RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-14_06:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.88 16.1387 0.485977 2 to 25 16.13 16.5844 0.517152 3 to 26 16.01 16.6296 0.520280 4 to 27 15.90 9.7802 0.087428 5 to 28 15.74 22.0425 0.816908 6 to 29 15.95 13.0211 0.265225 7 to 30 15.95 21.9728 0.814233 8 to 31 15.53 22.3470 0.828260 9 to 32 15.91 17.6613 0.589499 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.669457 Tough bday spacings test for dh-ranFile-2015-10-14_06:31: 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 7 32 75 113 95 73 51 22 21 9 2 (O-E)^2/E 0.5 0.6 0.0 2.4 0.1 0.3 0.0 2.0 2.5 0.9 1.0 Birthday Spacings: Sum(O-E)^2/E= 10.422, p= 0.596 RESULTS OF GCD FOR dh-ranFile-2015-10-14_06:31 Euclid's algorithm: p-value, steps to gcd: 0.928051 p-value, dist. of gcd's: 0.668296 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-14_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.922 0.443 0.092 0.327 0.340 0.329 0.064 0.454 Bits 8 to 15---> 0.739 0.225 0.500 0.797 0.187 0.224 0.637 0.619 Bits 16 to 23---> 0.703 0.561 0.535 0.923 0.592 0.164 0.178 0.679 Bits 24 to 31---> 0.861 0.749 0.848 0.884 0.672 0.530 0.854 0.729 KS test for the above 32 p values: 0.495 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-14_06:31, p-values for 5 runs: 0.6382, 0.9332, 0.5641, 0.1239, 0.4490 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-14_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 214 211.4 0.032 0.032 r= 29 5264 5134.0 3.291 3.323 r= 30 22976 23103.0 0.699 4.021 r= 31 11546 11551.5 0.003 4.024 chi-square = 4.024 with df = 3; p-value = 0.741 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-14_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5182 5134.0 0.449 1.178 r= 31 22887 23103.0 2.020 3.198 r= 32 11732 11551.5 2.820 6.018 chi-square = 6.018 with df = 3; p-value = 0.889 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-14_06:31 b-rank test for bits 1 to 8, p=0.46293 b-rank test for bits 2 to 9, p=0.17173 b-rank test for bits 3 to 10, p=0.33723 b-rank test for bits 4 to 11, p=0.05599 b-rank test for bits 5 to 12, p=0.15743 b-rank test for bits 6 to 13, p=0.50762 b-rank test for bits 7 to 14, p=0.26170 b-rank test for bits 8 to 15, p=0.07217 b-rank test for bits 9 to 16, p=0.13796 b-rank test for bits 10 to 17, p=0.32363 b-rank test for bits 11 to 18, p=0.57032 b-rank test for bits 12 to 19, p=0.52735 b-rank test for bits 13 to 20, p=0.07372 b-rank test for bits 14 to 21, p=0.06209 b-rank test for bits 15 to 22, p=0.30659 b-rank test for bits 16 to 23, p=0.65369 b-rank test for bits 17 to 24, p=0.18212 b-rank test for bits 18 to 25, p=0.91996 b-rank test for bits 19 to 26, p=0.13328 b-rank test for bits 20 to 27, p=0.03134 b-rank test for bits 21 to 28, p=0.02996 b-rank test for bits 22 to 29, p=0.43631 b-rank test for bits 23 to 30, p=0.18454 b-rank test for bits 24 to 31, p=0.07839 b-rank test for bits 25 to 32, p=0.39456 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 = 0.000207 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-14_06:31 (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 141640 -0.63 0.264584 2 141290 -1.45 0.073944 3 142398 1.14 0.873222 4 141806 -0.24 0.404613 5 140889 -2.38 0.008564 6 142550 1.50 0.932789 7 142540 1.47 0.929696 8 142300 0.91 0.819321 9 141817 -0.22 0.414601 10 141781 -0.30 0.382151 11 141396 -1.20 0.115192 12 142306 0.93 0.822985 13 141718 -0.45 0.327426 14 142057 0.35 0.634962 15 142445 1.25 0.894636 16 142232 0.75 0.774546 17 141552 -0.83 0.201892 18 141997 0.20 0.581150 19 141549 -0.84 0.199924 20 141908 -0.00 0.498760 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-14_06:31 Bits used No. missing words z-score p-value 23 to 32 142021 0.3851 0.649907 22 to 31 141937 0.0954 0.538007 21 to 30 141607 -1.0425 0.148586 20 to 29 141696 -0.7356 0.230981 19 to 28 141759 -0.5184 0.302097 18 to 27 142133 0.7713 0.779728 17 to 26 141956 0.1609 0.563926 16 to 25 142197 0.9920 0.839393 15 to 24 141416 -1.7011 0.044459 14 to 23 141921 0.0402 0.516050 13 to 22 141558 -1.2115 0.112855 12 to 21 141940 0.1058 0.542113 11 to 20 142260 1.2092 0.886708 10 to 19 142185 0.9506 0.829093 9 to 18 141392 -1.7839 0.037220 8 to 17 142416 1.7471 0.959693 7 to 16 142180 0.9333 0.824679 6 to 15 141512 -1.3701 0.085327 5 to 14 141922 0.0437 0.517424 4 to 13 141935 0.0885 0.535267 3 to 12 142101 0.6609 0.745672 2 to 11 141906 -0.0115 0.495419 1 to 10 142317 1.4058 0.920102 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-14_06:31 Bits used No. missing words z-score p-value 28 to 32 142207 1.0091 0.843525 27 to 31 142129 0.7446 0.771757 26 to 30 141588 -1.0893 0.138021 25 to 29 141335 -1.9469 0.025774 24 to 28 141980 0.2396 0.594664 23 to 27 141879 -0.1028 0.459056 22 to 26 142029 0.4057 0.657504 21 to 25 141536 -1.2655 0.102842 20 to 24 141972 0.2124 0.584118 19 to 23 141375 -1.8113 0.035048 18 to 22 141543 -1.2418 0.107156 17 to 21 141585 -1.0994 0.135792 16 to 20 141857 -0.1774 0.429601 15 to 19 141759 -0.5096 0.305168 14 to 18 142337 1.4497 0.926433 13 to 17 141385 -1.7774 0.037752 12 to 16 142056 0.4972 0.690471 11 to 15 141889 -0.0689 0.472529 10 to 14 141402 -1.7198 0.042738 9 to 13 142215 1.0362 0.849938 8 to 12 141485 -1.4384 0.075159 7 to 11 141684 -0.7638 0.222484 6 to 10 142029 0.4057 0.657504 5 to 9 142031 0.4124 0.659992 4 to 8 141837 -0.2452 0.403156 3 to 7 141718 -0.6486 0.258306 2 to 6 141918 0.0294 0.511723 1 to 5 142219 1.0497 0.853079 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-14_06:31 Bits used No. missing words z-score p-value 31 to 32 141830 -0.2340 0.407488 30 to 31 141711 -0.5850 0.279259 29 to 30 142004 0.2793 0.609978 28 to 29 141621 -0.8505 0.197515 27 to 28 141510 -1.1780 0.119405 26 to 27 141525 -1.1337 0.128457 25 to 26 141898 -0.0334 0.486669 24 to 25 141575 -0.9862 0.162012 23 to 24 141528 -1.1249 0.130323 22 to 23 142060 0.4445 0.671643 21 to 22 142125 0.6362 0.737675 20 to 21 142593 2.0167 0.978138 19 to 20 142419 1.5035 0.933639 18 to 19 142531 1.8338 0.966661 17 to 18 141608 -0.8889 0.187034 16 to 17 141815 -0.2783 0.390407 15 to 16 142044 0.3973 0.654411 14 to 15 142601 2.0403 0.979341 13 to 14 141603 -0.9036 0.183096 12 to 13 141842 -0.1986 0.421283 11 to 12 141568 -1.0069 0.156998 10 to 11 142097 0.5536 0.710073 9 to 10 142231 0.9489 0.828659 8 to 9 142001 0.2704 0.606579 7 to 8 141691 -0.6440 0.259774 6 to 7 142259 1.0315 0.848841 5 to 6 141847 -0.1839 0.427060 4 to 5 142032 0.3619 0.641271 3 to 4 142406 1.4651 0.928554 2 to 3 141775 -0.3963 0.345959 1 to 2 141564 -1.0187 0.154179 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-14_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2549.18 0.696 0.756653 Test results for specific bytes for dh-ranFile-2015-10-14_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2518.76 0.265 0.604625 2 to 9 2520.43 0.289 0.613666 3 to 10 2475.46 -0.347 0.364266 4 to 11 2517.59 0.249 0.598212 5 to 12 2427.07 -1.031 0.151168 6 to 13 2467.64 -0.458 0.323628 7 to 14 2403.17 -1.369 0.085448 8 to 15 2472.44 -0.390 0.348360 9 to 16 2421.14 -1.115 0.132382 10 to 17 2568.15 0.964 0.832426 11 to 18 2580.43 1.137 0.872327 12 to 19 2326.71 -2.451 0.007130 13 to 20 2519.20 0.271 0.606991 14 to 21 2412.49 -1.238 0.107945 15 to 22 2523.67 0.335 0.631075 16 to 23 2420.44 -1.125 0.130265 17 to 24 2418.85 -1.148 0.125547 18 to 25 2483.15 -0.238 0.405833 19 to 26 2594.48 1.336 0.909247 20 to 27 2448.07 -0.734 0.231350 21 to 28 2492.79 -0.102 0.459365 22 to 29 2445.27 -0.774 0.219450 23 to 30 2429.32 -1.000 0.158766 24 to 31 2478.43 -0.305 0.380146 25 to 32 2589.93 1.272 0.898273 CDPARK for dh-ranFile-2015-10-14_06:31: 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 3550 1.2329 0.891189 3499 -1.0959 0.136563 3492 -1.4155 0.078457 3533 0.4566 0.676028 3481 -1.9178 0.027568 3525 0.0913 0.536383 3521 -0.0913 0.463617 3528 0.2283 0.590298 3519 -0.1826 0.427537 Square side=100, avg. no. parked=3515.20 sample std.=19.83 p-value of the KSTEST for those 10 p-values: 0.499527 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-14_06:31 0.6211,0.7796,0.2632,0.5104,0.6642,0.3252,0.9159,0.2607,0.1330,0.8274, The KS test for those 10 p-values: 0.945335 The 3DSPHERES test for dh-ranFile-2015-10-14_06:31 sample no r^3 equiv. uni. 1 8.190 0.238895 2 20.671 0.497931 3 12.010 0.329904 4 26.778 0.590407 5 19.995 0.486494 6 12.633 0.343666 7 2.297 0.073715 8 67.349 0.894067 9 16.322 0.419617 10 13.544 0.363299 11 105.528 0.970330 12 16.639 0.425713 13 5.523 0.168148 14 25.661 0.574876 15 17.629 0.444363 16 21.171 0.506239 17 5.809 0.176049 18 48.246 0.799754 19 7.554 0.222595 20 80.000 0.930517 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.539659 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-14_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 0.8 -1.7 1.4 -0.3 -1.3 0.8 0.3 0.1 0.4 0.5 0.4 -0.1 -0.1 -1.1 1.2 0.5 -1.0 0.4 -1.0 -0.1 1.6 -0.8 -0.3 -1.2 1.0 -0.9 1.6 -0.8 -0.4 0.4 -0.5 0.8 0.3 -0.7 -1.2 1.5 0.5 -0.1 0.9 0.0 -1.1 Chi-square with 42 degrees of freedom:31.422292 z-score=-1.154123, p-value=0.116266 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-14_06:31 Test no p-value 1 0.214235 2 0.045839 3 0.033800 4 0.011600 5 0.090544 6 0.601632 7 0.065085 8 0.913456 9 0.095979 10 0.442667 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001999 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-14_06:31: (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 66973 1.41 66760 0.13 3 25000.00 24787 1.81 25040 0.06 4 6666.67 6569 1.43 6542 2.33 5 1388.89 1390 0.00 1373 0.18 6 238.10 253 0.93 238 0.00 7 34.72 24 3.31 44 2.48 8 4.96 3 0.77 2 1.77 p=0.86082 p=0.67494 Number of rngs required: 688289, p-value: 0.448 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-14_06:31 No. of wins: Observed Expected 98999 98585.9 z-score= 1.848, pvalue=0.96769 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67137 66666.7 3.318 3.318 2 37641 37654.3 0.005 3.323 3 26977 26954.7 0.018 3.341 4 19225 19313.5 0.405 3.746 5 13800 13851.4 0.191 3.937 6 9828 9943.5 1.343 5.280 7 6973 7145.0 4.142 9.422 8 5180 5139.1 0.326 9.748 9 3697 3699.9 0.002 9.750 10 2616 2666.3 0.949 10.699 11 1958 1923.3 0.625 11.324 12 1367 1388.7 0.340 11.664 13 991 1003.7 0.161 11.825 14 689 726.1 1.900 13.725 15 495 525.8 1.808 15.533 16 354 381.2 1.934 17.467 17 299 276.5 1.824 19.291 18 205 200.8 0.087 19.378 19 158 146.0 0.989 20.367 20 103 106.2 0.097 20.464 21 307 287.1 1.377 21.842 Chisq= 21.84 for 20 degrees of freedom, p= 0.65083 SUMMARY of craptest p-value for no. of wins: 0.967685 p-value for throws/game: 0.650830 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-14_06:31 No. of wins: Observed Expected 98571 98585.9 z-score=-0.066, pvalue=0.47351 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66917 66666.7 0.940 0.940 2 37581 37654.3 0.143 1.083 3 26752 26954.7 1.525 2.608 4 19447 19313.5 0.923 3.531 5 13880 13851.4 0.059 3.590 6 10031 9943.5 0.769 4.359 7 7124 7145.0 0.062 4.421 8 5087 5139.1 0.528 4.949 9 3674 3699.9 0.181 5.129 10 2604 2666.3 1.456 6.585 11 1914 1923.3 0.045 6.630 12 1346 1388.7 1.315 7.946 13 970 1003.7 1.132 9.078 14 729 726.1 0.011 9.089 15 542 525.8 0.497 9.586 16 384 381.2 0.021 9.608 17 284 276.5 0.201 9.809 18 186 200.8 1.095 10.904 19 147 146.0 0.007 10.911 20 110 106.2 0.135 11.046 21 291 287.1 0.053 11.098 Chisq= 11.10 for 20 degrees of freedom, p= 0.05637 SUMMARY of craptest p-value for no. of wins: 0.473507 p-value for throws/game: 0.056370 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0020,0.0071,0.0086,0.0116,0.0258,0.0276,0.0300,0.0313,0.0338, 0.0350,0.0372,0.0378,0.0427,0.0445,0.0458,0.0560,0.0564,0.0621,0.0635, 0.0651,0.0722,0.0737,0.0737,0.0739,0.0752,0.0784,0.0785,0.0853,0.0854, 0.0874,0.0905,0.0917,0.0960,0.1028,0.1072,0.1079,0.1129,0.1152,0.1163, 0.1194,0.1239,0.1255,0.1285,0.1303,0.1303,0.1324,0.1330,0.1333,0.1358, 0.1366,0.1380,0.1380,0.1486,0.1512,0.1542,0.1570,0.1574,0.1588,0.1620, 0.1645,0.1681,0.1717,0.1760,0.1783,0.1821,0.1831,0.1845,0.1869,0.1870, 0.1928,0.1975,0.1999,0.2019,0.2142,0.2195,0.2225,0.2226,0.2243,0.2250, 0.2310,0.2314,0.2389,0.2583,0.2598,0.2607,0.2617,0.2632,0.2646,0.2652, 0.2793,0.3021,0.3052,0.3066,0.3236,0.3236,0.3252,0.3274,0.3274,0.3287, 0.3299,0.3372,0.3403,0.3437,0.3460,0.3484,0.3633,0.3643,0.3801,0.3822, 0.3904,0.3946,0.4032,0.4046,0.4058,0.4075,0.4146,0.4196,0.4213,0.4257, 0.4271,0.4275,0.4296,0.4363,0.4426,0.4427,0.4444,0.4478,0.4490,0.4538, 0.4591,0.4594,0.4629,0.4636,0.4725,0.4735,0.4860,0.4865,0.4867,0.4953, 0.4954,0.4979,0.4988,0.4995,0.5002,0.5062,0.5076,0.5104,0.5117,0.5160, 0.5172,0.5174,0.5203,0.5274,0.5297,0.5351,0.5353,0.5364,0.5380,0.5397, 0.5421,0.5607,0.5639,0.5641,0.5703,0.5749,0.5812,0.5841,0.5895,0.5903, 0.5904,0.5915,0.5947,0.5957,0.5982,0.6016,0.6046,0.6066,0.6070,0.6100, 0.6137,0.6188,0.6211,0.6311,0.6350,0.6373,0.6382,0.6413,0.6499,0.6508, 0.6537,0.6544,0.6575,0.6575,0.6600,0.6642,0.6683,0.6695,0.6716,0.6716, 0.6749,0.6760,0.6788,0.6905,0.7025,0.7101,0.7287,0.7377,0.7386,0.7411, 0.7457,0.7487,0.7567,0.7718,0.7745,0.7796,0.7797,0.7971,0.7998,0.8142, 0.8169,0.8193,0.8230,0.8247,0.8274,0.8283,0.8287,0.8291,0.8324,0.8394, 0.8435,0.8479,0.8488,0.8499,0.8531,0.8541,0.8606,0.8608,0.8723,0.8732, 0.8838,0.8867,0.8893,0.8912,0.8941,0.8946,0.8983,0.9092,0.9135,0.9159, 0.9200,0.9201,0.9224,0.9233,0.9264,0.9281,0.9286,0.9297,0.9305,0.9328, 0.9332,0.9336,0.9453,0.9597,0.9667,0.9677,0.9703,0.9781,0.9793, Overall p-value after applying KStest on 269 p-values = 0.047665 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.