RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-10_06:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.76 29.5724 0.970402 2 to 25 15.86 6.2327 0.008519 3 to 26 15.76 24.0933 0.883079 4 to 27 15.65 33.3971 0.989966 5 to 28 15.73 14.8840 0.396166 6 to 29 15.93 13.9348 0.328288 7 to 30 15.67 29.3258 0.968362 8 to 31 15.66 21.6497 0.801430 9 to 32 15.83 17.6611 0.589485 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.038958 Tough bday spacings test for dh-ranFile-2016-09-10_06:31: 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 38 72 88 105 88 49 27 13 9 3 (O-E)^2/E 0.1 0.1 0.0 1.0 0.5 1.2 0.2 0.3 0.2 0.9 0.3 Birthday Spacings: Sum(O-E)^2/E= 4.789, p= 0.095 RESULTS OF GCD FOR dh-ranFile-2016-09-10_06:31 Euclid's algorithm: p-value, steps to gcd: 0.448807 p-value, dist. of gcd's: 0.217898 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-10_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.891 0.133 0.922 0.241 0.115 0.908 0.862 0.890 Bits 8 to 15---> 0.120 0.401 0.240 0.738 0.629 0.367 0.435 0.500 Bits 16 to 23---> 0.906 0.155 0.627 0.113 0.887 0.302 0.209 0.065 Bits 24 to 31---> 0.552 0.219 0.761 0.620 0.876 0.418 0.806 0.445 KS test for the above 32 p values: 0.294 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-10_06:31, p-values for 5 runs: 0.8583, 0.3926, 0.6363, 0.7727, 0.6447 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-10_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 221 211.4 0.434 0.434 r= 29 5100 5134.0 0.225 0.660 r= 30 23131 23103.0 0.034 0.693 r= 31 11548 11551.5 0.001 0.694 chi-square = 0.694 with df = 3; p-value = 0.125 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-10_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 174 211.4 6.622 6.622 r= 30 5126 5134.0 0.012 6.635 r= 31 23110 23103.0 0.002 6.637 r= 32 11590 11551.5 0.128 6.765 chi-square = 6.765 with df = 3; p-value = 0.920 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-10_06:31 b-rank test for bits 1 to 8, p=0.69536 b-rank test for bits 2 to 9, p=0.00798 b-rank test for bits 3 to 10, p=0.49084 b-rank test for bits 4 to 11, p=0.90286 b-rank test for bits 5 to 12, p=0.29750 b-rank test for bits 6 to 13, p=0.55169 b-rank test for bits 7 to 14, p=0.57410 b-rank test for bits 8 to 15, p=0.00173 b-rank test for bits 9 to 16, p=0.64349 b-rank test for bits 10 to 17, p=0.91555 b-rank test for bits 11 to 18, p=0.41893 b-rank test for bits 12 to 19, p=0.63534 b-rank test for bits 13 to 20, p=0.39051 b-rank test for bits 14 to 21, p=0.79204 b-rank test for bits 15 to 22, p=0.08088 b-rank test for bits 16 to 23, p=0.79222 b-rank test for bits 17 to 24, p=0.24749 b-rank test for bits 18 to 25, p=0.70359 b-rank test for bits 19 to 26, p=0.32790 b-rank test for bits 20 to 27, p=0.49596 b-rank test for bits 21 to 28, p=0.18098 b-rank test for bits 22 to 29, p=0.36792 b-rank test for bits 23 to 30, p=0.58295 b-rank test for bits 24 to 31, p=0.66999 b-rank test for bits 25 to 32, p=0.86885 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 = 0.650746 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-10_06:31 (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 142177 0.63 0.734145 2 142800 2.08 0.981283 3 141592 -0.74 0.229218 4 141859 -0.12 0.453195 5 142625 1.67 0.952750 6 141891 -0.04 0.482920 7 141930 0.05 0.519259 8 141715 -0.45 0.324899 9 142007 0.23 0.590255 10 141785 -0.29 0.385720 11 141974 0.15 0.560051 12 141859 -0.12 0.453195 13 143007 2.56 0.994836 14 141739 -0.40 0.345327 15 141441 -1.09 0.136927 16 142190 0.66 0.744014 17 141960 0.12 0.547120 18 141632 -0.65 0.258503 19 143509 3.74 0.999907 20 142530 1.45 0.926494 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-10_06:31 Bits used No. missing words z-score p-value 23 to 32 142328 1.4437 0.925587 22 to 31 142335 1.4678 0.928924 21 to 30 142115 0.7092 0.760902 20 to 29 141266 -2.2184 0.013264 19 to 28 142491 2.0058 0.977559 18 to 27 141411 -1.7184 0.042864 17 to 26 141952 0.1471 0.558488 16 to 25 141962 0.1816 0.572060 15 to 24 142086 0.6092 0.728806 14 to 23 142062 0.5264 0.700712 13 to 22 141628 -0.9701 0.165998 12 to 21 141998 0.3058 0.620106 11 to 20 141708 -0.6942 0.243765 10 to 19 142097 0.6471 0.741229 9 to 18 142138 0.7885 0.784803 8 to 17 141482 -1.4736 0.070301 7 to 16 141424 -1.6736 0.047109 6 to 15 141862 -0.1632 0.435178 5 to 14 141693 -0.7460 0.227844 4 to 13 142450 1.8644 0.968866 3 to 12 141969 0.2058 0.581510 2 to 11 142642 2.5264 0.994239 1 to 10 142117 0.7161 0.763036 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-10_06:31 Bits used No. missing words z-score p-value 28 to 32 141532 -1.2791 0.100434 27 to 31 142414 1.7107 0.956436 26 to 30 142058 0.5040 0.692857 25 to 29 141989 0.2701 0.606446 24 to 28 141737 -0.5842 0.279553 23 to 27 141959 0.1684 0.566855 22 to 26 142227 1.0768 0.859226 21 to 25 141884 -0.0859 0.465787 20 to 24 141816 -0.3164 0.375860 19 to 23 142139 0.7785 0.781875 18 to 22 141882 -0.0926 0.463093 17 to 21 142214 1.0328 0.849147 16 to 20 142040 0.4429 0.671099 15 to 19 142411 1.7006 0.955489 14 to 18 141697 -0.7198 0.235836 13 to 17 142084 0.5921 0.723109 12 to 16 141905 -0.0147 0.494145 11 to 15 141497 -1.3977 0.081097 10 to 14 141886 -0.0791 0.468483 9 to 13 142298 1.3175 0.906169 8 to 12 142098 0.6396 0.738770 7 to 11 142611 2.3785 0.991309 6 to 10 141818 -0.3096 0.378435 5 to 9 141939 0.1006 0.540057 4 to 8 142050 0.4768 0.683265 3 to 7 141658 -0.8520 0.197116 2 to 6 142294 1.3040 0.903877 1 to 5 141944 0.1175 0.546778 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-10_06:31 Bits used No. missing words z-score p-value 31 to 32 142350 1.2999 0.903184 30 to 31 142328 1.2350 0.891588 29 to 30 141870 -0.1160 0.453819 28 to 29 142570 1.9489 0.974345 27 to 28 142074 0.4858 0.686429 26 to 27 141637 -0.8033 0.210891 25 to 26 141637 -0.8033 0.210891 24 to 25 142165 0.7542 0.774632 23 to 24 141601 -0.9095 0.181536 22 to 23 142045 0.4002 0.655498 21 to 22 141837 -0.2134 0.415522 20 to 21 141964 0.1613 0.564059 19 to 20 141615 -0.8682 0.192634 18 to 19 142155 0.7247 0.765679 17 to 18 142458 1.6185 0.947222 16 to 17 142110 0.5919 0.723057 15 to 16 142039 0.3825 0.648958 14 to 15 141957 0.1406 0.555915 13 to 14 141468 -1.3019 0.096482 12 to 13 141743 -0.4906 0.311837 11 to 12 142381 1.3914 0.917941 10 to 11 141879 -0.0895 0.464355 9 to 10 141474 -1.2842 0.099543 8 to 9 141684 -0.6647 0.253124 7 to 8 142236 0.9636 0.832384 6 to 7 142090 0.5329 0.702966 5 to 6 142141 0.6834 0.752821 4 to 5 142351 1.3029 0.903689 3 to 4 142065 0.4592 0.676956 2 to 3 141715 -0.5732 0.283240 1 to 2 141514 -1.1662 0.121774 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-10_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2439.65 -0.853 0.196699 Test results for specific bytes for dh-ranFile-2016-09-10_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2586.40 1.222 0.889113 2 to 9 2644.60 2.045 0.979569 3 to 10 2509.94 0.141 0.555878 4 to 11 2483.11 -0.239 0.405609 5 to 12 2558.07 0.821 0.794263 6 to 13 2563.69 0.901 0.816137 7 to 14 2520.36 0.288 0.613277 8 to 15 2464.82 -0.498 0.309400 9 to 16 2465.05 -0.494 0.310564 10 to 17 2627.89 1.809 0.964751 11 to 18 2594.33 1.334 0.908892 12 to 19 2586.76 1.227 0.890087 13 to 20 2655.96 2.206 0.986297 14 to 21 2635.18 1.912 0.972048 15 to 22 2409.72 -1.277 0.100850 16 to 23 2380.73 -1.687 0.045832 17 to 24 2575.20 1.064 0.856225 18 to 25 2460.78 -0.555 0.289548 19 to 26 2510.97 0.155 0.561658 20 to 27 2504.42 0.063 0.524942 21 to 28 2460.62 -0.557 0.288808 22 to 29 2444.63 -0.783 0.216778 23 to 30 2427.85 -1.020 0.153768 24 to 31 2552.14 0.737 0.769541 25 to 32 2485.01 -0.212 0.416067 CDPARK for dh-ranFile-2016-09-10_06:31: 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 3489 -1.5525 0.060270 3510 -0.5936 0.276387 3473 -2.2831 0.011212 3476 -2.1461 0.015932 3534 0.5023 0.692266 3555 1.4612 0.928018 3522 -0.0457 0.481790 3507 -0.7306 0.232514 3533 0.4566 0.676028 3538 0.6849 0.753306 Square side=100, avg. no. parked=3513.70 sample std.=26.26 p-value of the KSTEST for those 10 p-values: 0.247042 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-10_06:31 0.7321,0.1166,0.3835,0.2983,0.4919,0.7519,0.8237,0.2245,0.8930,0.3883, The KS test for those 10 p-values: 0.945874 The 3DSPHERES test for dh-ranFile-2016-09-10_06:31 sample no r^3 equiv. uni. 1 8.844 0.255313 2 15.577 0.405018 3 4.301 0.133549 4 5.547 0.168807 5 25.561 0.573458 6 73.406 0.913435 7 3.565 0.112045 8 29.055 0.620348 9 44.378 0.772194 10 5.621 0.170871 11 158.860 0.994985 12 92.816 0.954674 13 52.471 0.826058 14 22.237 0.523467 15 11.754 0.324165 16 31.831 0.653903 17 1.874 0.060559 18 94.972 0.957816 19 35.296 0.691652 20 18.293 0.456520 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.827524 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-10_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.3 -0.1 -0.5 -2.2 -0.4 0.1 -0.5 0.4 1.6 0.8 0.1 -1.0 1.4 -0.1 -0.1 0.4 -1.4 -2.0 1.4 -0.9 -0.3 2.1 0.3 -0.1 0.3 -0.0 -0.7 -0.3 -0.2 0.1 0.4 -1.5 1.4 -1.7 1.0 -0.5 0.5 -1.2 -0.1 -0.6 1.0 -0.1 Chi-square with 42 degrees of freedom:39.912216 z-score=-0.227796, p-value=0.437008 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-10_06:31 Test no p-value 1 0.470767 2 0.830798 3 0.516264 4 0.760581 5 0.425406 6 0.932337 7 0.445401 8 0.139385 9 0.143165 10 0.883391 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.789193 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-10_06:31: (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 66479 0.53 66767 0.15 3 25000.00 25088 0.31 24979 0.02 4 6666.67 6729 0.58 6580 1.13 5 1388.89 1423 0.84 1400 0.09 6 238.10 225 0.72 239 0.00 7 34.72 50 6.72 31 0.40 8 4.96 5 0.00 3 0.77 p=0.86230 p=0.13840 Number of rngs required: 688559, p-value: 0.571 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-10_06:31 No. of wins: Observed Expected 98801 98585.9 z-score= 0.962, pvalue=0.83203 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66845 66666.7 0.477 0.477 2 37844 37654.3 0.955 1.433 3 26719 26954.7 2.062 3.494 4 19291 19313.5 0.026 3.520 5 13869 13851.4 0.022 3.543 6 9945 9943.5 0.000 3.543 7 7058 7145.0 1.060 4.603 8 5117 5139.1 0.095 4.698 9 3749 3699.9 0.653 5.350 10 2630 2666.3 0.494 5.844 11 1948 1923.3 0.316 6.161 12 1377 1388.7 0.099 6.260 13 964 1003.7 1.571 7.831 14 747 726.1 0.599 8.431 15 505 525.8 0.826 9.256 16 391 381.2 0.255 9.511 17 269 276.5 0.206 9.716 18 203 200.8 0.023 9.740 19 142 146.0 0.109 9.848 20 89 106.2 2.790 12.639 21 298 287.1 0.413 13.051 Chisq= 13.05 for 20 degrees of freedom, p= 0.12483 SUMMARY of craptest p-value for no. of wins: 0.832035 p-value for throws/game: 0.124833 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-10_06:31 No. of wins: Observed Expected 98880 98585.9 z-score= 1.316, pvalue=0.90584 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67036 66666.7 2.046 2.046 2 37526 37654.3 0.437 2.483 3 26885 26954.7 0.180 2.664 4 19322 19313.5 0.004 2.668 5 13822 13851.4 0.062 2.730 6 9868 9943.5 0.574 3.304 7 7276 7145.0 2.401 5.705 8 5145 5139.1 0.007 5.712 9 3619 3699.9 1.767 7.479 10 2692 2666.3 0.248 7.727 11 1891 1923.3 0.543 8.270 12 1330 1388.7 2.485 10.755 13 943 1003.7 3.673 14.428 14 750 726.1 0.784 15.211 15 512 525.8 0.364 15.576 16 408 381.2 1.891 17.467 17 263 276.5 0.663 18.130 18 189 200.8 0.697 18.827 19 129 146.0 1.976 20.803 20 122 106.2 2.346 23.148 21 272 287.1 0.796 23.944 Chisq= 23.94 for 20 degrees of freedom, p= 0.75516 SUMMARY of craptest p-value for no. of wins: 0.905841 p-value for throws/game: 0.755156 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0017,0.0080,0.0085,0.0112,0.0133,0.0159,0.0390,0.0429,0.0458,0.0471, 0.0603,0.0606,0.0650,0.0703,0.0809,0.0811,0.0952,0.0965,0.0995,0.1004, 0.1009,0.1120,0.1129,0.1148,0.1166,0.1200,0.1218,0.1248,0.1255,0.1329, 0.1335,0.1369,0.1384,0.1394,0.1432,0.1538,0.1548,0.1660,0.1688,0.1709, 0.1810,0.1815,0.1926,0.1967,0.1971,0.2093,0.2109,0.2109,0.2168,0.2179, 0.2190,0.2245,0.2278,0.2292,0.2325,0.2358,0.2403,0.2412,0.2438,0.2470, 0.2475,0.2531,0.2553,0.2585,0.2764,0.2796,0.2832,0.2888,0.2895,0.2937, 0.2975,0.2983,0.3024,0.3094,0.3106,0.3118,0.3242,0.3249,0.3279,0.3283, 0.3453,0.3667,0.3679,0.3759,0.3784,0.3835,0.3857,0.3883,0.3905,0.3926, 0.3962,0.4006,0.4050,0.4056,0.4155,0.4161,0.4179,0.4189,0.4254,0.4346, 0.4352,0.4370,0.4454,0.4454,0.4488,0.4532,0.4532,0.4538,0.4565,0.4631, 0.4644,0.4658,0.4685,0.4708,0.4818,0.4829,0.4908,0.4919,0.4941,0.4960, 0.5004,0.5163,0.5193,0.5235,0.5249,0.5401,0.5468,0.5471,0.5517,0.5517, 0.5559,0.5559,0.5585,0.5601,0.5617,0.5641,0.5669,0.5712,0.5721,0.5735, 0.5741,0.5815,0.5830,0.5895,0.5903,0.6064,0.6133,0.6196,0.6201,0.6203, 0.6269,0.6295,0.6353,0.6363,0.6435,0.6447,0.6490,0.6507,0.6539,0.6555, 0.6700,0.6711,0.6760,0.6770,0.6833,0.6864,0.6917,0.6923,0.6929,0.6954, 0.7007,0.7030,0.7036,0.7231,0.7231,0.7288,0.7321,0.7341,0.7378,0.7388, 0.7412,0.7440,0.7519,0.7528,0.7533,0.7552,0.7606,0.7609,0.7611,0.7630, 0.7657,0.7695,0.7722,0.7727,0.7746,0.7819,0.7848,0.7892,0.7920,0.7922, 0.7943,0.8014,0.8062,0.8161,0.8237,0.8261,0.8275,0.8308,0.8320,0.8324, 0.8491,0.8562,0.8583,0.8592,0.8623,0.8625,0.8689,0.8761,0.8831,0.8834, 0.8872,0.8891,0.8899,0.8901,0.8914,0.8916,0.8930,0.9029,0.9032,0.9037, 0.9039,0.9058,0.9059,0.9062,0.9085,0.9089,0.9134,0.9156,0.9179,0.9202, 0.9221,0.9256,0.9265,0.9280,0.9289,0.9323,0.9459,0.9472,0.9528,0.9547, 0.9555,0.9564,0.9578,0.9648,0.9684,0.9689,0.9704,0.9720,0.9743,0.9776, 0.9796,0.9813,0.9863,0.9900,0.9913,0.9942,0.9948,0.9950,0.9999, Overall p-value after applying KStest on 269 p-values = 0.010428 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.