516 b-rank test for bits 8 to 15, p=0.37504 b-rank test for bits 9 to 16, p=0.33202 b-rank test for bits 10 to 17, p=0.87160 b-rank test for bits 11 to 18, p=0.99149 b-rank test for bits 12 to 19, p=0.11555 b-rank test for bits 13 to 20, p=0.63908 b-rank test for bits 14 to 21, p=0.91337 b-rank test for bits 15 to 22, p=0.03465 b-rank test for bits 16 to 23, p=0.56946 b-rank test for bits 17 to 24, p=0.58416 b-rank test for bits 18 to 25, p=0.87841 b-rank test for bits 19 to 26, p=0.47084 b-rank test for bits 20 to 27, p=0.56638 b-rank test for bits 21 to 28, p=0.05144 b-rank test for bits 22 to 29, p=0.96819 b-rank test for bits 23 to 30, p=0.94482 b-rank test for bits 24 to 31, p=0.95081 b-rank test for bits 25 to 32, p=0.49524 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 = 0.039737 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-03_10:31 (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 141340 -1.33 0.091725 2 141167 -1.73 0.041422 3 141646 -0.62 0.269193 4 141499 -0.96 0.168851 5 141434 -1.11 0.133374 6 140904 -2.35 0.009414 7 141892 -0.04 0.483851 8 141946 0.09 0.534139 9 141669 -0.56 0.287222 10 142705 1.86 0.968489 11 141833 -0.18 0.429228 12 141990 0.19 0.574750 13 141758 -0.35 0.361829 14 141405 -1.18 0.119330 15 142179 0.63 0.735676 16 141783 -0.30 0.383935 17 142840 2.17 0.985165 18 141816 -0.22 0.413691 19 141938 0.07 0.526704 20 141419 -1.15 0.125974 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-03_10:31 Bits used No. missing words z-score p-value 23 to 32 141950 0.1402 0.555765 22 to 31 141800 -0.3770 0.353087 21 to 30 141884 -0.0873 0.465199 20 to 29 141753 -0.5391 0.294920 19 to 28 141948 0.1333 0.553040 18 to 27 142011 0.3506 0.637051 17 to 26 141846 -0.2184 0.413567 16 to 25 142031 0.4196 0.662594 15 to 24 142205 1.0196 0.846029 14 to 23 142028 0.4092 0.658806 13 to 22 142401 1.6954 0.955002 12 to 21 142409 1.7230 0.957556 11 to 20 142500 2.0368 0.979165 10 to 19 141638 -0.9356 0.174734 9 to 18 141403 -1.7460 0.040408 8 to 17 141891 -0.0632 0.474801 7 to 16 141797 -0.3873 0.349251 6 to 15 142103 0.6678 0.747878 5 to 14 141520 -1.3425 0.089714 4 to 13 142113 0.7023 0.758757 3 to 12 141689 -0.7598 0.223699 2 to 11 141779 -0.4494 0.326567 1 to 10 141962 0.1816 0.572060 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-03_10:31 Bits used No. missing words z-score p-value 28 to 32 141481 -1.4520 0.073256 27 to 31 141848 -0.2079 0.417654 26 to 30 142287 1.2802 0.899769 25 to 29 141658 -0.8520 0.197116 24 to 28 141769 -0.4757 0.317146 23 to 27 141749 -0.5435 0.293396 22 to 26 141778 -0.4452 0.328093 21 to 25 142389 1.6260 0.948025 20 to 24 142345 1.4768 0.930142 19 to 23 142025 0.3921 0.652509 18 to 22 141723 -0.6316 0.263815 17 to 21 141976 0.2260 0.589399 16 to 20 142215 1.0362 0.849938 15 to 19 141793 -0.3943 0.346665 14 to 18 141604 -1.0350 0.150331 13 to 17 141966 0.1921 0.576169 12 to 16 142291 1.2938 0.902132 11 to 15 141886 -0.0791 0.468483 10 to 14 141943 0.1141 0.545435 9 to 13 142138 0.7752 0.780875 8 to 12 141891 -0.0621 0.475227 7 to 11 142034 0.4226 0.663710 6 to 10 141512 -1.3469 0.089009 5 to 9 141657 -0.8554 0.196177 4 to 8 142032 0.4158 0.661233 3 to 7 141913 0.0124 0.504963 2 to 6 141422 -1.6520 0.049271 1 to 5 142010 0.3413 0.633544 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-03_10:31 Bits used No. missing words z-score p-value 31 to 32 142128 0.6450 0.740551 30 to 31 141648 -0.7709 0.220388 29 to 30 142128 0.6450 0.740551 28 to 29 142472 1.6598 0.951522 27 to 28 141860 -0.1455 0.442152 26 to 27 142252 1.0108 0.843950 25 to 26 142528 1.8250 0.965998 24 to 25 141698 -0.6234 0.266513 23 to 24 142420 1.5064 0.934018 22 to 23 141965 0.1642 0.565220 21 to 22 141979 0.2055 0.581416 20 to 21 142136 0.6686 0.748138 19 to 20 142015 0.3117 0.622370 18 to 19 142055 0.4297 0.666295 17 to 18 142213 0.8958 0.814815 16 to 17 142271 1.0669 0.856985 15 to 16 141971 0.1819 0.572176 14 to 15 141820 -0.2635 0.396079 13 to 14 141699 -0.6204 0.267483 12 to 13 141887 -0.0659 0.473741 11 to 12 141867 -0.1249 0.450314 10 to 11 141794 -0.3402 0.366851 9 to 10 142560 1.9194 0.972532 8 to 9 141277 -1.8653 0.031071 7 to 8 141076 -2.4582 0.006982 6 to 7 141910 0.0020 0.500789 5 to 6 142097 0.5536 0.710073 4 to 5 141641 -0.7915 0.214316 3 to 4 142247 0.9961 0.840394 2 to 3 141857 -0.1544 0.438661 1 to 2 142091 0.5359 0.703986 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-03_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2425.40 -1.055 0.145706 Test results for specific bytes for dh-ranFile-2015-06-03_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2358.18 -2.006 0.022446 2 to 9 2347.88 -2.151 0.015729 3 to 10 2529.39 0.416 0.661144 4 to 11 2350.05 -2.121 0.016975 5 to 12 2511.88 0.168 0.566717 6 to 13 2580.05 1.132 0.871199 7 to 14 2572.80 1.030 0.848405 8 to 15 2598.84 1.398 0.918922 9 to 16 2512.57 0.178 0.570556 10 to 17 2519.95 0.282 0.611091 11 to 18 2465.43 -0.489 0.312480 12 to 19 2438.69 -0.867 0.192952 13 to 20 2469.50 -0.431 0.333097 14 to 21 2375.79 -1.757 0.039491 15 to 22 2488.67 -0.160 0.436366 16 to 23 2405.49 -1.337 0.090676 17 to 24 2362.89 -1.939 0.026245 18 to 25 2463.06 -0.522 0.300678 19 to 26 2467.16 -0.464 0.321186 20 to 27 2516.68 0.236 0.593218 21 to 28 2421.39 -1.112 0.133132 22 to 29 2444.41 -0.786 0.215902 23 to 30 2433.91 -0.935 0.174976 24 to 31 2532.11 0.454 0.675104 25 to 32 2527.49 0.389 0.651298 CDPARK for dh-ranFile-2015-06-03_10:31: 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 3554 1.4155 0.921543 3562 1.7808 0.962529 3516 -0.3196 0.374623 3490 -1.5068 0.065925 3558 1.5982 0.944998 3520 -0.1370 0.445521 3526 0.1370 0.554479 3540 0.7763 0.781201 3512 -0.5023 0.307734 3516 -0.3196 0.374623 Square side=100, avg. no. parked=3529.40 sample std.=22.16 p-value of the KSTEST for those 10 p-values: 0.501078 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-03_10:31 0.8355,0.3823,0.7496,0.5221,0.7999,0.8288,0.9284,0.7938,0.8363,0.0187, The KS test for those 10 p-values: 0.048512 The 3DSPHERES test for dh-ranFile-2015-06-03_10:31 sample no r^3 equiv. uni. 1 3.468 0.109155 2 6.159 0.185600 3 52.007 0.823350 4 0.157 0.005227 5 2.214 0.071129 6 24.181 0.553368 7 4.095 0.127586 8 4.488 0.138949 9 59.152 0.860786 10 59.340 0.861653 11 16.427 0.421649 12 128.579 0.986240 13 17.700 0.445666 14 50.379 0.813494 15 2.460 0.078715 16 23.105 0.537070 17 22.920 0.534195 18 35.476 0.693500 19 48.048 0.798429 20 9.890 0.280845 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.630575 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-03_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.1 -0.6 -0.7 -0.9 -1.1 0.0 0.1 -0.6 -0.1 -0.1 1.9 -0.6 0.0 -0.7 -0.5 0.0 0.2 -0.2 1.7 0.9 -1.6 -0.3 0.2 0.1 0.4 -1.1 1.5 0.2 -1.0 -0.2 -1.2 0.1 -0.6 -0.4 -0.8 0.5 1.5 0.1 0.4 0.9 0.0 -1.1 Chi-square with 42 degrees of freedom:27.873046 z-score=-1.541377, p-value=0.046118 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-03_10:31 Test no p-value 1 0.095220 2 0.605630 3 0.632753 4 0.451365 5 0.141117 6 0.764307 7 0.193944 8 0.245957 9 0.414646 10 0.362346 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.342729 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-03_10:31: (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 66497 0.43 66654 0.00 3 25000.00 25046 0.08 25074 0.22 4 6666.67 6723 0.48 6617 0.37 5 1388.89 1452 2.87 1373 0.18 6 238.10 244 0.15 242 0.06 7 34.72 35 0.00 35 0.00 8 4.96 2 1.77 4 0.19 p=0.55117 p=0.01537 Number of rngs required: 690237, p-value: 0.985 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-03_10:31 No. of wins: Observed Expected 98580 98585.9 z-score=-0.026, pvalue=0.48955 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66684 66666.7 0.005 0.005 2 37565 37654.3 0.212 0.216 3 27119 26954.7 1.001 1.217 4 19148 19313.5 1.418 2.635 5 13888 13851.4 0.097 2.732 6 9795 9943.5 2.219 4.951 7 7237 7145.0 1.184 6.135 8 5195 5139.1 0.609 6.743 9 3767 3699.9 1.218 7.961 10 2667 2666.3 0.000 7.962 11 1866 1923.3 1.709 9.670 12 1414 1388.7 0.459 10.130 13 1079 1003.7 5.647 15.777 14 703 726.1 0.737 16.514 15 516 525.8 0.184 16.698 16 355 381.2 1.794 18.492 17 278 276.5 0.008 18.500 18 211 200.8 0.515 19.015 19 142 146.0 0.109 19.124 20 107 106.2 0.006 19.130 21 264 287.1 1.861 20.990 Chisq= 20.99 for 20 degrees of freedom, p= 0.60230 SUMMARY of craptest p-value for no. of wins: 0.489548 p-value for throws/game: 0.602301 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-03_10:31 No. of wins: Observed Expected 98845 98585.9 z-score= 1.159, pvalue=0.87678 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66994 66666.7 1.607 1.607 2 37842 37654.3 0.935 2.543 3 27011 26954.7 0.117 2.660 4 19149 19313.5 1.400 4.061 5 13539 13851.4 7.047 11.107 6 9954 9943.5 0.011 11.118 7 7258 7145.0 1.786 12.905 8 5018 5139.1 2.852 15.757 9 3698 3699.9 0.001 15.758 10 2575 2666.3 3.126 18.884 11 1937 1923.3 0.097 18.981 12 1364 1388.7 0.441 19.422 13 988 1003.7 0.246 19.668 14 642 726.1 9.750 29.418 15 553 525.8 1.403 30.821 16 390 381.2 0.205 31.026 17 286 276.5 0.324 31.350 18 219 200.8 1.644 32.994 19 157 146.0 0.831 33.825 20 118 106.2 1.308 35.133 21 308 287.1 1.519 36.652 Chisq= 36.65 for 20 degrees of freedom, p= 0.98712 SUMMARY of craptest p-value for no. of wins: 0.876778 p-value for throws/game: 0.987122 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0052,0.0070,0.0094,0.0154,0.0157,0.0170,0.0187,0.0224,0.0262,0.0311, 0.0347,0.0395,0.0397,0.0404,0.0414,0.0461,0.0485,0.0493,0.0514,0.0659, 0.0711,0.0733,0.0787,0.0817,0.0890,0.0897,0.0907,0.0917,0.0938,0.0952, 0.0967,0.0992,0.0998,0.1085,0.1092,0.1109,0.1156,0.1193,0.1213,0.1260, 0.1276,0.1331,0.1334,0.1375,0.1389,0.1411,0.1452,0.1457,0.1503,0.1551, 0.1675,0.1689,0.1747,0.1750,0.1856,0.1930,0.1939,0.1962,0.1969,0.1971, 0.2006,0.2143,0.2159,0.2204,0.2237,0.2383,0.2460,0.2566,0.2638,0.2648, 0.2665,0.2675,0.2692,0.2783,0.2808,0.2856,0.2872,0.2919,0.2923,0.2934, 0.2949,0.3007,0.3013,0.3052,0.3077,0.3125,0.3128,0.3171,0.3212,0.3266, 0.3281,0.3320,0.3331,0.3389,0.3427,0.3467,0.3493,0.3531,0.3533,0.3618, 0.3623,0.3669,0.3746,0.3746,0.3750,0.3793,0.3823,0.3839,0.3961,0.4136, 0.4137,0.4146,0.4177,0.4216,0.4292,0.4358,0.4364,0.4387,0.4398,0.4419, 0.4422,0.4455,0.4457,0.4503,0.4503,0.4514,0.4652,0.4685,0.4708,0.4737, 0.4748,0.4752,0.4839,0.4869,0.4895,0.4952,0.5008,0.5011,0.5050,0.5113, 0.5221,0.5267,0.5341,0.5342,0.5371,0.5406,0.5454,0.5512,0.5530,0.5534, 0.5545,0.5558,0.5652,0.5664,0.5667,0.5695,0.5706,0.5721,0.5722,0.5728, 0.5748,0.5762,0.5814,0.5815,0.5842,0.5894,0.5932,0.5940,0.6023,0.6056, 0.6111,0.6224,0.6306,0.6328,0.6335,0.6371,0.6391,0.6513,0.6525,0.6588, 0.6611,0.6612,0.6626,0.6637,0.6663,0.6685,0.6751,0.6799,0.6935,0.6949, 0.6957,0.7040,0.7101,0.7197,0.7357,0.7406,0.7406,0.7479,0.7481,0.7496, 0.7588,0.7624,0.7624,0.7643,0.7706,0.7809,0.7812,0.7938,0.7984,0.7999, 0.8092,0.8135,0.8148,0.8233,0.8288,0.8333,0.8355,0.8363,0.8404,0.8413, 0.8440,0.8460,0.8475,0.8484,0.8499,0.8570,0.8575,0.8608,0.8617,0.8712, 0.8716,0.8768,0.8784,0.8866,0.8922,0.8998,0.9021,0.9061,0.9086,0.9134, 0.9189,0.9215,0.9220,0.9284,0.9295,0.9301,0.9303,0.9319,0.9340,0.9448, 0.9450,0.9480,0.9508,0.9515,0.9544,0.9550,0.9576,0.9625,0.9660,0.9682, 0.9685,0.9725,0.9792,0.9851,0.9852,0.9862,0.9871,0.9915,0.9999, Overall p-value after applying KStest on 269 p-values = 0.781424 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.