RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-20_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.96 10.2629 0.107775 2 to 25 15.84 24.3523 0.889826 3 to 26 15.89 9.5878 0.079999 4 to 27 15.82 21.9366 0.812832 5 to 28 15.85 12.0111 0.200535 6 to 29 15.93 26.4714 0.933710 7 to 30 15.80 23.8637 0.876813 8 to 31 15.71 16.7447 0.528209 9 to 32 15.73 25.9752 0.925087 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.178207 Tough bday spacings test for dh-ranFile-2016-01-20_20:31: 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 32 59 103 102 93 49 21 20 8 4 (O-E)^2/E 0.0 0.6 2.8 0.3 0.2 2.8 0.2 2.6 1.8 0.3 0.0 Birthday Spacings: Sum(O-E)^2/E= 11.484, p= 0.679 RESULTS OF GCD FOR dh-ranFile-2016-01-20_20:31 Euclid's algorithm: p-value, steps to gcd: 0.335509 p-value, dist. of gcd's: 0.803749 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-20_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.202 0.281 0.584 0.362 0.603 0.133 0.014 0.123 Bits 8 to 15---> 0.646 0.546 0.380 0.841 0.567 0.412 0.707 0.577 Bits 16 to 23---> 0.556 0.435 0.481 0.235 0.206 0.381 0.708 0.180 Bits 24 to 31---> 0.089 0.860 0.753 0.169 0.855 0.342 0.960 0.433 KS test for the above 32 p values: 0.527 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-20_20:31, p-values for 5 runs: 0.4164, 0.8648, 0.7668, 0.6159, 0.8884 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-20_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 228 211.4 1.301 1.301 r= 29 5155 5134.0 0.086 1.386 r= 30 23163 23103.0 0.156 1.542 r= 31 11454 11551.5 0.823 2.365 chi-square = 2.365 with df = 3; p-value = 0.500 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-20_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 218 211.4 0.205 0.205 r= 30 5172 5134.0 0.281 0.486 r= 31 23087 23103.0 0.011 0.497 r= 32 11523 11551.5 0.070 0.568 chi-square = 0.568 with df = 3; p-value = 0.096 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-20_20:31 b-rank test for bits 1 to 8, p=0.30069 b-rank test for bits 2 to 9, p=0.47421 b-rank test for bits 3 to 10, p=0.44909 b-rank test for bits 4 to 11, p=0.29707 b-rank test for bits 5 to 12, p=0.46398 b-rank test for bits 6 to 13, p=0.46885 b-rank test for bits 7 to 14, p=0.41307 b-rank test for bits 8 to 15, p=0.58999 b-rank test for bits 9 to 16, p=0.44967 b-rank test for bits 10 to 17, p=0.26836 b-rank test for bits 11 to 18, p=0.94164 b-rank test for bits 12 to 19, p=0.05705 b-rank test for bits 13 to 20, p=0.23950 b-rank test for bits 14 to 21, p=0.78215 b-rank test for bits 15 to 22, p=0.52499 b-rank test for bits 16 to 23, p=0.84149 b-rank test for bits 17 to 24, p=0.39678 b-rank test for bits 18 to 25, p=0.93064 b-rank test for bits 19 to 26, p=0.09129 b-rank test for bits 20 to 27, p=0.02823 b-rank test for bits 21 to 28, p=0.94838 b-rank test for bits 22 to 29, p=0.77458 b-rank test for bits 23 to 30, p=0.88773 b-rank test for bits 24 to 31, p=0.01975 b-rank test for bits 25 to 32, p=0.64934 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 = 0.872258 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-20_20:31 (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 142180 0.63 0.736439 2 142195 0.67 0.747759 3 141937 0.06 0.525774 4 142396 1.14 0.872247 5 142346 1.02 0.846197 6 141600 -0.72 0.234922 7 141488 -0.98 0.162456 8 142288 0.88 0.811852 9 142035 0.29 0.615476 10 141213 -1.63 0.051875 11 141860 -0.12 0.454121 12 141242 -1.56 0.059477 13 141694 -0.50 0.307444 14 141890 -0.05 0.481989 15 141567 -0.80 0.211903 16 142044 0.31 0.623486 17 141827 -0.19 0.423730 18 141963 0.13 0.549895 19 141386 -1.22 0.110715 20 142580 1.57 0.941441 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-20_20:31 Bits used No. missing words z-score p-value 23 to 32 141930 0.0713 0.528411 22 to 31 141556 -1.2184 0.111540 21 to 30 141574 -1.1563 0.123777 20 to 29 142212 1.0437 0.851686 19 to 28 141687 -0.7667 0.221643 18 to 27 141840 -0.2391 0.405526 17 to 26 141763 -0.5046 0.306925 16 to 25 141976 0.2299 0.590914 15 to 24 141886 -0.0804 0.467940 14 to 23 142128 0.7540 0.774586 13 to 22 141441 -1.6149 0.053163 12 to 21 141756 -0.5287 0.298498 11 to 20 142046 0.4713 0.681278 10 to 19 141779 -0.4494 0.326567 9 to 18 142057 0.5092 0.694696 8 to 17 141991 0.2816 0.610883 7 to 16 141321 -2.0287 0.021243 6 to 15 141845 -0.2218 0.412224 5 to 14 141899 -0.0356 0.485792 4 to 13 142161 0.8678 0.807256 3 to 12 141915 0.0196 0.507800 2 to 11 141809 -0.3460 0.364684 1 to 10 141951 0.1437 0.557127 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-20_20:31 Bits used No. missing words z-score p-value 28 to 32 141960 0.1718 0.568188 27 to 31 141632 -0.9401 0.173583 26 to 30 141752 -0.5333 0.296905 25 to 29 141575 -1.1333 0.128540 24 to 28 141541 -1.2486 0.105910 23 to 27 141146 -2.5876 0.004833 22 to 26 142482 1.9413 0.973886 21 to 25 141496 -1.4011 0.080589 20 to 24 141807 -0.3469 0.364340 19 to 23 141929 0.0667 0.526581 18 to 22 141705 -0.6926 0.244267 17 to 21 142358 1.5209 0.935859 16 to 20 141758 -0.5130 0.303982 15 to 19 141640 -0.9130 0.180626 14 to 18 141770 -0.4723 0.318355 13 to 17 142253 1.1650 0.877987 12 to 16 141736 -0.5876 0.278414 11 to 15 141856 -0.1808 0.428270 10 to 14 141695 -0.7265 0.233753 9 to 13 142145 0.7989 0.787820 8 to 12 141632 -0.9401 0.173583 7 to 11 141591 -1.0791 0.140275 6 to 10 141815 -0.3198 0.374574 5 to 9 142286 1.2768 0.899172 4 to 8 141950 0.1379 0.554826 3 to 7 141260 -2.2011 0.013864 2 to 6 141876 -0.1130 0.455022 1 to 5 141579 -1.1198 0.131407 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-20_20:31 Bits used No. missing words z-score p-value 31 to 32 141572 -0.9951 0.159850 30 to 31 142205 0.8722 0.808446 29 to 30 141560 -1.0305 0.151394 28 to 29 142267 1.0551 0.854304 27 to 28 141363 -1.6116 0.053525 26 to 27 141176 -2.1632 0.015262 25 to 26 142782 2.5742 0.994977 24 to 25 141542 -1.0836 0.139278 23 to 24 141795 -0.3373 0.367962 22 to 23 142447 1.5860 0.943636 21 to 22 141861 -0.1426 0.443316 20 to 21 141913 0.0108 0.504319 19 to 20 141926 0.0492 0.519610 18 to 19 142174 0.7807 0.782522 17 to 18 141943 0.0993 0.539559 16 to 17 141996 0.2557 0.600895 15 to 16 141445 -1.3697 0.085390 14 to 15 141842 -0.1986 0.421283 13 to 14 141399 -1.5054 0.066111 12 to 13 141701 -0.6145 0.269428 11 to 12 141474 -1.2842 0.099543 10 to 11 141632 -0.8181 0.206655 9 to 10 142336 1.2586 0.895915 8 to 9 142247 0.9961 0.840394 7 to 8 142030 0.3560 0.639064 6 to 7 142239 0.9725 0.834594 5 to 6 141837 -0.2134 0.415522 4 to 5 141714 -0.5762 0.282242 3 to 4 141994 0.2498 0.598615 2 to 3 142207 0.8781 0.810051 1 to 2 141599 -0.9154 0.179984 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-20_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2461.34 -0.547 0.292297 Test results for specific bytes for dh-ranFile-2016-01-20_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2502.50 0.035 0.514112 2 to 9 2465.52 -0.488 0.312905 3 to 10 2446.77 -0.753 0.225808 4 to 11 2410.17 -1.270 0.101963 5 to 12 2409.26 -1.283 0.099696 6 to 13 2516.36 0.231 0.591485 7 to 14 2555.62 0.787 0.784248 8 to 15 2343.89 -2.208 0.013632 9 to 16 2423.19 -1.086 0.138674 10 to 17 2543.27 0.612 0.729697 11 to 18 2363.60 -1.929 0.026869 12 to 19 2438.79 -0.866 0.193361 13 to 20 2441.97 -0.821 0.205922 14 to 21 2550.00 0.707 0.760266 15 to 22 2410.58 -1.265 0.103020 16 to 23 2535.51 0.502 0.692250 17 to 24 2435.65 -0.910 0.181387 18 to 25 2537.73 0.534 0.703194 19 to 26 2437.23 -0.888 0.187334 20 to 27 2484.65 -0.217 0.414084 21 to 28 2628.26 1.814 0.965154 22 to 29 2512.72 0.180 0.571388 23 to 30 2443.96 -0.793 0.214029 24 to 31 2638.83 1.963 0.975200 25 to 32 2496.15 -0.054 0.478279 CDPARK for dh-ranFile-2016-01-20_20:31: 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 3501 -1.0046 0.157553 3548 1.1416 0.873180 3511 -0.5479 0.291865 3493 -1.3699 0.085365 3516 -0.3196 0.374623 3500 -1.0502 0.146807 3517 -0.2740 0.392053 3541 0.8219 0.794438 3520 -0.1370 0.445521 3471 -2.3744 0.008788 Square side=100, avg. no. parked=3511.80 sample std.=21.33 p-value of the KSTEST for those 10 p-values: 0.179313 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-20_20:31 0.2055,0.9201,0.7353,0.8273,0.2439,0.8159,0.3068,0.5215,0.2979,0.3053, The KS test for those 10 p-values: 0.724939 The 3DSPHERES test for dh-ranFile-2016-01-20_20:31 sample no r^3 equiv. uni. 1 19.386 0.475972 2 66.713 0.891800 3 94.820 0.957602 4 33.071 0.667919 5 11.217 0.311952 6 17.761 0.446798 7 2.129 0.068500 8 25.670 0.575004 9 4.673 0.144244 10 13.454 0.361402 11 1.353 0.044112 12 4.631 0.143037 13 6.837 0.203787 14 27.435 0.599280 15 7.505 0.221332 16 8.322 0.242259 17 5.015 0.153943 18 71.773 0.908594 19 0.922 0.030264 20 26.981 0.593169 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.203999 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-20_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.8 0.8 -0.8 2.0 1.2 -1.4 -0.8 0.7 -0.2 -0.2 -0.1 -1.2 -0.3 0.1 -0.4 -1.0 0.9 -0.7 -0.4 -1.7 1.2 0.5 2.2 2.0 0.2 0.2 0.5 -1.1 1.1 -0.6 1.0 0.5 0.4 -0.2 -0.8 -1.2 0.2 -0.8 -0.1 0.1 -1.0 0.8 Chi-square with 42 degrees of freedom:40.158677 z-score=-0.200905, p-value=0.447955 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-20_20:31 Test no p-value 1 0.749561 2 0.316713 3 0.464992 4 0.024419 5 0.789084 6 0.977591 7 0.804066 8 0.010166 9 0.028049 10 0.960333 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.134440 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-20_20:31: (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 66532 0.27 66512 0.36 3 25000.00 25285 3.25 25066 0.17 4 6666.67 6520 3.23 6782 2.00 5 1388.89 1374 0.16 1361 0.56 6 238.10 237 0.01 233 0.11 7 34.72 44 2.48 41 1.14 8 4.96 7 0.84 4 0.19 p=0.88478 p=0.39320 Number of rngs required: 688548, p-value: 0.566 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-20_20:31 No. of wins: Observed Expected 98445 98585.9 z-score=-0.630, pvalue=0.26435 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66887 66666.7 0.728 0.728 2 37621 37654.3 0.029 0.758 3 27090 26954.7 0.679 1.437 4 19402 19313.5 0.406 1.842 5 13757 13851.4 0.644 2.486 6 9830 9943.5 1.297 3.783 7 7075 7145.0 0.686 4.469 8 5142 5139.1 0.002 4.470 9 3695 3699.9 0.006 4.477 10 2663 2666.3 0.004 4.481 11 1934 1923.3 0.059 4.540 12 1298 1388.7 5.929 10.469 13 987 1003.7 0.278 10.748 14 747 726.1 0.599 11.347 15 497 525.8 1.581 12.928 16 379 381.2 0.012 12.940 17 277 276.5 0.001 12.941 18 213 200.8 0.737 13.678 19 141 146.0 0.170 13.849 20 102 106.2 0.167 14.016 21 263 287.1 2.025 16.041 Chisq= 16.04 for 20 degrees of freedom, p= 0.28593 SUMMARY of craptest p-value for no. of wins: 0.264347 p-value for throws/game: 0.285933 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-20_20:31 No. of wins: Observed Expected 99074 98585.9 z-score= 2.183, pvalue=0.98549 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66774 66666.7 0.173 0.173 2 37845 37654.3 0.966 1.138 3 26941 26954.7 0.007 1.145 4 19230 19313.5 0.361 1.506 5 13867 13851.4 0.018 1.524 6 10012 9943.5 0.471 1.995 7 7045 7145.0 1.400 3.395 8 4990 5139.1 4.324 7.719 9 3748 3699.9 0.626 8.346 10 2641 2666.3 0.240 8.586 11 1873 1923.3 1.317 9.903 12 1307 1388.7 4.811 14.714 13 1064 1003.7 3.621 18.335 14 720 726.1 0.052 18.387 15 519 525.8 0.089 18.475 16 365 381.2 0.684 19.160 17 258 276.5 1.243 20.403 18 237 200.8 6.514 26.917 19 119 146.0 4.988 31.905 20 130 106.2 5.326 37.231 21 315 287.1 2.708 39.940 Chisq= 39.94 for 20 degrees of freedom, p= 0.99492 SUMMARY of craptest p-value for no. of wins: 0.985491 p-value for throws/game: 0.994916 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0048,0.0088,0.0102,0.0136,0.0139,0.0144,0.0153,0.0197,0.0212,0.0244, 0.0269,0.0280,0.0282,0.0303,0.0441,0.0519,0.0532,0.0535,0.0571,0.0595, 0.0661,0.0685,0.0800,0.0806,0.0854,0.0854,0.0887,0.0913,0.0962,0.0995, 0.0997,0.1020,0.1030,0.1059,0.1078,0.1107,0.1115,0.1230,0.1238,0.1285, 0.1314,0.1331,0.1344,0.1387,0.1393,0.1403,0.1430,0.1442,0.1468,0.1514, 0.1539,0.1576,0.1599,0.1625,0.1688,0.1736,0.1736,0.1782,0.1793,0.1800, 0.1802,0.1806,0.1814,0.1873,0.1934,0.2005,0.2025,0.2038,0.2040,0.2055, 0.2059,0.2060,0.2067,0.2119,0.2140,0.2213,0.2216,0.2258,0.2338,0.2349, 0.2352,0.2395,0.2423,0.2439,0.2443,0.2643,0.2684,0.2694,0.2784,0.2809, 0.2822,0.2859,0.2919,0.2923,0.2969,0.2971,0.2979,0.2985,0.3007,0.3040, 0.3053,0.3068,0.3069,0.3074,0.3120,0.3129,0.3167,0.3184,0.3266,0.3355, 0.3424,0.3614,0.3623,0.3643,0.3647,0.3680,0.3746,0.3746,0.3795,0.3811, 0.3921,0.3932,0.3968,0.4055,0.4122,0.4124,0.4131,0.4141,0.4155,0.4164, 0.4213,0.4237,0.4283,0.4329,0.4352,0.4433,0.4455,0.4468,0.4480,0.4491, 0.4497,0.4541,0.4550,0.4640,0.4650,0.4679,0.4688,0.4742,0.4760,0.4783, 0.4812,0.4820,0.4858,0.4999,0.5043,0.5078,0.5141,0.5196,0.5215,0.5250, 0.5258,0.5266,0.5271,0.5282,0.5284,0.5396,0.5456,0.5499,0.5548,0.5559, 0.5571,0.5662,0.5672,0.5682,0.5714,0.5750,0.5773,0.5840,0.5900,0.5909, 0.5915,0.5932,0.5986,0.5993,0.6009,0.6032,0.6109,0.6155,0.6159,0.6235, 0.6391,0.6462,0.6493,0.6679,0.6790,0.6813,0.6922,0.6947,0.7032,0.7075, 0.7082,0.7249,0.7297,0.7353,0.7364,0.7478,0.7496,0.7528,0.7603,0.7668, 0.7746,0.7746,0.7822,0.7825,0.7842,0.7878,0.7891,0.7944,0.8037,0.8041, 0.8073,0.8084,0.8101,0.8119,0.8128,0.8159,0.8273,0.8346,0.8404,0.8409, 0.8415,0.8462,0.8517,0.8543,0.8555,0.8604,0.8648,0.8722,0.8723,0.8732, 0.8768,0.8780,0.8848,0.8877,0.8884,0.8898,0.8918,0.8959,0.8992,0.9086, 0.9201,0.9251,0.9306,0.9337,0.9359,0.9414,0.9416,0.9436,0.9484,0.9576, 0.9603,0.9605,0.9652,0.9739,0.9752,0.9776,0.9855,0.9949,0.9950, Overall p-value after applying KStest on 269 p-values = 0.023516 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.