RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-27_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.74 20.6046 0.755522 2 to 25 15.82 24.2029 0.885973 3 to 26 15.68 14.3423 0.357260 4 to 27 15.54 23.8421 0.876210 5 to 28 15.78 18.7329 0.655924 6 to 29 16.06 17.5000 0.578980 7 to 30 15.87 27.0359 0.942457 8 to 31 15.75 17.9303 0.606751 9 to 32 15.59 23.9988 0.880531 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.026569 Tough bday spacings test for dh-ranFile-2015-11-27_00:31: 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 31 79 94 89 84 49 25 20 11 6 (O-E)^2/E 0.9 0.9 0.4 0.1 0.8 0.4 0.2 0.8 1.8 2.9 0.9 Birthday Spacings: Sum(O-E)^2/E= 10.078, p= 0.566 RESULTS OF GCD FOR dh-ranFile-2015-11-27_00:31 Euclid's algorithm: p-value, steps to gcd: 0.400482 p-value, dist. of gcd's: 0.026200 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-27_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.251 0.757 0.085 0.894 0.229 0.272 0.245 0.751 Bits 8 to 15---> 0.356 0.500 0.931 0.934 0.825 0.224 0.142 0.833 Bits 16 to 23---> 0.881 0.148 0.699 0.380 0.565 0.997 0.424 0.516 Bits 24 to 31---> 0.239 0.901 0.669 0.060 0.642 0.488 0.147 0.641 KS test for the above 32 p values: 0.104 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-27_00:31, p-values for 5 runs: 0.2698, 0.5015, 0.9280, 0.5315, 0.9383 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-27_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 210 211.4 0.010 0.010 r= 29 5290 5134.0 4.740 4.749 r= 30 23072 23103.0 0.042 4.791 r= 31 11428 11551.5 1.321 6.112 chi-square = 6.112 with df = 3; p-value = 0.894 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-27_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5164 5134.0 0.175 0.236 r= 31 22989 23103.0 0.563 0.799 r= 32 11632 11551.5 0.561 1.360 chi-square = 1.360 with df = 3; p-value = 0.285 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-27_00:31 b-rank test for bits 1 to 8, p=0.70550 b-rank test for bits 2 to 9, p=0.65444 b-rank test for bits 3 to 10, p=0.50512 b-rank test for bits 4 to 11, p=0.64574 b-rank test for bits 5 to 12, p=0.41072 b-rank test for bits 6 to 13, p=0.10840 b-rank test for bits 7 to 14, p=0.73863 b-rank test for bits 8 to 15, p=0.42554 b-rank test for bits 9 to 16, p=0.02637 b-rank test for bits 10 to 17, p=0.15905 b-rank test for bits 11 to 18, p=0.49578 b-rank test for bits 12 to 19, p=0.11091 b-rank test for bits 13 to 20, p=0.17877 b-rank test for bits 14 to 21, p=0.23255 b-rank test for bits 15 to 22, p=0.95803 b-rank test for bits 16 to 23, p=0.30121 b-rank test for bits 17 to 24, p=0.69511 b-rank test for bits 18 to 25, p=0.09851 b-rank test for bits 19 to 26, p=0.14537 b-rank test for bits 20 to 27, p=0.47506 b-rank test for bits 21 to 28, p=0.60723 b-rank test for bits 22 to 29, p=0.61959 b-rank test for bits 23 to 30, p=0.40022 b-rank test for bits 24 to 31, p=0.27955 b-rank test for bits 25 to 32, p=0.15073 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 = 0.131452 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-27_00:31 (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 142099 0.44 0.671173 2 142111 0.47 0.681248 3 142099 0.44 0.671173 4 142397 1.14 0.872735 5 142275 0.85 0.803550 6 141845 -0.15 0.440263 7 141827 -0.19 0.423730 8 141586 -0.76 0.224991 9 140801 -2.59 0.004805 10 141470 -1.03 0.152335 11 141673 -0.55 0.290415 12 141319 -1.38 0.083905 13 141249 -1.54 0.061436 14 142176 0.62 0.733378 15 141885 -0.06 0.477334 16 141347 -1.31 0.094447 17 142487 1.35 0.911443 18 142115 0.48 0.684577 19 141256 -1.53 0.063446 20 142599 1.61 0.946451 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-27_00:31 Bits used No. missing words z-score p-value 23 to 32 142000 0.3127 0.622729 22 to 31 141483 -1.4701 0.070767 21 to 30 141948 0.1333 0.553040 20 to 29 141528 -1.3149 0.094267 19 to 28 141980 0.2437 0.596264 18 to 27 141968 0.2023 0.580163 17 to 26 141436 -1.6322 0.051322 16 to 25 141312 -2.0598 0.019711 15 to 24 141123 -2.7115 0.003349 14 to 23 142335 1.4678 0.928924 13 to 22 141594 -1.0873 0.138442 12 to 21 142494 2.0161 0.978105 11 to 20 141985 0.2609 0.602927 10 to 19 142086 0.6092 0.728806 9 to 18 141781 -0.4425 0.329058 8 to 17 141806 -0.3563 0.360804 7 to 16 141856 -0.1839 0.427047 6 to 15 141752 -0.5425 0.293731 5 to 14 142131 0.7644 0.777679 4 to 13 141822 -0.3011 0.381655 3 to 12 142140 0.7954 0.786814 2 to 11 141985 0.2609 0.602927 1 to 10 142044 0.4644 0.678812 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-27_00:31 Bits used No. missing words z-score p-value 28 to 32 141842 -0.2282 0.409731 27 to 31 141758 -0.5130 0.303982 26 to 30 141616 -0.9943 0.160029 25 to 29 141812 -0.3299 0.370726 24 to 28 142003 0.3175 0.624578 23 to 27 142493 1.9785 0.976066 22 to 26 141980 0.2396 0.594664 21 to 25 141738 -0.5808 0.280695 20 to 24 141685 -0.7604 0.223496 19 to 23 142041 0.4463 0.672324 18 to 22 142073 0.5548 0.710489 17 to 21 141598 -1.0554 0.145631 16 to 20 142459 1.8633 0.968789 15 to 19 141710 -0.6757 0.249617 14 to 18 141777 -0.4486 0.326869 13 to 17 141377 -1.8045 0.035576 12 to 16 142252 1.1616 0.877300 11 to 15 141795 -0.3876 0.349171 10 to 14 141617 -0.9909 0.160855 9 to 13 141866 -0.1469 0.441613 8 to 12 141965 0.1887 0.574841 7 to 11 141585 -1.0994 0.135792 6 to 10 142128 0.7413 0.770730 5 to 9 141588 -1.0893 0.138021 4 to 8 142043 0.4531 0.674768 3 to 7 141624 -0.9672 0.166717 2 to 6 141639 -0.9164 0.179736 1 to 5 141722 -0.6350 0.262709 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-27_00:31 Bits used No. missing words z-score p-value 31 to 32 141889 -0.0600 0.476090 30 to 31 141821 -0.2606 0.397216 29 to 30 141878 -0.0924 0.463183 28 to 29 142012 0.3029 0.619002 27 to 28 141879 -0.0895 0.464355 26 to 27 141555 -1.0452 0.147960 25 to 26 141817 -0.2724 0.392673 24 to 25 141708 -0.5939 0.276292 23 to 24 142246 0.9931 0.839676 22 to 23 142277 1.0846 0.860944 21 to 22 141926 0.0492 0.519610 20 to 21 141953 0.1288 0.551250 19 to 20 141804 -0.3107 0.378011 18 to 19 141856 -0.1573 0.437498 17 to 18 141609 -0.8859 0.187828 16 to 17 141983 0.2173 0.586019 15 to 16 141950 0.1200 0.547747 14 to 15 141975 0.1937 0.576801 13 to 14 141653 -0.7561 0.224784 12 to 13 141961 0.1524 0.560572 11 to 12 142416 1.4946 0.932491 10 to 11 142089 0.5300 0.701944 9 to 10 141909 -0.0010 0.499612 8 to 9 141831 -0.2311 0.408633 7 to 8 142009 0.2940 0.615626 6 to 7 141565 -1.0157 0.154881 5 to 6 141433 -1.4051 0.079995 4 to 5 141984 0.2203 0.587168 3 to 4 141896 -0.0393 0.484317 2 to 3 141683 -0.6676 0.252182 1 to 2 141350 -1.6499 0.049478 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-27_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2499.20 -0.011 0.495510 Test results for specific bytes for dh-ranFile-2015-11-27_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2374.96 -1.768 0.038499 2 to 9 2524.22 0.343 0.634038 3 to 10 2530.50 0.431 0.666873 4 to 11 2564.09 0.906 0.817639 5 to 12 2492.71 -0.103 0.458927 6 to 13 2558.69 0.830 0.796717 7 to 14 2433.49 -0.941 0.173457 8 to 15 2501.20 0.017 0.506782 9 to 16 2235.33 -3.743 0.000091 10 to 17 2583.61 1.182 0.881469 11 to 18 2449.38 -0.716 0.237022 12 to 19 2481.88 -0.256 0.398864 13 to 20 2395.52 -1.478 0.069765 14 to 21 2499.17 -0.012 0.495330 15 to 22 2492.75 -0.103 0.459176 16 to 23 2544.72 0.632 0.736465 17 to 24 2672.43 2.439 0.992628 18 to 25 2484.13 -0.225 0.411182 19 to 26 2472.89 -0.383 0.350739 20 to 27 2438.28 -0.873 0.191388 21 to 28 2544.08 0.623 0.733478 22 to 29 2545.15 0.638 0.738424 23 to 30 2559.32 0.839 0.799232 24 to 31 2440.47 -0.842 0.199935 25 to 32 2399.75 -1.418 0.078130 CDPARK for dh-ranFile-2015-11-27_00:31: 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 3543 0.9132 0.819442 3561 1.7352 0.958644 3528 0.2283 0.590298 3495 -1.2785 0.100530 3534 0.5023 0.692266 3527 0.1826 0.572463 3480 -1.9635 0.024796 3562 1.7808 0.962529 3488 -1.5982 0.055002 3524 0.0457 0.518210 Square side=100, avg. no. parked=3524.20 sample std.=27.15 p-value of the KSTEST for those 10 p-values: 0.476301 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-27_00:31 0.2162,0.3506,0.3741,0.6438,0.9698,0.8060,0.0642,0.7053,0.0786,0.1914, The KS test for those 10 p-values: 0.792948 The 3DSPHERES test for dh-ranFile-2015-11-27_00:31 sample no r^3 equiv. uni. 1 27.701 0.602814 2 6.877 0.204856 3 27.254 0.596856 4 100.316 0.964700 5 58.345 0.856991 6 16.130 0.415896 7 12.987 0.351367 8 6.747 0.201391 9 1.414 0.046051 10 6.134 0.184918 11 36.772 0.706459 12 3.155 0.099813 13 9.784 0.278294 14 50.511 0.814313 15 11.821 0.325674 16 6.486 0.194431 17 4.676 0.144321 18 38.283 0.720879 19 1.054 0.034531 20 15.278 0.399069 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.255139 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-27_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -1.2 -0.8 0.8 -0.6 -0.4 1.0 -0.7 0.6 -2.2 -1.5 -0.1 2.3 -0.2 -0.6 1.9 -0.2 -1.9 -0.4 -0.9 0.7 -0.8 0.1 0.8 0.8 1.2 -1.4 1.5 -0.1 1.9 0.4 0.9 2.4 -0.2 0.6 0.6 -0.2 -1.7 -0.4 -0.1 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:50.642010 z-score=0.942921, p-value=0.830641 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-27_00:31 Test no p-value 1 0.035489 2 0.000407 3 0.039941 4 0.732934 5 0.080022 6 0.170402 7 0.353678 8 0.030885 9 0.107795 10 0.113418 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000035 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-27_00:31: (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 66713 0.03 66468 0.59 3 25000.00 24987 0.01 25196 1.54 4 6666.67 6628 0.22 6681 0.03 5 1388.89 1378 0.09 1369 0.28 6 238.10 248 0.41 241 0.04 7 34.72 44 2.48 40 0.80 8 4.96 1 3.16 4 0.19 p=0.62037 p=0.25185 Number of rngs required: 688028, p-value: 0.333 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-27_00:31 No. of wins: Observed Expected 98451 98585.9 z-score=-0.603, pvalue=0.27320 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66807 66666.7 0.295 0.295 2 37799 37654.3 0.556 0.851 3 26909 26954.7 0.078 0.929 4 19290 19313.5 0.029 0.957 5 13750 13851.4 0.743 1.700 6 10000 9943.5 0.321 2.021 7 7007 7145.0 2.666 4.687 8 5191 5139.1 0.525 5.212 9 3690 3699.9 0.026 5.238 10 2626 2666.3 0.609 5.847 11 1965 1923.3 0.903 6.750 12 1304 1388.7 5.171 11.921 13 1000 1003.7 0.014 11.934 14 743 726.1 0.391 12.326 15 509 525.8 0.539 12.865 16 379 381.2 0.012 12.877 17 285 276.5 0.259 13.136 18 222 200.8 2.232 15.367 19 152 146.0 0.248 15.615 20 100 106.2 0.364 15.979 21 272 287.1 0.796 16.775 Chisq= 16.77 for 20 degrees of freedom, p= 0.33244 SUMMARY of craptest p-value for no. of wins: 0.273199 p-value for throws/game: 0.332442 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-27_00:31 No. of wins: Observed Expected 98787 98585.9 z-score= 0.900, pvalue=0.81584 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66665 66666.7 0.000 0.000 2 37638 37654.3 0.007 0.007 3 26676 26954.7 2.882 2.889 4 19482 19313.5 1.471 4.360 5 13846 13851.4 0.002 4.362 6 10097 9943.5 2.368 6.731 7 7186 7145.0 0.235 6.966 8 5204 5139.1 0.820 7.786 9 3540 3699.9 6.907 14.693 10 2646 2666.3 0.155 14.848 11 1898 1923.3 0.334 15.181 12 1426 1388.7 1.000 16.181 13 1053 1003.7 2.420 18.601 14 702 726.1 0.803 19.404 15 531 525.8 0.051 19.454 16 390 381.2 0.205 19.660 17 283 276.5 0.151 19.811 18 192 200.8 0.388 20.199 19 139 146.0 0.334 20.533 20 98 106.2 0.635 21.169 21 308 287.1 1.519 22.688 Chisq= 22.69 for 20 degrees of freedom, p= 0.69562 SUMMARY of craptest p-value for no. of wins: 0.815839 p-value for throws/game: 0.695622 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0001,0.0004,0.0033,0.0048,0.0197,0.0248,0.0262,0.0264,0.0266, 0.0309,0.0345,0.0355,0.0356,0.0385,0.0399,0.0461,0.0495,0.0513,0.0550, 0.0597,0.0614,0.0634,0.0642,0.0698,0.0708,0.0781,0.0786,0.0800,0.0800, 0.0839,0.0853,0.0943,0.0944,0.0985,0.0998,0.1005,0.1038,0.1078,0.1084, 0.1109,0.1134,0.1315,0.1358,0.1380,0.1384,0.1416,0.1443,0.1454,0.1456, 0.1473,0.1478,0.1480,0.1507,0.1523,0.1549,0.1591,0.1600,0.1609,0.1667, 0.1704,0.1735,0.1788,0.1797,0.1849,0.1878,0.1914,0.1914,0.1944,0.1999, 0.2014,0.2049,0.2162,0.2235,0.2241,0.2248,0.2250,0.2293,0.2325,0.2370, 0.2385,0.2450,0.2496,0.2514,0.2518,0.2522,0.2551,0.2627,0.2698,0.2723, 0.2732,0.2763,0.2783,0.2795,0.2807,0.2849,0.2904,0.2937,0.3012,0.3040, 0.3257,0.3269,0.3291,0.3324,0.3329,0.3492,0.3506,0.3507,0.3514,0.3537, 0.3565,0.3573,0.3608,0.3707,0.3741,0.3780,0.3799,0.3817,0.3927,0.3972, 0.3989,0.3991,0.4002,0.4005,0.4086,0.4097,0.4107,0.4112,0.4159,0.4237, 0.4244,0.4255,0.4270,0.4375,0.4403,0.4416,0.4589,0.4592,0.4632,0.4644, 0.4751,0.4761,0.4763,0.4773,0.4843,0.4876,0.4953,0.4955,0.4958,0.4996, 0.5001,0.5015,0.5051,0.5068,0.5160,0.5182,0.5196,0.5315,0.5477,0.5513, 0.5530,0.5606,0.5653,0.5663,0.5725,0.5748,0.5768,0.5790,0.5802,0.5860, 0.5872,0.5903,0.5947,0.5963,0.5969,0.6028,0.6029,0.6029,0.6068,0.6072, 0.6156,0.6190,0.6196,0.6204,0.6227,0.6246,0.6340,0.6406,0.6420,0.6438, 0.6457,0.6544,0.6559,0.6669,0.6686,0.6712,0.6712,0.6723,0.6748,0.6788, 0.6812,0.6846,0.6923,0.6951,0.6956,0.6991,0.7019,0.7053,0.7055,0.7065, 0.7105,0.7209,0.7288,0.7329,0.7334,0.7335,0.7365,0.7384,0.7386,0.7511, 0.7555,0.7569,0.7707,0.7777,0.7868,0.7929,0.7967,0.7992,0.8035,0.8060, 0.8143,0.8158,0.8176,0.8194,0.8254,0.8306,0.8327,0.8397,0.8570,0.8609, 0.8727,0.8762,0.8773,0.8805,0.8805,0.8815,0.8860,0.8937,0.8941,0.9014, 0.9114,0.9280,0.9289,0.9306,0.9325,0.9342,0.9383,0.9425,0.9465,0.9580, 0.9586,0.9625,0.9647,0.9688,0.9698,0.9761,0.9781,0.9926,0.9966, Overall p-value after applying KStest on 269 p-values = 0.014496 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.