RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-06_01:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.98 18.5012 0.642097 2 to 25 15.80 17.4729 0.577199 3 to 26 15.69 19.8625 0.718679 4 to 27 15.97 9.3469 0.071256 5 to 28 15.74 13.7565 0.315743 6 to 29 15.76 16.1737 0.488446 7 to 30 15.80 19.3159 0.689297 8 to 31 15.79 21.9939 0.815047 9 to 32 15.74 22.7815 0.843500 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.524062 Tough bday spacings test for dh-ranFile-2016-02-06_01:31: 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 14 32 85 101 91 72 53 28 14 5 5 (O-E)^2/E 2.6 0.6 1.9 0.1 0.5 0.5 0.0 0.1 0.1 0.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 6.862, p= 0.262 RESULTS OF GCD FOR dh-ranFile-2016-02-06_01:31 Euclid's algorithm: p-value, steps to gcd: 0.326417 p-value, dist. of gcd's: 0.645030 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-06_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.401 0.145 0.816 0.750 0.438 0.348 0.481 0.480 Bits 8 to 15---> 0.631 0.132 0.823 0.598 0.766 0.311 0.188 0.474 Bits 16 to 23---> 0.190 0.485 0.579 0.680 0.561 0.409 0.225 0.621 Bits 24 to 31---> 0.077 0.477 0.813 0.825 0.924 0.681 0.344 0.509 KS test for the above 32 p values: 0.699 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-06_01:31, p-values for 5 runs: 0.2561, 0.2350, 0.3293, 0.0326, 0.4959 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-06_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 193 211.4 1.605 1.605 r= 29 5196 5134.0 0.748 2.353 r= 30 23022 23103.0 0.284 2.637 r= 31 11589 11551.5 0.122 2.759 chi-square = 2.759 with df = 3; p-value = 0.570 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-06_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 221 211.4 0.434 0.434 r= 30 5132 5134.0 0.001 0.435 r= 31 23222 23103.0 0.612 1.048 r= 32 11425 11551.5 1.386 2.433 chi-square = 2.433 with df = 3; p-value = 0.513 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-06_01:31 b-rank test for bits 1 to 8, p=0.64273 b-rank test for bits 2 to 9, p=0.01960 b-rank test for bits 3 to 10, p=0.42032 b-rank test for bits 4 to 11, p=0.42712 b-rank test for bits 5 to 12, p=0.10078 b-rank test for bits 6 to 13, p=0.06392 b-rank test for bits 7 to 14, p=0.41021 b-rank test for bits 8 to 15, p=0.57974 b-rank test for bits 9 to 16, p=0.06536 b-rank test for bits 10 to 17, p=0.92050 b-rank test for bits 11 to 18, p=0.15370 b-rank test for bits 12 to 19, p=0.01059 b-rank test for bits 13 to 20, p=0.43748 b-rank test for bits 14 to 21, p=0.51068 b-rank test for bits 15 to 22, p=0.35207 b-rank test for bits 16 to 23, p=0.05860 b-rank test for bits 17 to 24, p=0.10059 b-rank test for bits 18 to 25, p=0.42860 b-rank test for bits 19 to 26, p=0.77800 b-rank test for bits 20 to 27, p=0.93766 b-rank test for bits 21 to 28, p=0.88864 b-rank test for bits 22 to 29, p=0.99667 b-rank test for bits 23 to 30, p=0.00008 b-rank test for bits 24 to 31, p=0.26011 b-rank test for bits 25 to 32, p=0.56734 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 = 0.046698 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-06_01:31 (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 141478 -1.01 0.156780 2 142589 1.59 0.943858 3 142430 1.22 0.888106 4 142583 1.57 0.942256 5 141848 -0.14 0.443029 6 141140 -1.80 0.036128 7 141987 0.18 0.572001 8 141813 -0.23 0.410962 9 142263 0.83 0.795692 10 141710 -0.47 0.320706 11 141118 -1.85 0.032236 12 142234 0.76 0.775947 13 142162 0.59 0.722522 14 142640 1.71 0.956105 15 142049 0.33 0.627913 16 142669 1.77 0.962045 17 141559 -0.82 0.206528 18 141246 -1.55 0.060590 19 142440 1.24 0.892491 20 141948 0.09 0.535996 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-06_01:31 Bits used No. missing words z-score p-value 23 to 32 141870 -0.1356 0.446061 22 to 31 142048 0.4782 0.683736 21 to 30 141851 -0.2011 0.420295 20 to 29 142156 0.8506 0.802500 19 to 28 142089 0.6196 0.732224 18 to 27 142225 1.0885 0.861817 17 to 26 141577 -1.1460 0.125905 16 to 25 142022 0.3885 0.651183 15 to 24 141698 -0.7287 0.233085 14 to 23 141805 -0.3598 0.359514 13 to 22 142108 0.6851 0.753350 12 to 21 142079 0.5851 0.720749 11 to 20 141831 -0.2701 0.393540 10 to 19 142245 1.1575 0.876462 9 to 18 142115 0.7092 0.760902 8 to 17 141853 -0.1942 0.422994 7 to 16 141839 -0.2425 0.404190 6 to 15 141644 -0.9149 0.180114 5 to 14 141739 -0.5873 0.278486 4 to 13 142393 1.6678 0.952325 3 to 12 141884 -0.0873 0.465199 2 to 11 142111 0.6954 0.756602 1 to 10 142048 0.4782 0.683736 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-06_01:31 Bits used No. missing words z-score p-value 28 to 32 142184 0.9311 0.824095 27 to 31 142388 1.6226 0.947664 26 to 30 142293 1.3006 0.903298 25 to 29 142055 0.4938 0.689275 24 to 28 141403 -1.7164 0.043047 23 to 27 141804 -0.3571 0.360527 22 to 26 141982 0.2463 0.597290 21 to 25 141961 0.1752 0.569520 20 to 24 141943 0.1141 0.545435 19 to 23 142074 0.5582 0.711647 18 to 22 141933 0.0802 0.531976 17 to 21 142255 1.1718 0.879354 16 to 20 142141 0.7853 0.783868 15 to 19 142031 0.4124 0.659992 14 to 18 141428 -1.6316 0.051379 13 to 17 141313 -2.0215 0.021616 12 to 16 141798 -0.3774 0.352942 11 to 15 141855 -0.1842 0.426940 10 to 14 141506 -1.3672 0.085778 9 to 13 142153 0.8260 0.795598 8 to 12 141713 -0.6655 0.252857 7 to 11 142152 0.8226 0.794635 6 to 10 141731 -0.6045 0.272753 5 to 9 142145 0.7989 0.787820 4 to 8 141827 -0.2791 0.390090 3 to 7 141766 -0.4859 0.313532 2 to 6 141597 -1.0587 0.144858 1 to 5 141863 -0.1571 0.437602 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-06_01:31 Bits used No. missing words z-score p-value 31 to 32 142484 1.6952 0.954980 30 to 31 142186 0.8161 0.792789 29 to 30 142116 0.6096 0.728952 28 to 29 141798 -0.3284 0.371302 27 to 28 142389 1.4150 0.921459 26 to 27 141968 0.1731 0.568701 25 to 26 141806 -0.3048 0.380256 24 to 25 141893 -0.0482 0.480790 23 to 24 142076 0.4917 0.688517 22 to 23 141241 -1.9715 0.024335 21 to 22 141938 0.0846 0.533699 20 to 21 141957 0.1406 0.555915 19 to 20 142464 1.6362 0.949101 18 to 19 142031 0.3589 0.640168 17 to 18 142065 0.4592 0.676956 16 to 17 141573 -0.9921 0.160569 15 to 16 141764 -0.4287 0.334070 14 to 15 141593 -0.9331 0.175377 13 to 14 141570 -1.0010 0.158420 12 to 13 141576 -0.9833 0.162736 11 to 12 142325 1.2262 0.889932 10 to 11 141600 -0.9125 0.180759 9 to 10 141969 0.1760 0.569860 8 to 9 142221 0.9194 0.821052 7 to 8 141941 0.0934 0.537216 6 to 7 142027 0.3471 0.635745 5 to 6 141981 0.2114 0.583719 4 to 5 141677 -0.6853 0.246565 3 to 4 141969 0.1760 0.569860 2 to 3 142449 1.5919 0.944302 1 to 2 141856 -0.1573 0.437498 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-06_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2440.17 -0.846 0.198722 Test results for specific bytes for dh-ranFile-2016-02-06_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2507.26 0.103 0.540874 2 to 9 2449.57 -0.713 0.237877 3 to 10 2528.70 0.406 0.657595 4 to 11 2576.96 1.088 0.861789 5 to 12 2498.73 -0.018 0.492846 6 to 13 2381.51 -1.676 0.046895 7 to 14 2297.78 -2.860 0.002119 8 to 15 2521.19 0.300 0.617789 9 to 16 2448.01 -0.735 0.231090 10 to 17 2563.23 0.894 0.814383 11 to 18 2484.79 -0.215 0.414859 12 to 19 2556.66 0.801 0.788529 13 to 20 2518.26 0.258 0.601890 14 to 21 2435.39 -0.914 0.180423 15 to 22 2441.05 -0.834 0.202234 16 to 23 2407.87 -1.303 0.096291 17 to 24 2559.96 0.848 0.801780 18 to 25 2516.11 0.228 0.590088 19 to 26 2459.99 -0.566 0.285755 20 to 27 2541.45 0.586 0.721110 21 to 28 2520.78 0.294 0.615572 22 to 29 2527.95 0.395 0.653701 23 to 30 2462.61 -0.529 0.298475 24 to 31 2550.81 0.719 0.763787 25 to 32 2457.71 -0.598 0.274883 CDPARK for dh-ranFile-2016-02-06_01:31: 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 3555 1.4612 0.928018 3530 0.3196 0.625377 3519 -0.1826 0.427537 3536 0.5936 0.723613 3525 0.0913 0.536383 3536 0.5936 0.723613 3563 1.8265 0.966111 3481 -1.9178 0.027568 3517 -0.2740 0.392053 3564 1.8721 0.969407 Square side=100, avg. no. parked=3532.60 sample std.=23.64 p-value of the KSTEST for those 10 p-values: 0.180734 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-06_01:31 0.1303,0.5572,0.0861,0.0659,0.7310,0.4164,0.5822,0.5633,0.6854,0.9153, The KS test for those 10 p-values: 0.816236 The 3DSPHERES test for dh-ranFile-2016-02-06_01:31 sample no r^3 equiv. uni. 1 27.502 0.600178 2 3.763 0.117886 3 52.805 0.827983 4 10.508 0.295509 5 9.141 0.262659 6 32.080 0.656764 7 55.367 0.842062 8 40.257 0.738647 9 68.361 0.897582 10 0.830 0.027273 11 21.293 0.508245 12 34.265 0.680874 13 1.784 0.057730 14 68.962 0.899615 15 1.474 0.047943 16 20.888 0.501565 17 85.956 0.943028 18 2.402 0.076959 19 6.446 0.193353 20 53.447 0.831625 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.610398 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-06_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 -0.6 0.9 0.0 -1.1 1.5 0.2 1.4 -0.1 1.4 -0.3 -0.6 0.2 -0.9 -0.6 0.2 0.8 0.1 -0.7 0.8 1.1 -0.5 -2.6 -0.2 -0.5 1.0 1.0 -0.2 -0.6 0.9 0.0 2.7 -1.0 -0.8 -0.7 -1.4 -0.4 -0.4 -1.3 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:39.842224 z-score=-0.235433, p-value=0.433900 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-06_01:31 Test no p-value 1 0.007705 2 0.004550 3 0.382026 4 0.915495 5 0.100613 6 0.208486 7 0.350385 8 0.743043 9 0.688312 10 0.032407 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.034665 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-06_01:31: (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 66694 0.01 66755 0.12 3 25000.00 24942 0.13 25027 0.03 4 6666.67 6685 0.05 6599 0.69 5 1388.89 1389 0.00 1350 1.09 6 238.10 247 0.33 231 0.21 7 34.72 37 0.15 31 0.40 8 4.96 5 0.00 6 0.22 p=0.00507 p=0.16051 Number of rngs required: 687192, p-value: 0.079 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-06_01:31 No. of wins: Observed Expected 98626 98585.9 z-score= 0.180, pvalue=0.57124 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66467 66666.7 0.598 0.598 2 37933 37654.3 2.062 2.661 3 27019 26954.7 0.153 2.814 4 19188 19313.5 0.815 3.629 5 13873 13851.4 0.034 3.662 6 9774 9943.5 2.891 6.553 7 7231 7145.0 1.035 7.588 8 5109 5139.1 0.176 7.764 9 3662 3699.9 0.388 8.151 10 2717 2666.3 0.964 9.115 11 1998 1923.3 2.899 12.014 12 1431 1388.7 1.286 13.300 13 1019 1003.7 0.233 13.533 14 694 726.1 1.423 14.956 15 531 525.8 0.051 15.006 16 379 381.2 0.012 15.019 17 245 276.5 3.597 18.616 18 204 200.8 0.050 18.666 19 154 146.0 0.440 19.106 20 111 106.2 0.216 19.321 21 261 287.1 2.375 21.696 Chisq= 21.70 for 20 degrees of freedom, p= 0.64280 SUMMARY of craptest p-value for no. of wins: 0.571242 p-value for throws/game: 0.642796 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-06_01:31 No. of wins: Observed Expected 98725 98585.9 z-score= 0.622, pvalue=0.73313 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66947 66666.7 1.179 1.179 2 37669 37654.3 0.006 1.185 3 26802 26954.7 0.865 2.050 4 19105 19313.5 2.250 4.300 5 13875 13851.4 0.040 4.340 6 10024 9943.5 0.651 4.991 7 7136 7145.0 0.011 5.003 8 5144 5139.1 0.005 5.007 9 3746 3699.9 0.575 5.583 10 2666 2666.3 0.000 5.583 11 1875 1923.3 1.214 6.797 12 1406 1388.7 0.215 7.012 13 986 1003.7 0.313 7.324 14 717 726.1 0.115 7.439 15 524 525.8 0.006 7.446 16 407 381.2 1.753 9.199 17 290 276.5 0.655 9.854 18 198 200.8 0.040 9.894 19 137 146.0 0.553 10.447 20 88 106.2 3.124 13.571 21 258 287.1 2.952 16.523 Chisq= 16.52 for 20 degrees of freedom, p= 0.31629 SUMMARY of craptest p-value for no. of wins: 0.733135 p-value for throws/game: 0.316289 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0021,0.0046,0.0051,0.0077,0.0106,0.0196,0.0216,0.0243,0.0273, 0.0276,0.0322,0.0324,0.0326,0.0347,0.0361,0.0430,0.0467,0.0469,0.0479, 0.0514,0.0577,0.0586,0.0606,0.0639,0.0654,0.0659,0.0713,0.0770,0.0770, 0.0789,0.0858,0.0861,0.0963,0.1006,0.1006,0.1008,0.1179,0.1259,0.1303, 0.1317,0.1449,0.1453,0.1537,0.1568,0.1584,0.1605,0.1606,0.1627,0.1754, 0.1801,0.1804,0.1807,0.1808,0.1884,0.1897,0.1934,0.1987,0.2022,0.2065, 0.2085,0.2251,0.2311,0.2331,0.2350,0.2379,0.2466,0.2529,0.2561,0.2601, 0.2616,0.2627,0.2728,0.2749,0.2785,0.2858,0.2955,0.2985,0.3106,0.3135, 0.3157,0.3163,0.3207,0.3264,0.3293,0.3341,0.3438,0.3479,0.3504,0.3521, 0.3529,0.3595,0.3605,0.3713,0.3803,0.3820,0.3901,0.3921,0.3935,0.4014, 0.4042,0.4091,0.4102,0.4110,0.4149,0.4164,0.4203,0.4203,0.4230,0.4269, 0.4271,0.4275,0.4286,0.4339,0.4375,0.4375,0.4376,0.4376,0.4430,0.4461, 0.4652,0.4744,0.4768,0.4800,0.4808,0.4814,0.4854,0.4884,0.4928,0.4959, 0.5016,0.5082,0.5091,0.5107,0.5125,0.5241,0.5320,0.5337,0.5360,0.5364, 0.5372,0.5409,0.5454,0.5559,0.5572,0.5607,0.5633,0.5673,0.5687,0.5695, 0.5697,0.5699,0.5699,0.5712,0.5720,0.5772,0.5790,0.5797,0.5822,0.5837, 0.5901,0.5973,0.5976,0.6002,0.6019,0.6104,0.6156,0.6178,0.6213,0.6254, 0.6279,0.6310,0.6357,0.6402,0.6421,0.6427,0.6428,0.6450,0.6512,0.6537, 0.6568,0.6576,0.6600,0.6770,0.6798,0.6809,0.6813,0.6837,0.6837,0.6854, 0.6883,0.6885,0.6893,0.6893,0.6986,0.7116,0.7187,0.7207,0.7211,0.7225, 0.7236,0.7236,0.7290,0.7310,0.7322,0.7331,0.7386,0.7430,0.7504,0.7533, 0.7566,0.7609,0.7638,0.7663,0.7759,0.7780,0.7839,0.7878,0.7885,0.7928, 0.7946,0.7956,0.7957,0.8018,0.8025,0.8127,0.8144,0.8150,0.8158,0.8162, 0.8211,0.8231,0.8241,0.8249,0.8280,0.8316,0.8421,0.8435,0.8618,0.8618, 0.8765,0.8794,0.8881,0.8886,0.8899,0.8925,0.8976,0.8996,0.9033,0.9153, 0.9155,0.9205,0.9215,0.9236,0.9280,0.9377,0.9423,0.9430,0.9439,0.9443, 0.9477,0.9491,0.9523,0.9550,0.9561,0.9620,0.9661,0.9694,0.9967, Overall p-value after applying KStest on 269 p-values = 0.357270 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.