RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-06-09_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.85 22.5626 0.835961 2 to 25 15.68 15.9023 0.469231 3 to 26 15.89 16.2792 0.495863 4 to 27 15.83 16.6309 0.520371 5 to 28 16.14 11.5015 0.170663 6 to 29 15.99 22.4445 0.831775 7 to 30 15.65 18.3655 0.633859 8 to 31 15.63 19.2123 0.683518 9 to 32 15.82 17.4002 0.572411 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.347708 Tough bday spacings test for dh-ranFile-2016-06-09_02:31: 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 12 38 67 101 93 89 41 34 13 6 6 (O-E)^2/E 0.9 0.1 0.5 0.1 0.2 1.5 2.4 0.6 0.2 0.1 0.9 Birthday Spacings: Sum(O-E)^2/E= 7.494, p= 0.322 RESULTS OF GCD FOR dh-ranFile-2016-06-09_02:31 Euclid's algorithm: p-value, steps to gcd: 0.565729 p-value, dist. of gcd's: 0.716716 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-06-09_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.675 0.382 0.266 0.969 0.286 0.384 0.236 0.090 Bits 8 to 15---> 0.123 0.450 0.504 0.920 0.212 0.353 0.656 0.244 Bits 16 to 23---> 0.383 0.390 0.874 0.013 0.971 0.707 0.361 0.120 Bits 24 to 31---> 0.066 0.740 0.892 0.848 0.765 0.195 0.413 0.312 KS test for the above 32 p values: 0.404 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-06-09_02:31, p-values for 5 runs: 0.0509, 0.6905, 0.5527, 0.4168, 0.7421 Rank test for binary matrices (31x31) for dh-ranFile-2016-06-09_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 208 211.4 0.055 0.055 r= 29 4957 5134.0 6.103 6.158 r= 30 23391 23103.0 3.589 9.747 r= 31 11444 11551.5 1.001 10.748 chi-square = 10.748 with df = 3; p-value = 0.987 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-06-09_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5214 5134.0 1.246 1.307 r= 31 22953 23103.0 0.975 2.281 r= 32 11618 11551.5 0.383 2.664 chi-square = 2.664 with df = 3; p-value = 0.554 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-06-09_02:31 b-rank test for bits 1 to 8, p=0.62019 b-rank test for bits 2 to 9, p=0.88411 b-rank test for bits 3 to 10, p=0.81399 b-rank test for bits 4 to 11, p=0.05413 b-rank test for bits 5 to 12, p=0.32720 b-rank test for bits 6 to 13, p=0.72149 b-rank test for bits 7 to 14, p=0.92205 b-rank test for bits 8 to 15, p=0.94476 b-rank test for bits 9 to 16, p=0.56585 b-rank test for bits 10 to 17, p=0.22905 b-rank test for bits 11 to 18, p=0.00028 b-rank test for bits 12 to 19, p=0.49549 b-rank test for bits 13 to 20, p=0.70344 b-rank test for bits 14 to 21, p=0.96432 b-rank test for bits 15 to 22, p=0.26215 b-rank test for bits 16 to 23, p=0.43574 b-rank test for bits 17 to 24, p=0.27905 b-rank test for bits 18 to 25, p=0.39280 b-rank test for bits 19 to 26, p=0.85249 b-rank test for bits 20 to 27, p=0.22932 b-rank test for bits 21 to 28, p=0.09025 b-rank test for bits 22 to 29, p=0.06265 b-rank test for bits 23 to 30, p=0.20083 b-rank test for bits 24 to 31, p=0.28987 b-rank test for bits 25 to 32, p=0.02565 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 = 0.458768 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-06-09_02:31 (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 142256 0.81 0.791023 2 141910 0.00 0.500625 3 142157 0.58 0.718594 4 142061 0.35 0.638469 5 142082 0.40 0.656686 6 141973 0.15 0.559129 7 141377 -1.24 0.106794 8 142144 0.55 0.708255 9 141157 -1.76 0.039392 10 141106 -1.88 0.030263 11 142077 0.39 0.652379 12 142430 1.22 0.888106 13 142908 2.33 0.990185 14 142432 1.22 0.888993 15 142368 1.07 0.858063 16 142129 0.51 0.696111 17 142235 0.76 0.776645 18 141427 -1.13 0.129884 19 142150 0.56 0.713049 20 142778 2.03 0.978802 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-06-09_02:31 Bits used No. missing words z-score p-value 23 to 32 141925 0.0540 0.521546 22 to 31 141691 -0.7529 0.225766 21 to 30 142219 1.0678 0.857201 20 to 29 141847 -0.2149 0.414911 19 to 28 142235 1.1230 0.869281 18 to 27 141859 -0.1736 0.431109 17 to 26 142034 0.4299 0.666365 16 to 25 141842 -0.2322 0.408202 15 to 24 141631 -0.9598 0.168588 14 to 23 141928 0.0644 0.525666 13 to 22 141559 -1.2080 0.113517 12 to 21 141749 -0.5529 0.290179 11 to 20 141587 -1.1115 0.133180 10 to 19 141649 -0.8977 0.184676 9 to 18 141937 0.0954 0.538007 8 to 17 141864 -0.1563 0.437894 7 to 16 141644 -0.9149 0.180114 6 to 15 142406 1.7127 0.956612 5 to 14 142234 1.1196 0.868548 4 to 13 141939 0.1023 0.540745 3 to 12 141620 -0.9977 0.159215 2 to 11 141798 -0.3839 0.350528 1 to 10 142289 1.3092 0.904768 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-06-09_02:31 Bits used No. missing words z-score p-value 28 to 32 141938 0.0972 0.538711 27 to 31 141660 -0.8452 0.199003 26 to 30 142124 0.7277 0.766600 25 to 29 142002 0.3141 0.623291 24 to 28 141697 -0.7198 0.235836 23 to 27 141937 0.0938 0.537365 22 to 26 142066 0.5311 0.702320 21 to 25 142006 0.3277 0.628429 20 to 24 141645 -0.8960 0.185117 19 to 23 141938 0.0972 0.538711 18 to 22 142177 0.9074 0.817891 17 to 21 141863 -0.1571 0.437602 16 to 20 141789 -0.4079 0.341674 15 to 19 142010 0.3413 0.633544 14 to 18 142026 0.3955 0.653760 13 to 17 142040 0.4429 0.671099 12 to 16 141883 -0.0893 0.464440 11 to 15 142011 0.3446 0.634819 10 to 14 141116 -2.6893 0.003581 9 to 13 142323 1.4023 0.919583 8 to 12 141593 -1.0723 0.141792 7 to 11 141865 -0.1503 0.440275 6 to 10 141865 -0.1503 0.440275 5 to 9 142238 1.1141 0.867390 4 to 8 142373 1.5718 0.941997 3 to 7 141759 -0.5096 0.305168 2 to 6 141575 -1.1333 0.128540 1 to 5 141997 0.2972 0.616838 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-06-09_02:31 Bits used No. missing words z-score p-value 31 to 32 141892 -0.0511 0.479615 30 to 31 141725 -0.5437 0.293308 29 to 30 141483 -1.2576 0.104266 28 to 29 142014 0.3088 0.621248 27 to 28 141642 -0.7886 0.215178 26 to 27 142495 1.7276 0.957974 25 to 26 142717 2.3825 0.991402 24 to 25 142049 0.4120 0.659832 23 to 24 141798 -0.3284 0.371302 22 to 23 142149 0.7070 0.760214 21 to 22 141403 -1.4936 0.067640 20 to 21 141577 -0.9803 0.163463 19 to 20 141941 0.0934 0.537216 18 to 19 141633 -0.8151 0.207498 17 to 18 142277 1.0846 0.860944 16 to 17 141909 -0.0010 0.499612 15 to 16 141428 -1.4199 0.077825 14 to 15 141548 -1.0659 0.143241 13 to 14 141427 -1.4228 0.077397 12 to 13 142031 0.3589 0.640168 11 to 12 141899 -0.0305 0.487845 10 to 11 142173 0.7778 0.781653 9 to 10 142107 0.5831 0.720086 8 to 9 141816 -0.2753 0.391539 7 to 8 141642 -0.7886 0.215178 6 to 7 142279 1.0905 0.862247 5 to 6 141702 -0.6116 0.270404 4 to 5 141838 -0.2104 0.416673 3 to 4 141664 -0.7237 0.234629 2 to 3 142640 2.1554 0.984434 1 to 2 142389 1.4150 0.921459 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-06-09_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2424.02 -1.075 0.141288 Test results for specific bytes for dh-ranFile-2016-06-09_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2565.79 0.930 0.823910 2 to 9 2483.78 -0.229 0.409312 3 to 10 2455.18 -0.634 0.263082 4 to 11 2452.38 -0.673 0.250328 5 to 12 2571.98 1.018 0.845650 6 to 13 2540.64 0.575 0.717267 7 to 14 2553.32 0.754 0.774599 8 to 15 2671.40 2.424 0.992323 9 to 16 2381.66 -1.674 0.047111 10 to 17 2531.39 0.444 0.671450 11 to 18 2386.06 -1.611 0.053546 12 to 19 2538.19 0.540 0.705420 13 to 20 2551.22 0.724 0.765588 14 to 21 2519.09 0.270 0.606428 15 to 22 2538.25 0.541 0.705711 16 to 23 2471.57 -0.402 0.343837 17 to 24 2588.54 1.252 0.894743 18 to 25 2553.43 0.756 0.775076 19 to 26 2488.99 -0.156 0.438130 20 to 27 2517.73 0.251 0.599001 21 to 28 2500.70 0.010 0.503933 22 to 29 2485.94 -0.199 0.421210 23 to 30 2597.58 1.380 0.916198 24 to 31 2625.53 1.775 0.962074 25 to 32 2411.29 -1.255 0.104817 CDPARK for dh-ranFile-2016-06-09_02:31: 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 3517 -0.2740 0.392053 3503 -0.9132 0.180558 3517 -0.2740 0.392053 3502 -0.9589 0.168804 3511 -0.5479 0.291865 3526 0.1370 0.554479 3497 -1.1872 0.117571 3516 -0.3196 0.374623 3543 0.9132 0.819442 3522 -0.0457 0.481790 Square side=100, avg. no. parked=3515.40 sample std.=12.71 p-value of the KSTEST for those 10 p-values: 0.194766 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-06-09_02:31 0.1335,0.3829,0.7218,0.9211,0.4222,0.7291,0.7404,0.9363,0.7156,0.2544, The KS test for those 10 p-values: 0.445815 The 3DSPHERES test for dh-ranFile-2016-06-09_02:31 sample no r^3 equiv. uni. 1 3.378 0.106493 2 84.961 0.941107 3 20.536 0.495668 4 14.219 0.377466 5 96.138 0.959425 6 28.514 0.613444 7 8.449 0.245442 8 50.939 0.816947 9 26.168 0.581996 10 2.844 0.090430 11 18.217 0.455139 12 2.963 0.094043 13 37.503 0.713527 14 15.361 0.400719 15 7.005 0.208250 16 14.343 0.380034 17 26.342 0.584421 18 18.263 0.455986 19 8.931 0.257478 20 84.472 0.940139 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.866640 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-06-09_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 1.1 0.9 -1.1 1.6 1.3 -0.5 -0.5 0.5 -0.3 -0.1 0.7 0.7 0.5 1.0 -0.1 -1.0 -1.4 1.5 -0.5 0.3 -1.1 -0.4 -0.2 -1.1 0.6 0.5 -1.0 -0.1 0.2 0.2 -0.1 -0.5 1.7 -0.5 0.0 0.2 1.3 -0.7 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:27.363811 z-score=-1.596939, p-value=0.039419 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-06-09_02:31 Test no p-value 1 0.099715 2 0.618374 3 0.046636 4 0.429334 5 0.131909 6 0.244713 7 0.963507 8 0.095590 9 0.109538 10 0.665964 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.073542 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-06-09_02:31: (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 66861 0.57 66644 0.01 3 25000.00 24973 0.03 24960 0.06 4 6666.67 6542 2.33 6719 0.41 5 1388.89 1349 1.15 1394 0.02 6 238.10 240 0.02 245 0.20 7 34.72 30 0.64 34 0.01 8 4.96 4 0.19 3 0.77 p=0.44529 p=0.03991 Number of rngs required: 687269, p-value: 0.093 RESULTS OF CRAPS TEST for dh-ranFile-2016-06-09_02:31 No. of wins: Observed Expected 98312 98585.9 z-score=-1.225, pvalue=0.11031 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66540 66666.7 0.241 0.241 2 37558 37654.3 0.246 0.487 3 27214 26954.7 2.494 2.981 4 19280 19313.5 0.058 3.039 5 13884 13851.4 0.077 3.115 6 9934 9943.5 0.009 3.125 7 7163 7145.0 0.045 3.170 8 5101 5139.1 0.282 3.452 9 3776 3699.9 1.567 5.019 10 2619 2666.3 0.839 5.858 11 1887 1923.3 0.686 6.544 12 1383 1388.7 0.024 6.568 13 1058 1003.7 2.936 9.503 14 723 726.1 0.014 9.517 15 494 525.8 1.927 11.445 16 402 381.2 1.140 12.585 17 290 276.5 0.655 13.240 18 192 200.8 0.388 13.628 19 143 146.0 0.061 13.689 20 113 106.2 0.433 14.123 21 246 287.1 5.887 20.010 Chisq= 20.01 for 20 degrees of freedom, p= 0.54271 SUMMARY of craptest p-value for no. of wins: 0.110315 p-value for throws/game: 0.542710 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-06-09_02:31 No. of wins: Observed Expected 98870 98585.9 z-score= 1.271, pvalue=0.89811 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66819 66666.7 0.348 0.348 2 37578 37654.3 0.155 0.503 3 26891 26954.7 0.151 0.653 4 19301 19313.5 0.008 0.662 5 13805 13851.4 0.156 0.817 6 9912 9943.5 0.100 0.917 7 7235 7145.0 1.133 2.050 8 5072 5139.1 0.875 2.926 9 3764 3699.9 1.112 4.037 10 2661 2666.3 0.011 4.048 11 1927 1923.3 0.007 4.055 12 1413 1388.7 0.424 4.479 13 974 1003.7 0.880 5.358 14 751 726.1 0.851 6.209 15 576 525.8 4.786 10.995 16 351 381.2 2.385 13.380 17 272 276.5 0.075 13.455 18 192 200.8 0.388 13.843 19 133 146.0 1.155 14.998 20 108 106.2 0.030 15.028 21 265 287.1 1.703 16.731 Chisq= 16.73 for 20 degrees of freedom, p= 0.32963 SUMMARY of craptest p-value for no. of wins: 0.898108 p-value for throws/game: 0.329627 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0036,0.0132,0.0256,0.0303,0.0394,0.0394,0.0399,0.0466,0.0471, 0.0509,0.0535,0.0541,0.0626,0.0664,0.0676,0.0735,0.0774,0.0778,0.0901, 0.0902,0.0904,0.0933,0.0940,0.0956,0.0997,0.1043,0.1048,0.1065,0.1068, 0.1095,0.1103,0.1135,0.1176,0.1196,0.1234,0.1285,0.1299,0.1319,0.1332, 0.1335,0.1413,0.1418,0.1432,0.1592,0.1635,0.1686,0.1688,0.1707,0.1801, 0.1806,0.1847,0.1851,0.1948,0.1951,0.1990,0.2008,0.2075,0.2083,0.2122, 0.2152,0.2152,0.2258,0.2290,0.2293,0.2346,0.2358,0.2365,0.2439,0.2447, 0.2454,0.2503,0.2544,0.2575,0.2621,0.2631,0.2663,0.2704,0.2790,0.2857, 0.2899,0.2902,0.2919,0.2933,0.3052,0.3124,0.3219,0.3272,0.3296,0.3417, 0.3438,0.3477,0.3505,0.3529,0.3607,0.3713,0.3746,0.3775,0.3800,0.3823, 0.3828,0.3829,0.3843,0.3903,0.3915,0.3921,0.3921,0.3928,0.4007,0.4036, 0.4082,0.4093,0.4127,0.4149,0.4167,0.4168,0.4212,0.4222,0.4293,0.4311, 0.4357,0.4376,0.4379,0.4381,0.4403,0.4403,0.4453,0.4458,0.4500,0.4551, 0.4560,0.4588,0.4644,0.4692,0.4796,0.4818,0.4878,0.4955,0.4957,0.4959, 0.4996,0.5006,0.5039,0.5039,0.5204,0.5215,0.5257,0.5372,0.5374,0.5380, 0.5387,0.5387,0.5407,0.5427,0.5527,0.5536,0.5545,0.5591,0.5657,0.5659, 0.5724,0.5820,0.5844,0.5990,0.6064,0.6134,0.6168,0.6184,0.6202,0.6212, 0.6233,0.6284,0.6335,0.6339,0.6348,0.6385,0.6402,0.6524,0.6538,0.6565, 0.6567,0.6598,0.6660,0.6664,0.6711,0.6714,0.6747,0.6835,0.6905,0.6961, 0.7023,0.7034,0.7054,0.7057,0.7073,0.7083,0.7130,0.7135,0.7156,0.7167, 0.7173,0.7186,0.7201,0.7215,0.7218,0.7291,0.7402,0.7404,0.7421,0.7602, 0.7655,0.7656,0.7666,0.7746,0.7751,0.7766,0.7817,0.7910,0.8140,0.8169, 0.8179,0.8194,0.8239,0.8318,0.8360,0.8457,0.8478,0.8525,0.8572,0.8581, 0.8609,0.8622,0.8666,0.8674,0.8685,0.8693,0.8740,0.8841,0.8881,0.8890, 0.8919,0.8947,0.8981,0.9048,0.9162,0.9196,0.9199,0.9211,0.9215,0.9221, 0.9363,0.9401,0.9411,0.9420,0.9448,0.9566,0.9580,0.9594,0.9621,0.9635, 0.9643,0.9694,0.9710,0.9788,0.9844,0.9868,0.9902,0.9914,0.9923, Overall p-value after applying KStest on 269 p-values = 0.890943 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.