RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-09_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.46 30.0407 0.973947 2 to 25 15.76 18.1618 0.621299 3 to 26 15.60 18.6716 0.652296 4 to 27 15.33 32.3061 0.986217 5 to 28 15.63 29.2680 0.967866 6 to 29 15.92 13.3653 0.288588 7 to 30 15.61 23.4164 0.863820 8 to 31 15.75 20.2043 0.736085 9 to 32 16.06 5.4132 0.003660 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.027688 Tough bday spacings test for dh-ranFile-2015-09-09_08:31: 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 5 35 75 88 97 89 51 31 20 8 1 (O-E)^2/E 1.9 0.1 0.0 1.0 0.0 1.5 0.0 0.1 1.8 0.3 2.3 Birthday Spacings: Sum(O-E)^2/E= 8.907, p= 0.459 RESULTS OF GCD FOR dh-ranFile-2015-09-09_08:31 Euclid's algorithm: p-value, steps to gcd: 0.472613 p-value, dist. of gcd's: 0.766543 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-09_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.954 0.304 0.619 0.293 0.579 0.558 0.889 0.739 Bits 8 to 15---> 0.522 0.285 0.410 0.097 0.879 0.080 0.775 0.487 Bits 16 to 23---> 0.928 0.669 0.292 0.984 0.593 0.416 0.987 0.755 Bits 24 to 31---> 0.500 0.153 0.127 0.019 0.223 0.750 0.214 0.897 KS test for the above 32 p values: 0.117 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-09_08:31, p-values for 5 runs: 0.0689, 0.5602, 0.3310, 0.3385, 0.7854 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-09_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 202 211.4 0.420 0.420 r= 29 5142 5134.0 0.012 0.432 r= 30 23127 23103.0 0.025 0.457 r= 31 11529 11551.5 0.044 0.501 chi-square = 0.501 with df = 3; p-value = 0.081 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-09_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 231 211.4 1.814 1.814 r= 30 5248 5134.0 2.531 4.345 r= 31 22996 23103.0 0.496 4.841 r= 32 11525 11551.5 0.061 4.902 chi-square = 4.902 with df = 3; p-value = 0.821 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-09_08:31 b-rank test for bits 1 to 8, p=0.77401 b-rank test for bits 2 to 9, p=0.04517 b-rank test for bits 3 to 10, p=0.16296 b-rank test for bits 4 to 11, p=0.26968 b-rank test for bits 5 to 12, p=0.75714 b-rank test for bits 6 to 13, p=0.72433 b-rank test for bits 7 to 14, p=0.13403 b-rank test for bits 8 to 15, p=0.44716 b-rank test for bits 9 to 16, p=0.28344 b-rank test for bits 10 to 17, p=0.86066 b-rank test for bits 11 to 18, p=0.24111 b-rank test for bits 12 to 19, p=0.31649 b-rank test for bits 13 to 20, p=0.26663 b-rank test for bits 14 to 21, p=0.83159 b-rank test for bits 15 to 22, p=0.48857 b-rank test for bits 16 to 23, p=0.29817 b-rank test for bits 17 to 24, p=0.15643 b-rank test for bits 18 to 25, p=0.86756 b-rank test for bits 19 to 26, p=0.22148 b-rank test for bits 20 to 27, p=0.20049 b-rank test for bits 21 to 28, p=0.36870 b-rank test for bits 22 to 29, p=0.14229 b-rank test for bits 23 to 30, p=0.43684 b-rank test for bits 24 to 31, p=0.44073 b-rank test for bits 25 to 32, p=0.86686 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 = 0.165399 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-09_08:31 (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 141720 -0.44 0.329114 2 141847 -0.15 0.442106 3 141285 -1.46 0.072322 4 141717 -0.45 0.326583 5 141457 -1.06 0.145291 6 142533 1.46 0.927466 7 141629 -0.65 0.256241 8 141976 0.16 0.561893 9 142384 1.11 0.866294 10 141914 0.01 0.504353 11 141978 0.16 0.563734 12 141605 -0.71 0.238526 13 141946 0.09 0.534139 14 142248 0.79 0.785611 15 142092 0.43 0.665237 16 142210 0.70 0.758816 17 141910 0.00 0.500625 18 142017 0.25 0.599312 19 141512 -0.93 0.176615 20 142126 0.51 0.693655 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-09_08:31 Bits used No. missing words z-score p-value 23 to 32 141431 -1.6494 0.049531 22 to 31 141547 -1.2494 0.105757 21 to 30 141807 -0.3529 0.362096 20 to 29 142040 0.4506 0.673856 19 to 28 141885 -0.0839 0.466569 18 to 27 142422 1.7678 0.961455 17 to 26 142046 0.4713 0.681278 16 to 25 141542 -1.2667 0.102639 15 to 24 141787 -0.4218 0.336575 14 to 23 142291 1.3161 0.905930 13 to 22 142492 2.0092 0.977742 12 to 21 142144 0.8092 0.790802 11 to 20 141264 -2.2253 0.013031 10 to 19 142394 1.6713 0.952666 9 to 18 141586 -1.1149 0.132440 8 to 17 141849 -0.2080 0.417601 7 to 16 141801 -0.3736 0.354369 6 to 15 142279 1.2747 0.898797 5 to 14 141937 0.0954 0.538007 4 to 13 141915 0.0196 0.507800 3 to 12 141836 -0.2529 0.400187 2 to 11 141894 -0.0529 0.478921 1 to 10 141756 -0.5287 0.298498 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-09_08:31 Bits used No. missing words z-score p-value 28 to 32 142031 0.4124 0.659992 27 to 31 141918 0.0294 0.511723 26 to 30 141815 -0.3198 0.374574 25 to 29 141968 0.1989 0.578822 24 to 28 142319 1.3887 0.917540 23 to 27 141921 0.0396 0.515778 22 to 26 141778 -0.4452 0.328093 21 to 25 141975 0.2226 0.588081 20 to 24 141765 -0.4893 0.312331 19 to 23 141563 -1.1740 0.120198 18 to 22 141954 0.1514 0.560179 17 to 21 141648 -0.8859 0.187845 16 to 20 141940 0.1040 0.541402 15 to 19 141992 0.2802 0.610352 14 to 18 141540 -1.2520 0.105291 13 to 17 141839 -0.2384 0.405783 12 to 16 142040 0.4429 0.671099 11 to 15 142096 0.6328 0.736561 10 to 14 141994 0.2870 0.612950 9 to 13 141983 0.2497 0.598602 8 to 12 142002 0.3141 0.623291 7 to 11 142151 0.8192 0.793670 6 to 10 141557 -1.1943 0.116173 5 to 9 141734 -0.5943 0.276143 4 to 8 141783 -0.4282 0.334239 3 to 7 142218 1.0463 0.852298 2 to 6 141716 -0.6554 0.256119 1 to 5 141751 -0.5367 0.295733 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-09_08:31 Bits used No. missing words z-score p-value 31 to 32 142204 0.8692 0.807640 30 to 31 142276 1.0816 0.860290 29 to 30 142047 0.4061 0.657668 28 to 29 141730 -0.5290 0.298404 27 to 28 142388 1.4120 0.921026 26 to 27 142175 0.7837 0.783388 25 to 26 141876 -0.0983 0.460840 24 to 25 142171 0.7719 0.779910 23 to 24 142321 1.2144 0.887696 22 to 23 141959 0.1465 0.558244 21 to 22 141782 -0.3756 0.353605 20 to 21 142326 1.2291 0.890486 19 to 20 141577 -0.9803 0.163463 18 to 19 141450 -1.3550 0.087716 17 to 18 142526 1.8191 0.965551 16 to 17 141886 -0.0688 0.472566 15 to 16 142055 0.4297 0.666295 14 to 15 141801 -0.3196 0.374652 13 to 14 141812 -0.2871 0.387014 12 to 13 141929 0.0580 0.523135 11 to 12 142086 0.5212 0.698869 10 to 11 142183 0.8073 0.790249 9 to 10 141666 -0.7178 0.236444 8 to 9 142315 1.1967 0.884282 7 to 8 141814 -0.2812 0.389275 6 to 7 142204 0.8692 0.807640 5 to 6 142106 0.5801 0.719092 4 to 5 141994 0.2498 0.598615 3 to 4 141982 0.2144 0.584869 2 to 3 142135 0.6657 0.747196 1 to 2 141741 -0.4965 0.309754 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-09_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2611.61 1.578 0.942759 Test results for specific bytes for dh-ranFile-2015-09-09_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2502.61 0.037 0.514734 2 to 9 2508.03 0.114 0.545183 3 to 10 2477.29 -0.321 0.374067 4 to 11 2487.20 -0.181 0.428165 5 to 12 2496.99 -0.042 0.483051 6 to 13 2503.27 0.046 0.518427 7 to 14 2558.28 0.824 0.795091 8 to 15 2405.78 -1.332 0.091358 9 to 16 2449.54 -0.714 0.237728 10 to 17 2549.02 0.693 0.755932 11 to 18 2387.83 -1.586 0.056340 12 to 19 2503.23 0.046 0.518196 13 to 20 2438.18 -0.874 0.190993 14 to 21 2404.48 -1.351 0.088373 15 to 22 2529.76 0.421 0.663056 16 to 23 2570.00 0.990 0.838916 17 to 24 2600.27 1.418 0.921899 18 to 25 2539.38 0.557 0.711210 19 to 26 2468.77 -0.442 0.329390 20 to 27 2603.47 1.463 0.928303 21 to 28 2367.42 -1.875 0.030394 22 to 29 2540.16 0.568 0.714988 23 to 30 2529.82 0.422 0.663400 24 to 31 2554.33 0.768 0.778879 25 to 32 2638.27 1.955 0.974730 CDPARK for dh-ranFile-2015-09-09_08:31: 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 3538 0.6849 0.753306 3561 1.7352 0.958644 3498 -1.1416 0.126820 3579 2.5571 0.994722 3548 1.1416 0.873180 3492 -1.4155 0.078457 3474 -2.2374 0.012629 3516 -0.3196 0.374623 3491 -1.4612 0.071982 3556 1.5068 0.934075 Square side=100, avg. no. parked=3525.30 sample std.=33.95 p-value of the KSTEST for those 10 p-values: 0.090512 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-09_08:31 0.0917,0.4636,0.6173,0.1380,0.8310,0.9863,0.0801,0.1164,0.3081,0.0853, The KS test for those 10 p-values: 0.115217 The 3DSPHERES test for dh-ranFile-2015-09-09_08:31 sample no r^3 equiv. uni. 1 13.039 0.352489 2 28.485 0.613069 3 2.370 0.075959 4 20.252 0.490879 5 20.273 0.491227 6 2.224 0.071446 7 5.701 0.173077 8 38.237 0.720444 9 25.972 0.579252 10 56.992 0.850394 11 12.053 0.330864 12 16.430 0.421694 13 36.399 0.702788 14 8.964 0.258296 15 12.086 0.331600 16 10.971 0.306283 17 24.353 0.555926 18 40.578 0.741431 19 97.265 0.960920 20 37.032 0.708995 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.771021 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-09_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 0.3 -0.5 -0.9 0.0 0.8 0.5 -0.1 0.3 0.6 -0.1 -0.4 -0.5 0.5 -0.8 1.1 -0.2 -1.2 1.2 0.2 -1.8 1.0 -1.5 -0.2 0.7 0.4 1.7 0.4 -0.8 -0.5 0.7 0.9 -0.4 2.3 -1.0 1.2 -1.7 -0.8 -1.8 0.1 1.0 -1.1 Chi-square with 42 degrees of freedom:38.402817 z-score=-0.392485, p-value=0.370347 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-09_08:31 Test no p-value 1 0.161662 2 0.765898 3 0.265788 4 0.661288 5 0.241486 6 0.065539 7 0.775161 8 0.118716 9 0.309980 10 0.295302 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.191290 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-09_08:31: (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 66887 0.73 66714 0.03 3 25000.00 24757 2.36 25026 0.03 4 6666.67 6628 0.22 6639 0.11 5 1388.89 1451 2.78 1355 0.83 6 238.10 240 0.02 225 0.72 7 34.72 34 0.01 37 0.15 8 4.96 2 1.77 3 0.77 p=0.75362 p=0.14832 Number of rngs required: 688091, p-value: 0.360 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-09_08:31 No. of wins: Observed Expected 98457 98585.9 z-score=-0.576, pvalue=0.28220 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66662 66666.7 0.000 0.000 2 37873 37654.3 1.270 1.270 3 26856 26954.7 0.362 1.632 4 19185 19313.5 0.854 2.486 5 13855 13851.4 0.001 2.487 6 9911 9943.5 0.107 2.594 7 7177 7145.0 0.143 2.737 8 5197 5139.1 0.653 3.390 9 3695 3699.9 0.006 3.396 10 2570 2666.3 3.478 6.874 11 1915 1923.3 0.036 6.910 12 1394 1388.7 0.020 6.930 13 1001 1003.7 0.007 6.938 14 754 726.1 1.069 8.006 15 507 525.8 0.675 8.681 16 406 381.2 1.620 10.301 17 288 276.5 0.475 10.776 18 183 200.8 1.583 12.359 19 125 146.0 3.016 15.376 20 105 106.2 0.014 15.389 21 341 287.1 10.113 25.503 Chisq= 25.50 for 20 degrees of freedom, p= 0.81713 SUMMARY of craptest p-value for no. of wins: 0.282196 p-value for throws/game: 0.817133 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-09_08:31 No. of wins: Observed Expected 98670 98585.9 z-score= 0.376, pvalue=0.64666 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66762 66666.7 0.136 0.136 2 37869 37654.3 1.224 1.360 3 27035 26954.7 0.239 1.599 4 19041 19313.5 3.844 5.443 5 13910 13851.4 0.248 5.691 6 9886 9943.5 0.333 6.024 7 7162 7145.0 0.040 6.064 8 5097 5139.1 0.344 6.409 9 3713 3699.9 0.047 6.455 10 2619 2666.3 0.839 7.294 11 1893 1923.3 0.478 7.772 12 1407 1388.7 0.240 8.013 13 930 1003.7 5.414 13.426 14 772 726.1 2.896 16.323 15 506 525.8 0.748 17.071 16 363 381.2 0.864 17.935 17 281 276.5 0.072 18.007 18 215 200.8 1.000 19.007 19 158 146.0 0.989 19.996 20 101 106.2 0.256 20.252 21 280 287.1 0.176 20.428 Chisq= 20.43 for 20 degrees of freedom, p= 0.56856 SUMMARY of craptest p-value for no. of wins: 0.646664 p-value for throws/game: 0.568556 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0037,0.0126,0.0130,0.0187,0.0277,0.0304,0.0452,0.0495,0.0563,0.0655, 0.0689,0.0714,0.0720,0.0723,0.0760,0.0785,0.0797,0.0801,0.0813,0.0853, 0.0877,0.0884,0.0905,0.0914,0.0917,0.0967,0.1026,0.1053,0.1058,0.1152, 0.1162,0.1164,0.1169,0.1187,0.1202,0.1267,0.1268,0.1324,0.1340,0.1380, 0.1423,0.1453,0.1483,0.1526,0.1564,0.1617,0.1630,0.1635,0.1654,0.1731, 0.1766,0.1878,0.1910,0.1913,0.2005,0.2136,0.2215,0.2231,0.2364,0.2377, 0.2385,0.2411,0.2415,0.2561,0.2562,0.2583,0.2658,0.2666,0.2697,0.2761, 0.2822,0.2834,0.2847,0.2886,0.2924,0.2926,0.2953,0.2957,0.2982,0.2984, 0.2985,0.3043,0.3063,0.3081,0.3098,0.3100,0.3123,0.3165,0.3266,0.3281, 0.3291,0.3294,0.3309,0.3310,0.3316,0.3342,0.3366,0.3385,0.3525,0.3536, 0.3544,0.3597,0.3621,0.3687,0.3703,0.3741,0.3746,0.3746,0.3747,0.3870, 0.3893,0.4002,0.4058,0.4099,0.4158,0.4176,0.4217,0.4282,0.4368,0.4407, 0.4421,0.4472,0.4590,0.4608,0.4636,0.4666,0.4726,0.4726,0.4789,0.4831, 0.4874,0.4886,0.4909,0.4912,0.4999,0.5006,0.5044,0.5078,0.5117,0.5147, 0.5158,0.5182,0.5184,0.5225,0.5231,0.5341,0.5380,0.5414,0.5452,0.5559, 0.5579,0.5582,0.5602,0.5602,0.5619,0.5637,0.5686,0.5788,0.5792,0.5793, 0.5849,0.5881,0.5931,0.5986,0.5986,0.5993,0.6104,0.6130,0.6131,0.6173, 0.6195,0.6213,0.6233,0.6467,0.6523,0.6577,0.6600,0.6613,0.6631,0.6634, 0.6652,0.6663,0.6686,0.6711,0.6739,0.6813,0.6937,0.6989,0.7028,0.7090, 0.7112,0.7150,0.7191,0.7204,0.7243,0.7361,0.7366,0.7392,0.7414,0.7472, 0.7502,0.7533,0.7536,0.7552,0.7559,0.7571,0.7588,0.7659,0.7665,0.7710, 0.7740,0.7752,0.7753,0.7789,0.7799,0.7834,0.7854,0.7856,0.7902,0.7908, 0.7937,0.7951,0.8076,0.8076,0.8171,0.8208,0.8310,0.8316,0.8389,0.8504, 0.8523,0.8603,0.8607,0.8638,0.8663,0.8669,0.8676,0.8732,0.8789,0.8843, 0.8877,0.8889,0.8905,0.8967,0.8988,0.9059,0.9175,0.9210,0.9219,0.9275, 0.9278,0.9283,0.9341,0.9428,0.9527,0.9542,0.9586,0.9609,0.9615,0.9656, 0.9679,0.9739,0.9747,0.9777,0.9837,0.9862,0.9863,0.9866,0.9947, Overall p-value after applying KStest on 269 p-values = 0.915842 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.