RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-05_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.05 13.4898 0.297170 2 to 25 16.05 18.2023 0.623812 3 to 26 15.85 12.6678 0.241873 4 to 27 15.67 22.4110 0.830574 5 to 28 15.46 27.8278 0.953009 6 to 29 15.91 13.4779 0.296350 7 to 30 15.64 11.5045 0.170833 8 to 31 15.98 19.6953 0.709891 9 to 32 16.01 20.7098 0.760458 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.853539 Tough bday spacings test for dh-ranFile-2015-06-05_12:31: 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 8 44 67 97 87 82 59 37 11 3 5 (O-E)^2/E 0.1 1.5 0.5 0.0 1.2 0.2 0.9 1.8 1.0 2.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.402, p= 0.506 RESULTS OF GCD FOR dh-ranFile-2015-06-05_12:31 Euclid's algorithm: p-value, steps to gcd: 0.540028 p-value, dist. of gcd's: 0.989328 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-05_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.892 0.365 0.344 0.699 0.024 0.803 0.897 0.407 Bits 8 to 15---> 0.882 0.800 0.350 0.695 0.656 0.828 0.994 0.852 Bits 16 to 23---> 0.071 0.108 0.315 0.378 0.935 0.564 0.159 0.205 Bits 24 to 31---> 0.426 0.898 0.225 0.254 0.024 0.146 0.655 0.775 KS test for the above 32 p values: 0.220 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-05_12:31, p-values for 5 runs: 0.7621, 0.2580, 0.3931, 0.5578, 0.6417 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-05_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 239 211.4 3.598 3.598 r= 29 5127 5134.0 0.010 3.608 r= 30 23050 23103.0 0.122 3.730 r= 31 11584 11551.5 0.091 3.821 chi-square = 3.821 with df = 3; p-value = 0.719 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-05_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 5218 5134.0 1.374 1.376 r= 31 23030 23103.0 0.231 1.607 r= 32 11540 11551.5 0.011 1.618 chi-square = 1.618 with df = 3; p-value = 0.345 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-05_12:31 b-rank test for bits 1 to 8, p=0.08411 b-rank test for bits 2 to 9, p=0.23338 b-rank test for bits 3 to 10, p=0.02683 b-rank test for bits 4 to 11, p=0.30111 b-rank test for bits 5 to 12, p=0.02366 b-rank test for bits 6 to 13, p=0.54703 b-rank test for bits 7 to 14, p=0.21443 b-rank test for bits 8 to 15, p=0.86412 b-rank test for bits 9 to 16, p=0.96045 b-rank test for bits 10 to 17, p=0.72581 b-rank test for bits 11 to 18, p=0.65676 b-rank test for bits 12 to 19, p=0.66578 b-rank test for bits 13 to 20, p=0.67222 b-rank test for bits 14 to 21, p=0.65564 b-rank test for bits 15 to 22, p=0.23089 b-rank test for bits 16 to 23, p=0.41027 b-rank test for bits 17 to 24, p=0.52872 b-rank test for bits 18 to 25, p=0.43290 b-rank test for bits 19 to 26, p=0.02982 b-rank test for bits 20 to 27, p=0.29012 b-rank test for bits 21 to 28, p=0.98479 b-rank test for bits 22 to 29, p=0.32790 b-rank test for bits 23 to 30, p=0.76856 b-rank test for bits 24 to 31, p=0.16752 b-rank test for bits 25 to 32, p=0.97913 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 = 0.712913 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-05_12:31 (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 142195 0.67 0.747759 2 141826 -0.19 0.422815 3 141263 -1.51 0.065507 4 142339 1.00 0.842287 5 141946 0.09 0.534139 6 141213 -1.63 0.051875 7 141719 -0.44 0.328270 8 141734 -0.41 0.341032 9 141815 -0.22 0.412781 10 142261 0.82 0.794364 11 142418 1.19 0.882678 12 142162 0.59 0.722522 13 141237 -1.57 0.058107 14 142053 0.34 0.631443 15 141773 -0.32 0.375042 16 141718 -0.45 0.327426 17 141171 -1.73 0.042257 18 141719 -0.44 0.328270 19 141347 -1.31 0.094447 20 140666 -2.90 0.001836 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-05_12:31 Bits used No. missing words z-score p-value 23 to 32 141943 0.1161 0.546215 22 to 31 141740 -0.5839 0.279645 21 to 30 141878 -0.1080 0.456984 20 to 29 141936 0.0920 0.536637 19 to 28 141944 0.1196 0.547581 18 to 27 141666 -0.8391 0.200715 17 to 26 142190 0.9678 0.833435 16 to 25 142213 1.0471 0.852482 15 to 24 142119 0.7230 0.765160 14 to 23 142018 0.3747 0.646067 13 to 22 141592 -1.0942 0.136925 12 to 21 141774 -0.4667 0.320373 11 to 20 141962 0.1816 0.572060 10 to 19 141761 -0.5115 0.304507 9 to 18 142170 0.8989 0.815637 8 to 17 141714 -0.6736 0.250298 7 to 16 141812 -0.3356 0.368579 6 to 15 142387 1.6471 0.950235 5 to 14 141929 0.0678 0.527039 4 to 13 142030 0.4161 0.661333 3 to 12 142206 1.0230 0.846846 2 to 11 142000 0.3127 0.622729 1 to 10 142249 1.1713 0.879256 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-05_12:31 Bits used No. missing words z-score p-value 28 to 32 141802 -0.3638 0.357992 27 to 31 141945 0.1209 0.548121 26 to 30 141726 -0.6215 0.267149 25 to 29 141905 -0.0147 0.494145 24 to 28 141895 -0.0486 0.480629 23 to 27 141832 -0.2621 0.396609 22 to 26 141540 -1.2520 0.105291 21 to 25 142298 1.3175 0.906169 20 to 24 141563 -1.1740 0.120198 19 to 23 141484 -1.4418 0.074680 18 to 22 141915 0.0192 0.507667 17 to 21 141993 0.2836 0.611652 16 to 20 141920 0.0362 0.514426 15 to 19 142035 0.4260 0.664946 14 to 18 142191 0.9548 0.830164 13 to 17 141211 -2.3672 0.008961 12 to 16 141781 -0.4350 0.331775 11 to 15 142065 0.5277 0.701145 10 to 14 141825 -0.2859 0.387491 9 to 13 141711 -0.6723 0.250695 8 to 12 142145 0.7989 0.787820 7 to 11 141853 -0.1909 0.424283 6 to 10 141612 -1.0079 0.156752 5 to 9 141817 -0.3130 0.377147 4 to 8 141980 0.2396 0.594664 3 to 7 141779 -0.4418 0.329318 2 to 6 141915 0.0192 0.507667 1 to 5 142129 0.7446 0.771757 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-05_12:31 Bits used No. missing words z-score p-value 31 to 32 142068 0.4681 0.680127 30 to 31 141951 0.1229 0.548915 29 to 30 141840 -0.2045 0.418976 28 to 29 141842 -0.1986 0.421283 27 to 28 141947 0.1111 0.544240 26 to 27 141982 0.2144 0.584869 25 to 26 141646 -0.7768 0.218643 24 to 25 141870 -0.1160 0.453819 23 to 24 141503 -1.1986 0.115339 22 to 23 141974 0.1908 0.575646 21 to 22 141854 -0.1632 0.435174 20 to 21 141880 -0.0865 0.465527 19 to 20 142092 0.5388 0.705005 18 to 19 141712 -0.5821 0.280252 17 to 18 141668 -0.7119 0.238267 16 to 17 142390 1.4179 0.921891 15 to 16 142123 0.6303 0.735749 14 to 15 142137 0.6716 0.749079 13 to 14 141483 -1.2576 0.104266 12 to 13 141600 -0.9125 0.180759 11 to 12 142751 2.4828 0.993482 10 to 11 141695 -0.6322 0.263614 9 to 10 141798 -0.3284 0.371302 8 to 9 141580 -0.9715 0.165656 7 to 8 141299 -1.8004 0.035900 6 to 7 142165 0.7542 0.774632 5 to 6 141581 -0.9685 0.166391 4 to 5 142040 0.3855 0.650051 3 to 4 142120 0.6214 0.732847 2 to 3 142087 0.5241 0.699896 1 to 2 142169 0.7660 0.778158 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-05_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2404.46 -1.351 0.088334 Test results for specific bytes for dh-ranFile-2015-06-05_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2657.02 2.221 0.986812 2 to 9 2477.66 -0.316 0.376037 3 to 10 2474.00 -0.368 0.356537 4 to 11 2522.95 0.325 0.627244 5 to 12 2632.06 1.868 0.969091 6 to 13 2369.54 -1.845 0.032521 7 to 14 2559.38 0.840 0.799476 8 to 15 2569.09 0.977 0.835729 9 to 16 2496.69 -0.047 0.481355 10 to 17 2585.94 1.215 0.887883 11 to 18 2591.99 1.301 0.903360 12 to 19 2498.30 -0.024 0.490385 13 to 20 2681.72 2.570 0.994913 14 to 21 2465.35 -0.490 0.312035 15 to 22 2526.39 0.373 0.645480 16 to 23 2557.41 0.812 0.791562 17 to 24 2499.67 -0.005 0.498159 18 to 25 2583.29 1.178 0.880568 19 to 26 2396.37 -1.466 0.071381 20 to 27 2364.08 -1.922 0.027287 21 to 28 2418.40 -1.154 0.124254 22 to 29 2421.64 -1.108 0.133884 23 to 30 2497.52 -0.035 0.486014 24 to 31 2448.66 -0.726 0.233903 25 to 32 2402.30 -1.382 0.083542 CDPARK for dh-ranFile-2015-06-05_12:31: 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 3538 0.6849 0.753306 3525 0.0913 0.536383 3509 -0.6393 0.261324 3537 0.6393 0.738676 3516 -0.3196 0.374623 3536 0.5936 0.723613 3530 0.3196 0.625377 3506 -0.7763 0.218799 3500 -1.0502 0.146807 3558 1.5982 0.944998 Square side=100, avg. no. parked=3525.50 sample std.=16.94 p-value of the KSTEST for those 10 p-values: 0.902491 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-05_12:31 0.4355,0.2685,0.9240,0.6716,0.0497,0.0278,0.4910,0.1203,0.4024,0.6230, The KS test for those 10 p-values: 0.477138 The 3DSPHERES test for dh-ranFile-2015-06-05_12:31 sample no r^3 equiv. uni. 1 23.226 0.538923 2 13.293 0.357964 3 12.827 0.347917 4 71.939 0.909097 5 9.298 0.266508 6 6.170 0.185901 7 81.704 0.934354 8 13.060 0.352942 9 3.986 0.124431 10 34.742 0.685908 11 52.110 0.823950 12 6.736 0.201120 13 62.608 0.875934 14 48.408 0.800827 15 28.921 0.618648 16 66.453 0.890857 17 4.275 0.132825 18 67.462 0.894468 19 61.323 0.870503 20 5.050 0.154927 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.383965 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-05_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.9 0.8 -0.8 -1.5 -1.9 -0.7 -0.7 -0.9 -1.0 -0.1 -1.4 0.9 -0.0 1.3 1.0 0.7 -1.3 -1.2 2.4 -0.5 -0.1 -0.7 0.2 0.2 0.3 0.1 0.0 -0.6 1.5 1.7 -1.4 0.4 -1.5 -1.2 -1.0 0.7 -1.0 0.5 -0.1 0.9 -1.0 -0.1 Chi-square with 42 degrees of freedom:43.069458 z-score=0.116687, p-value=0.574711 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-05_12:31 Test no p-value 1 0.524227 2 0.007356 3 0.993801 4 0.125827 5 0.114278 6 0.405310 7 0.619836 8 0.517236 9 0.032492 10 0.091504 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.055249 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-05_12:31: (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 66479 0.53 66905 0.85 3 25000.00 25085 0.29 24858 0.81 4 6666.67 6754 1.14 6562 1.64 5 1388.89 1400 0.09 1402 0.12 6 238.10 246 0.26 223 0.96 7 34.72 32 0.21 43 1.97 8 4.96 3 0.77 6 0.22 p=0.22967 p=0.63810 Number of rngs required: 688324, p-value: 0.464 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-05_12:31 No. of wins: Observed Expected 98313 98585.9 z-score=-1.220, pvalue=0.11116 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66665 66666.7 0.000 0.000 2 37481 37654.3 0.798 0.798 3 27054 26954.7 0.366 1.163 4 19114 19313.5 2.060 3.223 5 13825 13851.4 0.050 3.274 6 10114 9943.5 2.922 6.196 7 7147 7145.0 0.001 6.196 8 5247 5139.1 2.267 8.463 9 3760 3699.9 0.977 9.440 10 2630 2666.3 0.494 9.935 11 1928 1923.3 0.011 9.946 12 1404 1388.7 0.168 10.114 13 997 1003.7 0.045 10.158 14 716 726.1 0.142 10.300 15 521 525.8 0.044 10.345 16 379 381.2 0.012 10.357 17 302 276.5 2.344 12.701 18 195 200.8 0.169 12.870 19 143 146.0 0.061 12.931 20 93 106.2 1.644 14.575 21 285 287.1 0.016 14.591 Chisq= 14.59 for 20 degrees of freedom, p= 0.20068 SUMMARY of craptest p-value for no. of wins: 0.111160 p-value for throws/game: 0.200679 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-05_12:31 No. of wins: Observed Expected 98595 98585.9 z-score= 0.041, pvalue=0.51631 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66602 66666.7 0.063 0.063 2 37656 37654.3 0.000 0.063 3 26856 26954.7 0.362 0.424 4 19474 19313.5 1.334 1.759 5 13789 13851.4 0.281 2.040 6 9951 9943.5 0.006 2.046 7 7147 7145.0 0.001 2.046 8 5123 5139.1 0.050 2.097 9 3724 3699.9 0.157 2.254 10 2678 2666.3 0.051 2.305 11 1915 1923.3 0.036 2.341 12 1402 1388.7 0.127 2.468 13 1003 1003.7 0.001 2.469 14 717 726.1 0.115 2.584 15 523 525.8 0.015 2.599 16 386 381.2 0.062 2.661 17 304 276.5 2.727 5.387 18 205 200.8 0.087 5.474 19 165 146.0 2.477 7.951 20 103 106.2 0.097 8.048 21 277 287.1 0.356 8.405 Chisq= 8.40 for 20 degrees of freedom, p= 0.01117 SUMMARY of craptest p-value for no. of wins: 0.516307 p-value for throws/game: 0.011166 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0018,0.0074,0.0090,0.0112,0.0237,0.0241,0.0241,0.0268,0.0273,0.0278, 0.0298,0.0325,0.0325,0.0359,0.0423,0.0497,0.0519,0.0552,0.0581,0.0655, 0.0705,0.0714,0.0747,0.0835,0.0841,0.0883,0.0915,0.0944,0.1043,0.1053, 0.1076,0.1112,0.1143,0.1153,0.1202,0.1203,0.1243,0.1244,0.1258,0.1328, 0.1339,0.1369,0.1456,0.1468,0.1549,0.1568,0.1591,0.1657,0.1664,0.1675, 0.1708,0.1808,0.1859,0.2007,0.2007,0.2011,0.2047,0.2144,0.2186,0.2188, 0.2199,0.2251,0.2297,0.2309,0.2334,0.2339,0.2383,0.2419,0.2503,0.2507, 0.2540,0.2580,0.2613,0.2636,0.2665,0.2671,0.2685,0.2796,0.2803,0.2901, 0.2963,0.2972,0.3011,0.3045,0.3120,0.3152,0.3204,0.3274,0.3279,0.3283, 0.3283,0.3293,0.3318,0.3410,0.3439,0.3447,0.3479,0.3503,0.3529,0.3565, 0.3580,0.3580,0.3653,0.3686,0.3713,0.3746,0.3750,0.3760,0.3771,0.3779, 0.3840,0.3875,0.3931,0.3966,0.4024,0.4053,0.4074,0.4103,0.4128,0.4190, 0.4213,0.4228,0.4243,0.4257,0.4329,0.4352,0.4355,0.4538,0.4570,0.4638, 0.4655,0.4771,0.4806,0.4814,0.4860,0.4904,0.4910,0.4941,0.4982,0.5056, 0.5077,0.5077,0.5144,0.5163,0.5172,0.5242,0.5270,0.5287,0.5341,0.5364, 0.5366,0.5389,0.5400,0.5442,0.5462,0.5470,0.5476,0.5481,0.5489,0.5578, 0.5635,0.5721,0.5747,0.5756,0.5849,0.5947,0.6117,0.6186,0.6198,0.6227, 0.6230,0.6238,0.6254,0.6272,0.6314,0.6381,0.6417,0.6455,0.6461,0.6501, 0.6547,0.6556,0.6563,0.6568,0.6613,0.6649,0.6658,0.6716,0.6722,0.6801, 0.6859,0.6952,0.6990,0.6999,0.7011,0.7050,0.7099,0.7129,0.7186,0.7225, 0.7236,0.7258,0.7328,0.7357,0.7387,0.7478,0.7491,0.7533,0.7605,0.7621, 0.7652,0.7686,0.7718,0.7746,0.7752,0.7782,0.7878,0.7916,0.7944,0.7995, 0.8002,0.8008,0.8028,0.8156,0.8240,0.8276,0.8302,0.8306,0.8334,0.8357, 0.8423,0.8468,0.8521,0.8525,0.8535,0.8641,0.8705,0.8759,0.8793,0.8806, 0.8820,0.8827,0.8879,0.8909,0.8919,0.8945,0.8965,0.8981,0.9025,0.9034, 0.9062,0.9091,0.9219,0.9240,0.9344,0.9346,0.9450,0.9502,0.9530,0.9604, 0.9691,0.9791,0.9848,0.9868,0.9893,0.9935,0.9938,0.9938,0.9949, Overall p-value after applying KStest on 269 p-values = 0.773759 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.