RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-14_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.53 25.1363 0.908301 2 to 25 15.67 23.4396 0.864522 3 to 26 15.53 25.9277 0.924212 4 to 27 15.52 32.5652 0.987210 5 to 28 15.70 37.4709 0.997096 6 to 29 15.51 23.7034 0.872280 7 to 30 15.60 14.8342 0.392579 8 to 31 15.87 15.3901 0.432591 9 to 32 15.75 22.7964 0.844003 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.000595 Tough bday spacings test for dh-ranFile-2015-07-14_00:31: 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 37 79 118 86 75 44 36 10 7 4 (O-E)^2/E 2.9 0.0 0.4 4.2 1.4 0.1 1.3 1.3 1.6 0.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 13.297, p= 0.792 RESULTS OF GCD FOR dh-ranFile-2015-07-14_00:31 Euclid's algorithm: p-value, steps to gcd: 0.000635 p-value, dist. of gcd's: 0.911273 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-14_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.826 0.253 0.353 0.031 0.568 0.853 0.714 0.082 Bits 8 to 15---> 0.825 0.220 0.467 0.999 0.884 0.722 0.144 0.916 Bits 16 to 23---> 0.279 0.533 0.044 0.990 0.935 0.689 0.042 0.514 Bits 24 to 31---> 0.150 0.671 0.011 0.984 0.843 0.348 0.138 0.702 KS test for the above 32 p values: 0.700 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-14_00:31, p-values for 5 runs: 0.7312, 0.6608, 0.5421, 0.6224, 0.6454 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-14_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 195 211.4 1.275 1.275 r= 29 5210 5134.0 1.125 2.400 r= 30 22998 23103.0 0.478 2.877 r= 31 11597 11551.5 0.179 3.056 chi-square = 3.056 with df = 3; p-value = 0.617 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-14_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5146 5134.0 0.028 0.089 r= 31 23119 23103.0 0.011 0.100 r= 32 11520 11551.5 0.086 0.186 chi-square = 0.186 with df = 3; p-value = 0.020 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-14_00:31 b-rank test for bits 1 to 8, p=0.04179 b-rank test for bits 2 to 9, p=0.53722 b-rank test for bits 3 to 10, p=0.92610 b-rank test for bits 4 to 11, p=0.42062 b-rank test for bits 5 to 12, p=0.06791 b-rank test for bits 6 to 13, p=0.10062 b-rank test for bits 7 to 14, p=0.34186 b-rank test for bits 8 to 15, p=0.80723 b-rank test for bits 9 to 16, p=0.69267 b-rank test for bits 10 to 17, p=0.33180 b-rank test for bits 11 to 18, p=0.61972 b-rank test for bits 12 to 19, p=0.10666 b-rank test for bits 13 to 20, p=0.47862 b-rank test for bits 14 to 21, p=0.58147 b-rank test for bits 15 to 22, p=0.44743 b-rank test for bits 16 to 23, p=0.18454 b-rank test for bits 17 to 24, p=0.47449 b-rank test for bits 18 to 25, p=0.62819 b-rank test for bits 19 to 26, p=0.03810 b-rank test for bits 20 to 27, p=0.97731 b-rank test for bits 21 to 28, p=0.83096 b-rank test for bits 22 to 29, p=0.50850 b-rank test for bits 23 to 30, p=0.55228 b-rank test for bits 24 to 31, p=0.88243 b-rank test for bits 25 to 32, p=0.98864 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 = 0.896210 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-14_00:31 (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 141395 -1.20 0.114739 2 141364 -1.27 0.101308 3 142824 2.14 0.983704 4 141856 -0.12 0.450419 5 141437 -1.10 0.134889 6 141533 -0.88 0.189626 7 141744 -0.39 0.349643 8 143283 3.21 0.999335 9 141569 -0.80 0.213259 10 141712 -0.46 0.322381 11 142480 1.33 0.908790 12 142018 0.25 0.600214 13 142037 0.30 0.617261 14 141486 -0.99 0.161310 15 142142 0.54 0.706649 16 141696 -0.50 0.309089 17 141915 0.01 0.505285 18 141969 0.14 0.555439 19 142338 1.00 0.841723 20 141908 -0.00 0.498760 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-14_00:31 Bits used No. missing words z-score p-value 23 to 32 142488 1.9954 0.977001 22 to 31 141589 -1.1046 0.134669 21 to 30 142365 1.5713 0.941941 20 to 29 142295 1.3299 0.908224 19 to 28 141950 0.1402 0.555765 18 to 27 142216 1.0575 0.854854 17 to 26 141886 -0.0804 0.467940 16 to 25 141960 0.1747 0.569352 15 to 24 141421 -1.6839 0.046101 14 to 23 141995 0.2954 0.616161 13 to 22 142298 1.3402 0.909917 12 to 21 142272 1.2506 0.894457 11 to 20 142138 0.7885 0.784803 10 to 19 142020 0.3816 0.648629 9 to 18 142558 2.2368 0.987350 8 to 17 141903 -0.0218 0.491293 7 to 16 142072 0.5609 0.712578 6 to 15 141687 -0.7667 0.221643 5 to 14 142003 0.3230 0.626652 4 to 13 141644 -0.9149 0.180114 3 to 12 142421 1.7644 0.961166 2 to 11 141850 -0.2046 0.418948 1 to 10 141653 -0.8839 0.188376 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-14_00:31 Bits used No. missing words z-score p-value 28 to 32 141747 -0.5503 0.291067 27 to 31 141685 -0.7604 0.223496 26 to 30 142207 1.0091 0.843525 25 to 29 141698 -0.7164 0.236881 24 to 28 141942 0.1107 0.544091 23 to 27 141886 -0.0791 0.468483 22 to 26 142123 0.7243 0.765561 21 to 25 141906 -0.0113 0.495497 20 to 24 141468 -1.4960 0.067322 19 to 23 142293 1.3006 0.903298 18 to 22 142100 0.6463 0.740970 17 to 21 142007 0.3311 0.629710 16 to 20 142194 0.9650 0.832723 15 to 19 141399 -1.7299 0.041821 14 to 18 142164 0.8633 0.806011 13 to 17 142022 0.3819 0.648744 12 to 16 142216 1.0396 0.850728 11 to 15 142303 1.3345 0.908976 10 to 14 142008 0.3345 0.630989 9 to 13 141923 0.0463 0.518480 8 to 12 141789 -0.4079 0.341674 7 to 11 141409 -1.6960 0.044940 6 to 10 141713 -0.6655 0.252857 5 to 9 142135 0.7650 0.777859 4 to 8 142042 0.4497 0.673547 3 to 7 141878 -0.1062 0.457711 2 to 6 141853 -0.1909 0.424283 1 to 5 142074 0.5582 0.711647 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-14_00:31 Bits used No. missing words z-score p-value 31 to 32 142032 0.3619 0.641271 30 to 31 141326 -1.7207 0.042649 29 to 30 141825 -0.2488 0.401773 28 to 29 142062 0.4504 0.673772 27 to 28 142078 0.4976 0.690600 26 to 27 141943 0.0993 0.539559 25 to 26 141795 -0.3373 0.367962 24 to 25 141865 -0.1308 0.447980 23 to 24 141874 -0.1042 0.458498 22 to 23 141763 -0.4317 0.332997 21 to 22 142017 0.3176 0.624610 20 to 21 142214 0.8987 0.815602 19 to 20 141762 -0.4346 0.331926 18 to 19 142104 0.5742 0.717100 17 to 18 141797 -0.3314 0.370187 16 to 17 142008 0.2911 0.614498 15 to 16 141770 -0.4110 0.340535 14 to 15 142162 0.7453 0.771967 13 to 14 142194 0.8397 0.799471 12 to 13 142004 0.2793 0.609978 11 to 12 141967 0.1701 0.567541 10 to 11 141829 -0.2370 0.406343 9 to 10 142223 0.9253 0.822590 8 to 9 142381 1.3914 0.917941 7 to 8 141993 0.2468 0.597474 6 to 7 142551 1.8928 0.970810 5 to 6 142369 1.3560 0.912444 4 to 5 142194 0.8397 0.799471 3 to 4 142247 0.9961 0.840394 2 to 3 141506 -1.1898 0.117070 1 to 2 141759 -0.4435 0.328720 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-14_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2507.85 0.111 0.544173 Test results for specific bytes for dh-ranFile-2015-07-14_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2427.91 -1.019 0.153996 2 to 9 2502.56 0.036 0.514432 3 to 10 2570.39 0.995 0.840237 4 to 11 2433.02 -0.947 0.171771 5 to 12 2530.56 0.432 0.667218 6 to 13 2609.85 1.553 0.939848 7 to 14 2536.09 0.510 0.695116 8 to 15 2456.56 -0.614 0.269497 9 to 16 2489.96 -0.142 0.443565 10 to 17 2349.22 -2.132 0.016487 11 to 18 2444.78 -0.781 0.217416 12 to 19 2428.22 -1.015 0.155040 13 to 20 2558.91 0.833 0.797616 14 to 21 2547.48 0.671 0.749043 15 to 22 2564.83 0.917 0.820369 16 to 23 2665.35 2.338 0.990316 17 to 24 2456.82 -0.611 0.270718 18 to 25 2560.27 0.852 0.802973 19 to 26 2570.95 1.003 0.842154 20 to 27 2445.28 -0.774 0.219497 21 to 28 2468.58 -0.444 0.328379 22 to 29 2503.50 0.050 0.519756 23 to 30 2488.91 -0.157 0.437704 24 to 31 2520.45 0.289 0.613795 25 to 32 2443.50 -0.799 0.212132 CDPARK for dh-ranFile-2015-07-14_00:31: 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 3504 -0.8676 0.192812 3555 1.4612 0.928018 3513 -0.4566 0.323972 3517 -0.2740 0.392053 3505 -0.8219 0.205562 3535 0.5479 0.708135 3517 -0.2740 0.392053 3547 1.0959 0.863437 3519 -0.1826 0.427537 3496 -1.2329 0.108811 Square side=100, avg. no. parked=3520.80 sample std.=18.16 p-value of the KSTEST for those 10 p-values: 0.765906 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-14_00:31 0.6725,0.1440,0.5795,0.5734,0.2874,0.5212,0.5588,0.9352,0.5693,0.1630, The KS test for those 10 p-values: 0.589377 The 3DSPHERES test for dh-ranFile-2015-07-14_00:31 sample no r^3 equiv. uni. 1 10.698 0.299944 2 10.396 0.292856 3 5.058 0.155148 4 15.003 0.393538 5 41.316 0.747715 6 43.846 0.768119 7 87.710 0.946263 8 15.064 0.394764 9 65.929 0.888935 10 20.560 0.496070 11 21.888 0.517905 12 34.867 0.687211 13 135.813 0.989188 14 38.130 0.719453 15 50.918 0.816815 16 89.118 0.948727 17 102.292 0.966950 18 85.107 0.941392 19 7.703 0.226447 20 18.247 0.455694 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.046818 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-14_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -1.6 0.3 -0.1 -2.2 0.3 -1.1 0.4 0.6 0.5 -1.1 -2.4 -0.4 1.0 1.5 -0.2 0.9 -1.2 -0.1 0.8 0.5 0.0 -0.6 0.2 -0.6 0.9 -0.5 -1.6 -0.4 1.0 0.2 0.5 0.7 1.1 0.3 -0.1 1.0 -0.7 1.7 1.0 0.9 1.0 -1.1 Chi-square with 42 degrees of freedom:40.913777 z-score=-0.118517, p-value=0.481426 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-14_00:31 Test no p-value 1 0.030383 2 0.987225 3 0.322147 4 0.357535 5 0.082701 6 0.190126 7 0.996469 8 0.012528 9 0.134111 10 0.322193 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.020146 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-14_00:31: (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 66823 0.37 66819 0.35 3 25000.00 25000 0.00 24750 2.50 4 6666.67 6495 4.42 6732 0.64 5 1388.89 1411 0.35 1435 1.53 6 238.10 229 0.35 221 1.23 7 34.72 37 0.15 37 0.15 8 4.96 4 0.19 5 0.00 p=0.55659 p=0.61974 Number of rngs required: 688305, p-value: 0.455 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-14_00:31 No. of wins: Observed Expected 98653 98585.9 z-score= 0.300, pvalue=0.61802 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66845 66666.7 0.477 0.477 2 37573 37654.3 0.176 0.653 3 27010 26954.7 0.113 0.766 4 19169 19313.5 1.081 1.847 5 13731 13851.4 1.047 2.893 6 10130 9943.5 3.496 6.390 7 7201 7145.0 0.439 6.828 8 5127 5139.1 0.028 6.857 9 3666 3699.9 0.310 7.167 10 2694 2666.3 0.288 7.454 11 1874 1923.3 1.265 8.720 12 1398 1388.7 0.062 8.781 13 933 1003.7 4.982 13.763 14 736 726.1 0.134 13.897 15 526 525.8 0.000 13.897 16 364 381.2 0.772 14.669 17 285 276.5 0.259 14.928 18 213 200.8 0.737 15.665 19 153 146.0 0.337 16.003 20 100 106.2 0.364 16.366 21 272 287.1 0.796 17.162 Chisq= 17.16 for 20 degrees of freedom, p= 0.35757 SUMMARY of craptest p-value for no. of wins: 0.618024 p-value for throws/game: 0.357565 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-14_00:31 No. of wins: Observed Expected 98206 98585.9 z-score=-1.699, pvalue=0.04466 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66386 66666.7 1.182 1.182 2 37750 37654.3 0.243 1.425 3 26940 26954.7 0.008 1.433 4 19283 19313.5 0.048 1.481 5 13782 13851.4 0.348 1.829 6 9933 9943.5 0.011 1.840 7 7197 7145.0 0.378 2.218 8 5171 5139.1 0.198 2.416 9 3732 3699.9 0.279 2.695 10 2728 2666.3 1.428 4.123 11 1982 1923.3 1.790 5.913 12 1396 1388.7 0.038 5.951 13 997 1003.7 0.045 5.996 14 810 726.1 9.685 15.681 15 511 525.8 0.419 16.099 16 441 381.2 9.398 25.497 17 251 276.5 2.359 27.856 18 202 200.8 0.007 27.862 19 135 146.0 0.827 28.689 20 99 106.2 0.490 29.179 21 274 287.1 0.599 29.778 Chisq= 29.78 for 20 degrees of freedom, p= 0.92647 SUMMARY of craptest p-value for no. of wins: 0.044664 p-value for throws/game: 0.926469 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0006,0.0006,0.0113,0.0125,0.0165,0.0201,0.0201,0.0304,0.0306,0.0381, 0.0416,0.0418,0.0418,0.0426,0.0438,0.0447,0.0449,0.0461,0.0468,0.0673, 0.0679,0.0822,0.0827,0.1006,0.1013,0.1067,0.1088,0.1147,0.1171,0.1341, 0.1347,0.1349,0.1381,0.1440,0.1444,0.1498,0.1540,0.1550,0.1551,0.1613, 0.1630,0.1718,0.1801,0.1845,0.1884,0.1896,0.1901,0.1928,0.2056,0.2121, 0.2133,0.2174,0.2195,0.2199,0.2216,0.2235,0.2264,0.2369,0.2529,0.2532, 0.2695,0.2707,0.2790,0.2874,0.2911,0.2929,0.2999,0.3091,0.3221,0.3222, 0.3224,0.3240,0.3284,0.3287,0.3318,0.3319,0.3330,0.3405,0.3417,0.3419, 0.3480,0.3496,0.3534,0.3575,0.3576,0.3680,0.3702,0.3921,0.3921,0.3926, 0.3935,0.3948,0.4018,0.4063,0.4189,0.4206,0.4243,0.4275,0.4326,0.4377, 0.4436,0.4474,0.4480,0.4504,0.4551,0.4557,0.4577,0.4585,0.4665,0.4679, 0.4685,0.4745,0.4786,0.4814,0.4913,0.4955,0.4961,0.4988,0.5053,0.5085, 0.5139,0.5144,0.5179,0.5185,0.5198,0.5212,0.5328,0.5372,0.5396,0.5421, 0.5441,0.5442,0.5523,0.5554,0.5558,0.5566,0.5588,0.5675,0.5684,0.5693, 0.5694,0.5734,0.5795,0.5815,0.5894,0.5975,0.6002,0.6100,0.6138,0.6145, 0.6162,0.6170,0.6173,0.6180,0.6197,0.6197,0.6224,0.6246,0.6267,0.6282, 0.6297,0.6310,0.6413,0.6454,0.6486,0.6487,0.6608,0.6672,0.6706,0.6725, 0.6735,0.6738,0.6872,0.6892,0.6906,0.6927,0.6951,0.7000,0.7018,0.7066, 0.7081,0.7116,0.7126,0.7137,0.7171,0.7195,0.7216,0.7312,0.7410,0.7477, 0.7490,0.7656,0.7659,0.7681,0.7720,0.7779,0.7848,0.7924,0.7976,0.7995, 0.7995,0.8030,0.8060,0.8072,0.8156,0.8168,0.8204,0.8226,0.8249,0.8262, 0.8310,0.8327,0.8402,0.8404,0.8417,0.8422,0.8426,0.8435,0.8440,0.8507, 0.8531,0.8549,0.8634,0.8645,0.8723,0.8824,0.8840,0.8889,0.8945,0.8962, 0.9033,0.9082,0.9083,0.9088,0.9090,0.9099,0.9113,0.9124,0.9160,0.9179, 0.9242,0.9261,0.9265,0.9280,0.9346,0.9352,0.9398,0.9414,0.9419,0.9463, 0.9487,0.9612,0.9670,0.9708,0.9770,0.9773,0.9837,0.9840,0.9872,0.9872, 0.9874,0.9886,0.9892,0.9900,0.9903,0.9965,0.9971,0.9993,0.9995, Overall p-value after applying KStest on 269 p-values = 0.030795 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.