RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-11_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.94 16.2234 0.491943 2 to 25 15.85 21.4029 0.791214 3 to 26 16.16 14.1721 0.345113 4 to 27 16.03 13.4833 0.296723 5 to 28 15.66 22.5981 0.837203 6 to 29 15.83 13.3526 0.287717 7 to 30 15.63 21.5080 0.795612 8 to 31 15.89 26.1409 0.928069 9 to 32 15.75 15.1981 0.418785 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.517061 Tough bday spacings test for dh-ranFile-2015-10-11_17:31: 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 8 35 72 95 88 88 52 32 17 7 6 (O-E)^2/E 0.1 0.1 0.0 0.1 1.0 1.2 0.0 0.2 0.3 0.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 3.927, p= 0.049 RESULTS OF GCD FOR dh-ranFile-2015-10-11_17:31 Euclid's algorithm: p-value, steps to gcd: 0.623431 p-value, dist. of gcd's: 0.967247 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-11_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.694 0.034 0.846 0.571 0.586 0.958 0.269 0.848 Bits 8 to 15---> 0.742 0.279 0.894 0.310 0.019 0.143 0.525 0.186 Bits 16 to 23---> 0.392 0.236 0.741 0.130 0.869 0.987 0.886 0.632 Bits 24 to 31---> 0.058 0.928 0.987 0.588 0.911 0.783 0.793 0.100 KS test for the above 32 p values: 0.801 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-11_17:31, p-values for 5 runs: 0.2012, 0.0722, 0.2830, 0.6199, 0.2694 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-11_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 227 211.4 1.148 1.148 r= 29 5184 5134.0 0.487 1.635 r= 30 23034 23103.0 0.206 1.842 r= 31 11555 11551.5 0.001 1.843 chi-square = 1.843 with df = 3; p-value = 0.394 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-11_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 220 211.4 0.348 0.348 r= 30 5136 5134.0 0.001 0.349 r= 31 23066 23103.0 0.059 0.409 r= 32 11578 11551.5 0.061 0.469 chi-square = 0.469 with df = 3; p-value = 0.074 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-11_17:31 b-rank test for bits 1 to 8, p=0.00458 b-rank test for bits 2 to 9, p=0.58081 b-rank test for bits 3 to 10, p=0.18462 b-rank test for bits 4 to 11, p=0.50246 b-rank test for bits 5 to 12, p=0.91475 b-rank test for bits 6 to 13, p=0.44481 b-rank test for bits 7 to 14, p=0.51978 b-rank test for bits 8 to 15, p=0.26258 b-rank test for bits 9 to 16, p=0.03910 b-rank test for bits 10 to 17, p=0.59827 b-rank test for bits 11 to 18, p=0.55241 b-rank test for bits 12 to 19, p=0.76426 b-rank test for bits 13 to 20, p=0.24967 b-rank test for bits 14 to 21, p=0.32591 b-rank test for bits 15 to 22, p=0.00977 b-rank test for bits 16 to 23, p=0.45621 b-rank test for bits 17 to 24, p=0.06751 b-rank test for bits 18 to 25, p=0.51416 b-rank test for bits 19 to 26, p=0.59400 b-rank test for bits 20 to 27, p=0.23087 b-rank test for bits 21 to 28, p=0.79831 b-rank test for bits 22 to 29, p=0.99228 b-rank test for bits 23 to 30, p=0.54514 b-rank test for bits 24 to 31, p=0.26792 b-rank test for bits 25 to 32, p=0.32269 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 = 0.240853 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-11_17:31 (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 142115 0.48 0.684577 2 141689 -0.51 0.303350 3 142222 0.73 0.767469 4 142290 0.89 0.813110 5 141805 -0.24 0.403708 6 141567 -0.80 0.211903 7 142209 0.70 0.758087 8 141767 -0.33 0.369738 9 142081 0.40 0.655826 10 142515 1.42 0.921483 11 141667 -0.57 0.285632 12 141660 -0.58 0.280099 13 141803 -0.25 0.401899 14 141802 -0.25 0.400996 15 141713 -0.46 0.323219 16 142481 1.34 0.909173 17 142173 0.62 0.731070 18 142573 1.55 0.939505 19 141188 -1.69 0.045960 20 142226 0.74 0.770315 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-11_17:31 Bits used No. missing words z-score p-value 23 to 32 142431 1.7989 0.963980 22 to 31 142012 0.3540 0.638344 21 to 30 141742 -0.5770 0.281970 20 to 29 141829 -0.2770 0.390890 19 to 28 141893 -0.0563 0.477547 18 to 27 142085 0.6058 0.727663 17 to 26 141935 0.0885 0.535267 16 to 25 142151 0.8333 0.797675 15 to 24 142266 1.2299 0.890632 14 to 23 142193 0.9782 0.836006 13 to 22 141885 -0.0839 0.466569 12 to 21 141662 -0.8529 0.196868 11 to 20 142190 0.9678 0.833435 10 to 19 142291 1.3161 0.905930 9 to 18 141669 -0.8287 0.203630 8 to 17 141905 -0.0149 0.494044 7 to 16 141522 -1.3356 0.090837 6 to 15 141670 -0.8253 0.204608 5 to 14 141916 0.0230 0.509175 4 to 13 141721 -0.6494 0.258036 3 to 12 142056 0.5058 0.693487 2 to 11 142038 0.4437 0.671367 1 to 10 142085 0.6058 0.727663 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-11_17:31 Bits used No. missing words z-score p-value 28 to 32 141804 -0.3571 0.360527 27 to 31 141503 -1.3774 0.084196 26 to 30 141816 -0.3164 0.375860 25 to 29 142460 1.8667 0.969027 24 to 28 141923 0.0463 0.518480 23 to 27 142682 2.6192 0.995593 22 to 26 141832 -0.2621 0.396609 21 to 25 142075 0.5616 0.712803 20 to 24 141672 -0.8045 0.210552 19 to 23 141712 -0.6689 0.251775 18 to 22 141663 -0.8350 0.201854 17 to 21 141980 0.2396 0.594664 16 to 20 142724 2.7616 0.997124 15 to 19 141704 -0.6960 0.243204 14 to 18 142082 0.5853 0.720834 13 to 17 142388 1.6226 0.947664 12 to 16 141443 -1.5808 0.056964 11 to 15 141895 -0.0486 0.480629 10 to 14 141960 0.1718 0.568188 9 to 13 142025 0.3921 0.652509 8 to 12 142111 0.6836 0.752895 7 to 11 141585 -1.0994 0.135792 6 to 10 141782 -0.4316 0.333006 5 to 9 141733 -0.5977 0.275010 4 to 8 141820 -0.3028 0.381016 3 to 7 142007 0.3311 0.629710 2 to 6 141907 -0.0079 0.496849 1 to 5 141810 -0.3367 0.368167 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-11_17:31 Bits used No. missing words z-score p-value 31 to 32 142242 0.9813 0.836784 30 to 31 141966 0.1672 0.566381 29 to 30 141341 -1.6765 0.046821 28 to 29 142248 0.9990 0.841109 27 to 28 141645 -0.7797 0.217774 26 to 27 141892 -0.0511 0.479615 25 to 26 141726 -0.5408 0.294324 24 to 25 142033 0.3648 0.642373 23 to 24 141933 0.0698 0.527833 22 to 23 141943 0.0993 0.539559 21 to 22 142219 0.9135 0.819505 20 to 21 142189 0.8250 0.795310 19 to 20 141506 -1.1898 0.117070 18 to 19 141465 -1.3107 0.094978 17 to 18 142275 1.0787 0.859633 16 to 17 141929 0.0580 0.523135 15 to 16 141693 -0.6381 0.261691 14 to 15 142261 1.0374 0.850219 13 to 14 142015 0.3117 0.622370 12 to 13 141997 0.2586 0.602033 11 to 12 141660 -0.7355 0.231022 10 to 11 141717 -0.5673 0.285240 9 to 10 142027 0.3471 0.635745 8 to 9 142365 1.3442 0.910552 7 to 8 142503 1.7512 0.960048 6 to 7 141917 0.0226 0.509025 5 to 6 141256 -1.9272 0.026976 4 to 5 141981 0.2114 0.583719 3 to 4 141437 -1.3933 0.081764 2 to 3 142021 0.3294 0.629077 1 to 2 141456 -1.3373 0.090569 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-11_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2398.66 -1.433 0.075914 Test results for specific bytes for dh-ranFile-2015-10-11_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2509.59 0.136 0.553960 2 to 9 2524.13 0.341 0.633543 3 to 10 2595.89 1.356 0.912459 4 to 11 2471.47 -0.403 0.343324 5 to 12 2585.34 1.207 0.886268 6 to 13 2370.26 -1.835 0.033270 7 to 14 2587.19 1.233 0.891226 8 to 15 2563.23 0.894 0.814391 9 to 16 2484.53 -0.219 0.413407 10 to 17 2533.82 0.478 0.683779 11 to 18 2532.47 0.459 0.676948 12 to 19 2402.65 -1.377 0.084298 13 to 20 2432.76 -0.951 0.170838 14 to 21 2513.32 0.188 0.574719 15 to 22 2474.88 -0.355 0.361188 16 to 23 2527.53 0.389 0.651467 17 to 24 2555.27 0.782 0.782782 18 to 25 2462.95 -0.524 0.300127 19 to 26 2563.73 0.901 0.816298 20 to 27 2543.03 0.609 0.728587 21 to 28 2483.59 -0.232 0.408214 22 to 29 2595.37 1.349 0.911283 23 to 30 2404.18 -1.355 0.087685 24 to 31 2561.18 0.865 0.806543 25 to 32 2550.35 0.712 0.761796 CDPARK for dh-ranFile-2015-10-11_17:31: 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 3551 1.2785 0.899470 3484 -1.7808 0.037471 3506 -0.7763 0.218799 3553 1.3699 0.914635 3541 0.8219 0.794438 3553 1.3699 0.914635 3528 0.2283 0.590298 3561 1.7352 0.958644 3505 -0.8219 0.205562 3500 -1.0502 0.146807 Square side=100, avg. no. parked=3528.20 sample std.=26.02 p-value of the KSTEST for those 10 p-values: 0.232541 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-11_17:31 0.2086,0.0503,0.5207,0.9157,0.8967,0.2459,0.2258,0.8632,0.0825,0.9943, The KS test for those 10 p-values: 0.329767 The 3DSPHERES test for dh-ranFile-2015-10-11_17:31 sample no r^3 equiv. uni. 1 54.159 0.835578 2 37.269 0.711279 3 6.919 0.205959 4 52.674 0.827232 5 12.116 0.332261 6 9.372 0.268319 7 25.574 0.573635 8 4.997 0.153444 9 16.632 0.425578 10 22.411 0.526237 11 2.131 0.068558 12 36.651 0.705270 13 23.054 0.536270 14 41.273 0.747354 15 5.171 0.158321 16 4.520 0.139871 17 14.819 0.389794 18 10.985 0.306612 19 19.513 0.478181 20 50.522 0.814385 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.624206 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-11_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.3 0.6 -1.4 -0.2 1.0 1.0 0.3 -1.0 -0.3 0.5 1.4 0.2 -0.1 -1.1 -0.6 0.2 0.6 0.8 -0.9 1.3 -1.1 -0.2 -0.8 0.4 0.6 -1.3 -0.3 0.9 -1.2 -0.3 1.8 0.8 -0.1 -0.8 1.5 -0.9 -0.4 -0.8 -0.1 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:32.578880 z-score=-1.027928, p-value=0.148599 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-11_17:31 Test no p-value 1 0.009656 2 0.387405 3 0.453713 4 0.338163 5 0.759986 6 0.007719 7 0.119647 8 0.099941 9 0.424362 10 0.614677 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.046575 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-11_17:31: (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 67020 1.87 66330 1.70 3 25000.00 24811 1.43 25214 1.83 4 6666.67 6528 2.88 6782 2.00 5 1388.89 1372 0.21 1387 0.00 6 238.10 240 0.02 231 0.21 7 34.72 25 2.72 46 3.66 8 4.96 3 0.77 9 3.29 p=0.87117 p=0.95188 Number of rngs required: 688001, p-value: 0.322 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-11_17:31 No. of wins: Observed Expected 98298 98585.9 z-score=-1.287, pvalue=0.09897 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66288 66666.7 2.151 2.151 2 37974 37654.3 2.714 4.865 3 26904 26954.7 0.095 4.960 4 19362 19313.5 0.122 5.082 5 13980 13851.4 1.194 6.276 6 9951 9943.5 0.006 6.281 7 7136 7145.0 0.011 6.293 8 5124 5139.1 0.044 6.337 9 3627 3699.9 1.435 7.772 10 2676 2666.3 0.035 7.807 11 1876 1923.3 1.165 8.972 12 1427 1388.7 1.054 10.026 13 988 1003.7 0.246 10.272 14 731 726.1 0.033 10.305 15 517 525.8 0.148 10.453 16 386 381.2 0.062 10.515 17 308 276.5 3.579 14.094 18 223 200.8 2.447 16.541 19 152 146.0 0.248 16.789 20 100 106.2 0.364 17.153 21 270 287.1 1.020 18.173 Chisq= 18.17 for 20 degrees of freedom, p= 0.42399 SUMMARY of craptest p-value for no. of wins: 0.098965 p-value for throws/game: 0.423992 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-11_17:31 No. of wins: Observed Expected 98458 98585.9 z-score=-0.572, pvalue=0.28371 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66812 66666.7 0.317 0.317 2 37708 37654.3 0.077 0.393 3 26821 26954.7 0.663 1.057 4 19372 19313.5 0.177 1.234 5 13781 13851.4 0.358 1.592 6 10135 9943.5 3.686 5.279 7 7100 7145.0 0.284 5.562 8 5130 5139.1 0.016 5.578 9 3632 3699.9 1.245 6.823 10 2559 2666.3 4.318 11.141 11 1937 1923.3 0.097 11.238 12 1394 1388.7 0.020 11.258 13 981 1003.7 0.514 11.772 14 746 726.1 0.543 12.315 15 501 525.8 1.173 13.488 16 369 381.2 0.387 13.876 17 277 276.5 0.001 13.877 18 178 200.8 2.595 16.472 19 154 146.0 0.440 16.912 20 112 106.2 0.315 17.227 21 301 287.1 0.672 17.899 Chisq= 17.90 for 20 degrees of freedom, p= 0.40591 SUMMARY of craptest p-value for no. of wins: 0.283709 p-value for throws/game: 0.405909 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0046,0.0077,0.0097,0.0098,0.0194,0.0270,0.0333,0.0343,0.0375,0.0391, 0.0460,0.0466,0.0468,0.0494,0.0503,0.0570,0.0582,0.0675,0.0686,0.0722, 0.0744,0.0759,0.0818,0.0825,0.0842,0.0843,0.0877,0.0906,0.0908,0.0950, 0.0990,0.0999,0.0999,0.1171,0.1196,0.1298,0.1358,0.1399,0.1430,0.1468, 0.1486,0.1534,0.1583,0.1708,0.1846,0.1861,0.1969,0.2012,0.2019,0.2036, 0.2046,0.2056,0.2060,0.2086,0.2106,0.2119,0.2178,0.2188,0.2258,0.2309, 0.2310,0.2325,0.2365,0.2409,0.2432,0.2459,0.2497,0.2518,0.2580,0.2617, 0.2626,0.2679,0.2683,0.2689,0.2694,0.2750,0.2792,0.2801,0.2820,0.2830, 0.2837,0.2852,0.2856,0.2877,0.2943,0.2967,0.3001,0.3034,0.3066,0.3104, 0.3216,0.3227,0.3232,0.3259,0.3298,0.3323,0.3330,0.3382,0.3433,0.3451, 0.3605,0.3612,0.3682,0.3697,0.3759,0.3810,0.3874,0.3898,0.3909,0.3921, 0.3943,0.3966,0.4010,0.4019,0.4037,0.4059,0.4082,0.4134,0.4188,0.4240, 0.4244,0.4256,0.4448,0.4537,0.4562,0.4666,0.4775,0.4782,0.4796,0.4806, 0.4919,0.4940,0.4968,0.5025,0.5090,0.5092,0.5142,0.5171,0.5185,0.5198, 0.5207,0.5231,0.5251,0.5262,0.5278,0.5353,0.5363,0.5396,0.5451,0.5524, 0.5540,0.5664,0.5682,0.5714,0.5736,0.5747,0.5808,0.5837,0.5861,0.5878, 0.5903,0.5940,0.5947,0.5983,0.6020,0.6147,0.6199,0.6224,0.6234,0.6242, 0.6291,0.6297,0.6316,0.6335,0.6357,0.6383,0.6424,0.6515,0.6525,0.6558, 0.6714,0.6769,0.6838,0.6846,0.6935,0.6939,0.7053,0.7113,0.7128,0.7208, 0.7277,0.7277,0.7286,0.7311,0.7406,0.7423,0.7474,0.7529,0.7581,0.7600, 0.7618,0.7643,0.7675,0.7703,0.7828,0.7832,0.7912,0.7933,0.7944,0.7953, 0.7956,0.7977,0.7983,0.8005,0.8065,0.8131,0.8144,0.8144,0.8163,0.8195, 0.8272,0.8334,0.8356,0.8360,0.8368,0.8372,0.8411,0.8463,0.8480,0.8502, 0.8596,0.8632,0.8691,0.8712,0.8857,0.8863,0.8906,0.8912,0.8944,0.8967, 0.8995,0.9059,0.9092,0.9106,0.9112,0.9113,0.9125,0.9146,0.9146,0.9147, 0.9157,0.9215,0.9278,0.9281,0.9395,0.9477,0.9519,0.9584,0.9586,0.9600, 0.9640,0.9672,0.9690,0.9866,0.9868,0.9923,0.9943,0.9956,0.9971, Overall p-value after applying KStest on 269 p-values = 0.977750 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.