RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-27_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.63 21.7189 0.804229 2 to 25 15.72 20.4217 0.746771 3 to 26 15.93 13.3027 0.284302 4 to 27 15.68 16.9505 0.542274 5 to 28 15.70 16.0447 0.479328 6 to 29 15.92 5.0094 0.002256 7 to 30 15.77 19.1778 0.681575 8 to 31 15.98 8.6705 0.049965 9 to 32 15.87 18.2618 0.627491 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.499364 Tough bday spacings test for dh-ranFile-2015-11-27_16:31: 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 9 39 75 85 102 78 58 29 13 9 3 (O-E)^2/E 0.0 0.2 0.0 1.6 0.2 0.0 0.7 0.0 0.2 0.9 0.3 Birthday Spacings: Sum(O-E)^2/E= 4.101, p= 0.057 RESULTS OF GCD FOR dh-ranFile-2015-11-27_16:31 Euclid's algorithm: p-value, steps to gcd: 0.791955 p-value, dist. of gcd's: 0.629529 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-27_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.067 0.746 0.749 0.732 0.977 0.519 0.841 0.552 Bits 8 to 15---> 0.163 0.559 0.203 0.858 0.924 0.363 0.852 0.349 Bits 16 to 23---> 0.163 0.063 0.606 0.264 0.656 0.780 0.487 0.913 Bits 24 to 31---> 0.963 0.138 0.617 0.500 0.758 0.643 0.237 0.430 KS test for the above 32 p values: 0.418 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-27_16:31, p-values for 5 runs: 0.5970, 0.6988, 0.0379, 0.3764, 0.2736 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-27_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 204 211.4 0.260 0.260 r= 29 5093 5134.0 0.328 0.588 r= 30 23135 23103.0 0.044 0.632 r= 31 11568 11551.5 0.024 0.656 chi-square = 0.656 with df = 3; p-value = 0.116 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-27_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 223 211.4 0.634 0.634 r= 30 5161 5134.0 0.142 0.776 r= 31 23165 23103.0 0.166 0.943 r= 32 11451 11551.5 0.875 1.817 chi-square = 1.817 with df = 3; p-value = 0.389 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-27_16:31 b-rank test for bits 1 to 8, p=0.28641 b-rank test for bits 2 to 9, p=0.83987 b-rank test for bits 3 to 10, p=0.75301 b-rank test for bits 4 to 11, p=0.42520 b-rank test for bits 5 to 12, p=0.22655 b-rank test for bits 6 to 13, p=0.10981 b-rank test for bits 7 to 14, p=0.42636 b-rank test for bits 8 to 15, p=0.25568 b-rank test for bits 9 to 16, p=0.67072 b-rank test for bits 10 to 17, p=0.96136 b-rank test for bits 11 to 18, p=0.92328 b-rank test for bits 12 to 19, p=0.89196 b-rank test for bits 13 to 20, p=0.05575 b-rank test for bits 14 to 21, p=0.98678 b-rank test for bits 15 to 22, p=0.90356 b-rank test for bits 16 to 23, p=0.59993 b-rank test for bits 17 to 24, p=0.64483 b-rank test for bits 18 to 25, p=0.51687 b-rank test for bits 19 to 26, p=0.06324 b-rank test for bits 20 to 27, p=0.55034 b-rank test for bits 21 to 28, p=0.79562 b-rank test for bits 22 to 29, p=0.20962 b-rank test for bits 23 to 30, p=0.95305 b-rank test for bits 24 to 31, p=0.65685 b-rank test for bits 25 to 32, p=0.51337 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 = 0.398810 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-27_16:31 (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 142023 0.27 0.604720 2 141363 -1.28 0.100894 3 141260 -1.52 0.064617 4 141920 0.02 0.509945 5 142592 1.60 0.944647 6 143026 2.61 0.995460 7 141551 -0.84 0.201235 8 141548 -0.84 0.199271 9 141871 -0.09 0.464320 10 142873 2.25 0.987825 11 142705 1.86 0.968489 12 142169 0.61 0.727977 13 141806 -0.24 0.404613 14 142125 0.50 0.692835 15 142631 1.69 0.954116 16 142304 0.92 0.821769 17 141911 0.00 0.501557 18 142051 0.33 0.629680 19 141936 0.06 0.524843 20 142459 1.28 0.900477 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-27_16:31 Bits used No. missing words z-score p-value 23 to 32 142253 1.1851 0.882005 22 to 31 142247 1.1644 0.877865 21 to 30 141538 -1.2804 0.100194 20 to 29 141574 -1.1563 0.123777 19 to 28 142157 0.8540 0.803457 18 to 27 141714 -0.6736 0.250298 17 to 26 141871 -0.1322 0.447424 16 to 25 141793 -0.4011 0.344159 15 to 24 142029 0.4127 0.660070 14 to 23 141755 -0.5322 0.297303 13 to 22 141827 -0.2839 0.388245 12 to 21 141975 0.2264 0.589574 11 to 20 141423 -1.6770 0.046771 10 to 19 141977 0.2333 0.592253 9 to 18 141898 -0.0391 0.484418 8 to 17 141704 -0.7080 0.239462 7 to 16 142293 1.3230 0.907082 6 to 15 142268 1.2368 0.891918 5 to 14 141994 0.2920 0.614844 4 to 13 141902 -0.0253 0.489918 3 to 12 141623 -0.9873 0.161737 2 to 11 141993 0.2885 0.613525 1 to 10 142322 1.4230 0.922632 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-27_16:31 Bits used No. missing words z-score p-value 28 to 32 142275 1.2396 0.892431 27 to 31 141651 -0.8757 0.190598 26 to 30 141825 -0.2859 0.387491 25 to 29 141886 -0.0791 0.468483 24 to 28 142111 0.6836 0.752895 23 to 27 141807 -0.3469 0.364340 22 to 26 141556 -1.1977 0.115511 21 to 25 141757 -0.5164 0.302797 20 to 24 141990 0.2735 0.607749 19 to 23 142373 1.5718 0.941997 18 to 22 142153 0.8260 0.795598 17 to 21 142286 1.2768 0.899172 16 to 20 142382 1.6023 0.945452 15 to 19 141417 -1.6689 0.047567 14 to 18 141961 0.1752 0.569520 13 to 17 141752 -0.5333 0.296905 12 to 16 142326 1.4124 0.921090 11 to 15 142002 0.3141 0.623291 10 to 14 141972 0.2124 0.584118 9 to 13 142006 0.3277 0.628429 8 to 12 141678 -0.7842 0.216470 7 to 11 141862 -0.1604 0.436267 6 to 10 141725 -0.6248 0.266036 5 to 9 141778 -0.4452 0.328093 4 to 8 141804 -0.3571 0.360527 3 to 7 142066 0.5311 0.702320 2 to 6 142006 0.3277 0.628429 1 to 5 142000 0.3074 0.620714 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-27_16:31 Bits used No. missing words z-score p-value 31 to 32 141724 -0.5467 0.292294 30 to 31 141882 -0.0806 0.467872 29 to 30 141974 0.1908 0.575646 28 to 29 141647 -0.7738 0.219514 27 to 28 141781 -0.3786 0.352509 26 to 27 141821 -0.2606 0.397216 25 to 26 141881 -0.0836 0.466699 24 to 25 141479 -1.2694 0.102147 23 to 24 141248 -1.9508 0.025539 22 to 23 141762 -0.4346 0.331926 21 to 22 141907 -0.0069 0.497258 20 to 21 141903 -0.0187 0.492551 19 to 20 141815 -0.2783 0.390407 18 to 19 141554 -1.0482 0.147280 17 to 18 141607 -0.8918 0.186242 16 to 17 141769 -0.4140 0.339454 15 to 16 141342 -1.6735 0.047111 14 to 15 141330 -1.7089 0.043731 13 to 14 142191 0.8309 0.796981 12 to 13 141691 -0.6440 0.259774 11 to 12 141939 0.0875 0.534872 10 to 11 142686 2.2911 0.989020 9 to 10 141745 -0.4847 0.313927 8 to 9 142223 0.9253 0.822590 7 to 8 141445 -1.3697 0.085390 6 to 7 141837 -0.2134 0.415522 5 to 6 141679 -0.6794 0.248430 4 to 5 141647 -0.7738 0.219514 3 to 4 142297 1.1436 0.873599 2 to 3 141890 -0.0570 0.477264 1 to 2 141994 0.2498 0.598615 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-27_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2531.11 0.440 0.670003 Test results for specific bytes for dh-ranFile-2015-11-27_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2500.26 0.004 0.501446 2 to 9 2471.80 -0.399 0.345036 3 to 10 2472.97 -0.382 0.351146 4 to 11 2524.19 0.342 0.633857 5 to 12 2375.90 -1.755 0.039627 6 to 13 2504.48 0.063 0.525243 7 to 14 2421.71 -1.107 0.134117 8 to 15 2473.06 -0.381 0.351617 9 to 16 2418.16 -1.157 0.123566 10 to 17 2598.96 1.399 0.919168 11 to 18 2394.12 -1.497 0.067150 12 to 19 2496.02 -0.056 0.477570 13 to 20 2502.57 0.036 0.514489 14 to 21 2422.65 -1.094 0.137010 15 to 22 2651.34 2.140 0.983833 16 to 23 2477.76 -0.315 0.376570 17 to 24 2470.44 -0.418 0.337983 18 to 25 2445.12 -0.776 0.218841 19 to 26 2462.50 -0.530 0.297928 20 to 27 2389.29 -1.566 0.058709 21 to 28 2465.18 -0.492 0.311229 22 to 29 2472.08 -0.395 0.346486 23 to 30 2507.34 0.104 0.541332 24 to 31 2433.03 -0.947 0.171808 25 to 32 2558.50 0.827 0.795986 CDPARK for dh-ranFile-2015-11-27_16:31: 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 3524 0.0457 0.518210 3521 -0.0913 0.463617 3533 0.4566 0.676028 3520 -0.1370 0.445521 3546 1.0502 0.853193 3511 -0.5479 0.291865 3553 1.3699 0.914635 3524 0.0457 0.518210 3503 -0.9132 0.180558 3509 -0.6393 0.261324 Square side=100, avg. no. parked=3524.40 sample std.=15.05 p-value of the KSTEST for those 10 p-values: 0.779451 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-27_16:31 0.9073,0.2073,0.8824,0.5691,0.8324,0.0738,0.2521,0.8442,0.5085,0.2657, The KS test for those 10 p-values: 0.803225 The 3DSPHERES test for dh-ranFile-2015-11-27_16:31 sample no r^3 equiv. uni. 1 32.119 0.657209 2 6.205 0.186844 3 130.581 0.987128 4 15.976 0.412889 5 38.235 0.720433 6 44.467 0.772868 7 28.463 0.612783 8 52.084 0.823797 9 43.103 0.762306 10 34.746 0.685946 11 6.764 0.201848 12 9.172 0.263410 13 11.990 0.329455 14 39.590 0.732771 15 0.945 0.031007 16 67.691 0.895270 17 30.740 0.641079 18 62.510 0.875528 19 126.532 0.985268 20 33.071 0.667919 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.108091 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-27_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.1 0.6 -2.3 -0.7 1.1 0.7 1.8 2.3 -1.4 -0.3 1.4 2.0 0.4 -0.7 -0.1 -0.3 -0.2 -0.5 -0.2 -1.3 -0.5 -1.4 0.0 0.9 -0.6 -0.1 0.1 -0.8 1.6 -0.6 0.8 -1.7 1.2 3.3 -0.5 1.9 1.1 0.1 2.6 -0.6 1.0 -1.1 Chi-square with 42 degrees of freedom:66.475260 z-score=2.670470, p-value=0.990565 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-27_16:31 Test no p-value 1 0.990010 2 0.063107 3 0.872921 4 0.041098 5 0.063437 6 0.490763 7 0.921581 8 0.206125 9 0.319677 10 0.129655 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.131847 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-27_16:31: (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 66674 0.00 66745 0.09 3 25000.00 25074 0.22 24859 0.80 4 6666.67 6597 0.73 6666 0.00 5 1388.89 1369 0.28 1449 2.60 6 238.10 254 1.06 246 0.26 7 34.72 29 0.94 28 1.30 8 4.96 2 1.77 6 0.22 p=0.45670 p=0.49032 Number of rngs required: 687484, p-value: 0.143 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-27_16:31 No. of wins: Observed Expected 98728 98585.9 z-score= 0.636, pvalue=0.73753 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66845 66666.7 0.477 0.477 2 37575 37654.3 0.167 0.644 3 26902 26954.7 0.103 0.747 4 19249 19313.5 0.215 0.962 5 13833 13851.4 0.024 0.987 6 9944 9943.5 0.000 0.987 7 7218 7145.0 0.745 1.732 8 5102 5139.1 0.267 2.000 9 3658 3699.9 0.474 2.473 10 2655 2666.3 0.048 2.521 11 1929 1923.3 0.017 2.538 12 1371 1388.7 0.227 2.765 13 1011 1003.7 0.053 2.818 14 730 726.1 0.021 2.838 15 568 525.8 3.381 6.219 16 408 381.2 1.891 8.110 17 274 276.5 0.023 8.134 18 211 200.8 0.515 8.649 19 137 146.0 0.553 9.202 20 120 106.2 1.789 10.991 21 260 287.1 2.561 13.551 Chisq= 13.55 for 20 degrees of freedom, p= 0.14749 SUMMARY of craptest p-value for no. of wins: 0.737527 p-value for throws/game: 0.147493 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-27_16:31 No. of wins: Observed Expected 98189 98585.9 z-score=-1.775, pvalue=0.03795 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66512 66666.7 0.359 0.359 2 37577 37654.3 0.159 0.518 3 26915 26954.7 0.059 0.576 4 19173 19313.5 1.022 1.598 5 13975 13851.4 1.103 2.700 6 10046 9943.5 1.056 3.756 7 7090 7145.0 0.424 4.180 8 5278 5139.1 3.756 7.935 9 3761 3699.9 1.010 8.946 10 2725 2666.3 1.292 10.238 11 1891 1923.3 0.543 10.781 12 1419 1388.7 0.659 11.441 13 1000 1003.7 0.014 11.455 14 715 726.1 0.171 11.625 15 519 525.8 0.089 11.714 16 356 381.2 1.660 13.374 17 276 276.5 0.001 13.375 18 207 200.8 0.190 13.565 19 158 146.0 0.989 14.554 20 119 106.2 1.539 16.092 21 288 287.1 0.003 16.095 Chisq= 16.10 for 20 degrees of freedom, p= 0.28930 SUMMARY of craptest p-value for no. of wins: 0.037950 p-value for throws/game: 0.289295 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0023,0.0255,0.0310,0.0379,0.0380,0.0396,0.0411,0.0437,0.0468,0.0471, 0.0476,0.0500,0.0557,0.0573,0.0587,0.0631,0.0632,0.0632,0.0634,0.0646, 0.0669,0.0671,0.0738,0.0854,0.1002,0.1009,0.1021,0.1081,0.1098,0.1155, 0.1164,0.1236,0.1238,0.1297,0.1318,0.1341,0.1370,0.1381,0.1433,0.1473, 0.1475,0.1617,0.1627,0.1627,0.1718,0.1806,0.1862,0.1868,0.1906,0.1993, 0.2012,0.2018,0.2027,0.2061,0.2073,0.2096,0.2165,0.2188,0.2195,0.2195, 0.2265,0.2366,0.2395,0.2484,0.2503,0.2521,0.2557,0.2598,0.2613,0.2634, 0.2641,0.2657,0.2660,0.2736,0.2843,0.2864,0.2893,0.2919,0.2923,0.2969, 0.2973,0.2979,0.3028,0.3112,0.3139,0.3197,0.3281,0.3295,0.3319,0.3380, 0.3395,0.3442,0.3450,0.3465,0.3488,0.3511,0.3516,0.3525,0.3605,0.3629, 0.3643,0.3764,0.3766,0.3875,0.3882,0.3888,0.3904,0.3972,0.3988,0.4046, 0.4129,0.4155,0.4183,0.4252,0.4264,0.4302,0.4363,0.4455,0.4474,0.4567, 0.4636,0.4643,0.4667,0.4679,0.4685,0.4773,0.4776,0.4793,0.4844,0.4869, 0.4899,0.4903,0.4908,0.4926,0.4973,0.4994,0.4996,0.5014,0.5016,0.5085, 0.5099,0.5134,0.5145,0.5169,0.5182,0.5182,0.5192,0.5248,0.5252,0.5349, 0.5413,0.5423,0.5503,0.5519,0.5594,0.5691,0.5695,0.5756,0.5841,0.5896, 0.5923,0.5970,0.5986,0.5999,0.6047,0.6062,0.6077,0.6128,0.6135,0.6148, 0.6169,0.6207,0.6233,0.6275,0.6284,0.6284,0.6295,0.6297,0.6339,0.6411, 0.6427,0.6448,0.6562,0.6569,0.6572,0.6601,0.6679,0.6700,0.6707,0.6760, 0.6816,0.6859,0.6928,0.6988,0.7023,0.7204,0.7280,0.7319,0.7328,0.7375, 0.7463,0.7468,0.7487,0.7529,0.7530,0.7580,0.7623,0.7729,0.7795,0.7805, 0.7920,0.7956,0.7956,0.7960,0.7970,0.8032,0.8035,0.8042,0.8218,0.8226, 0.8238,0.8324,0.8399,0.8413,0.8442,0.8517,0.8532,0.8584,0.8729,0.8736, 0.8755,0.8779,0.8820,0.8824,0.8919,0.8920,0.8924,0.8953,0.8992,0.9005, 0.9036,0.9071,0.9073,0.9132,0.9146,0.9192,0.9211,0.9216,0.9226,0.9233, 0.9244,0.9420,0.9446,0.9455,0.9530,0.9541,0.9614,0.9627,0.9685,0.9770, 0.9838,0.9853,0.9868,0.9871,0.9878,0.9890,0.9900,0.9906,0.9955, Overall p-value after applying KStest on 269 p-values = 0.885538 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.