RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-17_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.93 11.2715 0.157895 2 to 25 16.04 26.6799 0.937068 3 to 26 15.72 17.7606 0.595906 4 to 27 15.67 16.0967 0.483006 5 to 28 15.67 19.8475 0.717895 6 to 29 15.60 33.6457 0.990675 7 to 30 15.67 24.1240 0.883895 8 to 31 15.82 23.9087 0.878063 9 to 32 15.71 14.8250 0.391916 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.107789 Tough bday spacings test for dh-ranFile-2016-01-17_11:31: 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 11 45 69 105 87 74 56 25 19 7 2 (O-E)^2/E 0.4 1.9 0.2 0.5 1.2 0.2 0.3 0.8 1.1 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 7.733, p= 0.345 RESULTS OF GCD FOR dh-ranFile-2016-01-17_11:31 Euclid's algorithm: p-value, steps to gcd: 0.123459 p-value, dist. of gcd's: 0.301432 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-17_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.390 0.890 0.034 0.037 0.648 0.420 0.099 0.490 Bits 8 to 15---> 0.982 0.635 0.263 0.769 0.251 0.467 0.300 0.076 Bits 16 to 23---> 0.598 0.926 0.329 0.388 0.075 0.267 0.264 0.318 Bits 24 to 31---> 0.078 0.770 0.453 0.124 0.071 0.287 0.184 0.736 KS test for the above 32 p values: 0.945 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-17_11:31, p-values for 5 runs: 0.0083, 0.8891, 0.9632, 0.6187, 0.3211 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-17_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 201 211.4 0.513 0.513 r= 29 5036 5134.0 1.871 2.384 r= 30 23289 23103.0 1.497 3.881 r= 31 11474 11551.5 0.520 4.401 chi-square = 4.401 with df = 3; p-value = 0.779 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-17_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 193 211.4 1.605 1.605 r= 30 5233 5134.0 1.909 3.513 r= 31 23057 23103.0 0.092 3.605 r= 32 11517 11551.5 0.103 3.708 chi-square = 3.708 with df = 3; p-value = 0.705 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-17_11:31 b-rank test for bits 1 to 8, p=0.43867 b-rank test for bits 2 to 9, p=0.34214 b-rank test for bits 3 to 10, p=0.72138 b-rank test for bits 4 to 11, p=0.71332 b-rank test for bits 5 to 12, p=0.06297 b-rank test for bits 6 to 13, p=0.00215 b-rank test for bits 7 to 14, p=0.39922 b-rank test for bits 8 to 15, p=0.72759 b-rank test for bits 9 to 16, p=0.93420 b-rank test for bits 10 to 17, p=0.73444 b-rank test for bits 11 to 18, p=0.29702 b-rank test for bits 12 to 19, p=0.23000 b-rank test for bits 13 to 20, p=0.29553 b-rank test for bits 14 to 21, p=0.12362 b-rank test for bits 15 to 22, p=0.16071 b-rank test for bits 16 to 23, p=0.89229 b-rank test for bits 17 to 24, p=0.27396 b-rank test for bits 18 to 25, p=0.04346 b-rank test for bits 19 to 26, p=0.11073 b-rank test for bits 20 to 27, p=0.45001 b-rank test for bits 21 to 28, p=0.66531 b-rank test for bits 22 to 29, p=0.66101 b-rank test for bits 23 to 30, p=0.78930 b-rank test for bits 24 to 31, p=0.13021 b-rank test for bits 25 to 32, p=0.10597 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 = 0.177720 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-17_11:31 (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 141787 -0.29 0.387509 2 141486 -0.99 0.161310 3 142439 1.24 0.892058 4 141510 -0.93 0.175406 5 141962 0.12 0.548971 6 141434 -1.11 0.133374 7 141837 -0.17 0.432900 8 141963 0.13 0.549895 9 141628 -0.66 0.255490 10 142568 1.54 0.938092 11 142603 1.62 0.947462 12 141871 -0.09 0.464320 13 141580 -0.77 0.220809 14 142141 0.54 0.705844 15 141519 -0.91 0.180888 16 142231 0.75 0.773844 17 142358 1.05 0.852749 18 142121 0.49 0.689543 19 141980 0.17 0.565574 20 142325 0.97 0.834274 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-17_11:31 Bits used No. missing words z-score p-value 23 to 32 141303 -2.0908 0.018273 22 to 31 142131 0.7644 0.777679 21 to 30 141655 -0.8770 0.190243 20 to 29 142130 0.7609 0.776651 19 to 28 141691 -0.7529 0.225766 18 to 27 141854 -0.1908 0.424344 17 to 26 141548 -1.2460 0.106389 16 to 25 141595 -1.0839 0.139205 15 to 24 142038 0.4437 0.671367 14 to 23 141828 -0.2804 0.389567 13 to 22 141801 -0.3736 0.354369 12 to 21 141719 -0.6563 0.255812 11 to 20 141454 -1.5701 0.058196 10 to 19 141528 -1.3149 0.094267 9 to 18 141519 -1.3460 0.089157 8 to 17 142329 1.4471 0.926071 7 to 16 141782 -0.4391 0.330306 6 to 15 141686 -0.7701 0.220619 5 to 14 141414 -1.7080 0.043815 4 to 13 141325 -2.0149 0.021956 3 to 12 141903 -0.0218 0.491293 2 to 11 141641 -0.9253 0.177411 1 to 10 141949 0.1368 0.554403 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-17_11:31 Bits used No. missing words z-score p-value 28 to 32 141802 -0.3638 0.357992 27 to 31 142366 1.5480 0.939193 26 to 30 142242 1.1277 0.870276 25 to 29 141851 -0.1977 0.421629 24 to 28 141858 -0.1740 0.430933 23 to 27 141430 -1.6248 0.052098 22 to 26 142033 0.4192 0.662473 21 to 25 142103 0.6565 0.744252 20 to 24 141585 -1.0994 0.135792 19 to 23 141897 -0.0418 0.483330 18 to 22 141838 -0.2418 0.404469 17 to 21 141745 -0.5571 0.288746 16 to 20 141706 -0.6893 0.245332 15 to 19 142103 0.6565 0.744252 14 to 18 142353 1.5040 0.933705 13 to 17 141951 0.1413 0.556166 12 to 16 142084 0.5921 0.723109 11 to 15 142101 0.6497 0.742066 10 to 14 142601 2.3446 0.990477 9 to 13 141614 -1.0011 0.158385 8 to 12 141792 -0.3977 0.345415 7 to 11 141758 -0.5130 0.303982 6 to 10 142060 0.5107 0.695236 5 to 9 141910 0.0023 0.500906 4 to 8 141900 -0.0316 0.487385 3 to 7 141912 0.0091 0.503611 2 to 6 141930 0.0701 0.527930 1 to 5 142406 1.6836 0.953873 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-17_11:31 Bits used No. missing words z-score p-value 31 to 32 141618 -0.8594 0.195065 30 to 31 141742 -0.4936 0.310795 29 to 30 142121 0.6244 0.733816 28 to 29 142036 0.3737 0.645671 27 to 28 141617 -0.8623 0.194253 26 to 27 142027 0.3471 0.635745 25 to 26 142340 1.2704 0.898031 24 to 25 142117 0.6126 0.729928 23 to 24 141806 -0.3048 0.380256 22 to 23 141959 0.1465 0.558244 21 to 22 141831 -0.2311 0.408633 20 to 21 141773 -0.4022 0.343786 19 to 20 142521 1.8043 0.964411 18 to 19 141761 -0.4376 0.330856 17 to 18 141946 0.1082 0.543070 16 to 17 141306 -1.7797 0.037560 15 to 16 141890 -0.0570 0.477264 14 to 15 141838 -0.2104 0.416673 13 to 14 141924 0.0433 0.517259 12 to 13 142287 1.1141 0.867376 11 to 12 142050 0.4150 0.660913 10 to 11 141800 -0.3225 0.373534 9 to 10 141734 -0.5172 0.302509 8 to 9 141733 -0.5201 0.301480 7 to 8 142313 1.1908 0.883127 6 to 7 142268 1.0580 0.854978 5 to 6 142289 1.1200 0.868637 4 to 5 142052 0.4209 0.663070 3 to 4 142328 1.2350 0.891588 2 to 3 141982 0.2144 0.584869 1 to 2 142357 1.3206 0.906676 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-17_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2421.20 -1.114 0.132554 Test results for specific bytes for dh-ranFile-2016-01-17_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2455.63 -0.627 0.265178 2 to 9 2528.00 0.396 0.653930 3 to 10 2512.25 0.173 0.568773 4 to 11 2459.22 -0.577 0.282079 5 to 12 2441.81 -0.823 0.205260 6 to 13 2406.65 -1.320 0.093399 7 to 14 2414.51 -1.209 0.113335 8 to 15 2515.41 0.218 0.586234 9 to 16 2446.78 -0.753 0.225826 10 to 17 2393.76 -1.502 0.066495 11 to 18 2531.06 0.439 0.669738 12 to 19 2589.35 1.264 0.896812 13 to 20 2394.53 -1.492 0.067902 14 to 21 2555.77 0.789 0.784841 15 to 22 2426.94 -1.033 0.150753 16 to 23 2525.08 0.355 0.638584 17 to 24 2444.11 -0.790 0.214661 18 to 25 2595.10 1.345 0.910666 19 to 26 2473.76 -0.371 0.355284 20 to 27 2488.01 -0.170 0.432661 21 to 28 2429.29 -1.000 0.158674 22 to 29 2481.34 -0.264 0.395951 23 to 30 2402.29 -1.382 0.083507 24 to 31 2471.46 -0.404 0.343227 25 to 32 2683.44 2.594 0.995261 CDPARK for dh-ranFile-2016-01-17_11:31: 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 3532 0.4110 0.659449 3503 -0.9132 0.180558 3515 -0.3653 0.357445 3522 -0.0457 0.481790 3515 -0.3653 0.357445 3515 -0.3653 0.357445 3557 1.5525 0.939730 3478 -2.0548 0.019949 3486 -1.6895 0.045562 3535 0.5479 0.708135 Square side=100, avg. no. parked=3515.80 sample std.=22.02 p-value of the KSTEST for those 10 p-values: 0.514390 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-17_11:31 0.4579,0.4985,0.2415,0.0916,0.8231,0.8268,0.1769,0.7439,0.2967,0.1355, The KS test for those 10 p-values: 0.674769 The 3DSPHERES test for dh-ranFile-2016-01-17_11:31 sample no r^3 equiv. uni. 1 7.395 0.218475 2 26.988 0.593265 3 40.443 0.740266 4 45.509 0.780624 5 24.975 0.565042 6 12.804 0.347402 7 1.483 0.048245 8 9.517 0.271841 9 79.989 0.930490 10 14.925 0.391952 11 10.667 0.299232 12 19.474 0.477502 13 70.493 0.904609 14 124.003 0.983972 15 0.247 0.008207 16 9.765 0.277833 17 11.052 0.308165 18 102.149 0.966792 19 41.003 0.745068 20 32.447 0.660937 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.851012 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-17_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 -1.6 -0.3 -0.3 0.0 1.0 -0.6 0.8 0.6 1.1 -0.3 -0.8 -1.1 0.8 0.8 0.4 -0.3 -0.1 -1.0 0.1 -0.6 0.2 0.0 0.3 1.1 -1.8 -0.0 -0.1 -0.6 -0.5 -0.7 1.9 0.8 1.5 0.6 -0.2 0.5 1.3 -1.3 -0.6 1.0 -0.1 Chi-square with 42 degrees of freedom:28.798093 z-score=-1.440446, p-value=0.060319 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-17_11:31 Test no p-value 1 0.017484 2 0.863438 3 0.993930 4 0.366930 5 0.256405 6 0.977023 7 0.709288 8 0.084310 9 0.006748 10 0.109827 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.080141 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-17_11:31: (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 66600 0.07 66693 0.01 3 25000.00 25161 1.04 24946 0.12 4 6666.67 6578 1.18 6664 0.00 5 1388.89 1386 0.01 1423 0.84 6 238.10 229 0.35 231 0.21 7 34.72 38 0.31 36 0.05 8 4.96 7 0.84 6 0.22 p=0.29428 p=0.03678 Number of rngs required: 688200, p-value: 0.408 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-17_11:31 No. of wins: Observed Expected 98524 98585.9 z-score=-0.277, pvalue=0.39102 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66545 66666.7 0.222 0.222 2 38079 37654.3 4.790 5.012 3 27011 26954.7 0.117 5.129 4 19178 19313.5 0.950 6.079 5 13713 13851.4 1.383 7.463 6 9903 9943.5 0.165 7.628 7 7090 7145.0 0.424 8.052 8 5134 5139.1 0.005 8.057 9 3737 3699.9 0.373 8.429 10 2663 2666.3 0.004 8.433 11 1898 1923.3 0.334 8.767 12 1369 1388.7 0.281 9.048 13 1029 1003.7 0.637 9.685 14 755 726.1 1.147 10.832 15 498 525.8 1.474 12.305 16 377 381.2 0.045 12.350 17 289 276.5 0.561 12.912 18 200 200.8 0.003 12.915 19 147 146.0 0.007 12.922 20 105 106.2 0.014 12.936 21 280 287.1 0.176 13.112 Chisq= 13.11 for 20 degrees of freedom, p= 0.12749 SUMMARY of craptest p-value for no. of wins: 0.391018 p-value for throws/game: 0.127490 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-17_11:31 No. of wins: Observed Expected 98662 98585.9 z-score= 0.341, pvalue=0.63328 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66893 66666.7 0.768 0.768 2 37475 37654.3 0.854 1.622 3 27177 26954.7 1.833 3.455 4 19489 19313.5 1.595 5.051 5 13754 13851.4 0.685 5.736 6 9823 9943.5 1.461 7.197 7 7091 7145.0 0.409 7.606 8 5150 5139.1 0.023 7.629 9 3729 3699.9 0.229 7.858 10 2624 2666.3 0.671 8.529 11 1844 1923.3 3.272 11.801 12 1366 1388.7 0.372 12.174 13 973 1003.7 0.940 13.114 14 730 726.1 0.021 13.134 15 527 525.8 0.003 13.137 16 381 381.2 0.000 13.137 17 282 276.5 0.108 13.245 18 182 200.8 1.765 15.010 19 137 146.0 0.553 15.563 20 98 106.2 0.635 16.198 21 275 287.1 0.511 16.709 Chisq= 16.71 for 20 degrees of freedom, p= 0.32825 SUMMARY of craptest p-value for no. of wins: 0.633278 p-value for throws/game: 0.328251 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0021,0.0067,0.0082,0.0083,0.0175,0.0183,0.0199,0.0220,0.0344,0.0368, 0.0370,0.0376,0.0435,0.0438,0.0456,0.0482,0.0521,0.0582,0.0603,0.0630, 0.0665,0.0679,0.0708,0.0749,0.0763,0.0779,0.0801,0.0835,0.0843,0.0892, 0.0916,0.0934,0.0943,0.0991,0.1060,0.1064,0.1078,0.1098,0.1107,0.1133, 0.1235,0.1236,0.1239,0.1275,0.1302,0.1326,0.1334,0.1355,0.1358,0.1392, 0.1508,0.1579,0.1584,0.1587,0.1607,0.1613,0.1754,0.1769,0.1774,0.1777, 0.1806,0.1809,0.1844,0.1902,0.1943,0.1951,0.2053,0.2147,0.2185,0.2206, 0.2208,0.2258,0.2258,0.2300,0.2415,0.2453,0.2508,0.2555,0.2558,0.2564, 0.2628,0.2643,0.2652,0.2673,0.2718,0.2740,0.2778,0.2821,0.2874,0.2887, 0.2943,0.2955,0.2967,0.2970,0.2992,0.2996,0.3014,0.3015,0.3025,0.3040, 0.3082,0.3108,0.3183,0.3211,0.3283,0.3287,0.3303,0.3309,0.3421,0.3432, 0.3438,0.3451,0.3454,0.3474,0.3544,0.3553,0.3574,0.3574,0.3574,0.3580, 0.3669,0.3735,0.3803,0.3875,0.3879,0.3896,0.3897,0.3910,0.3919,0.3920, 0.3960,0.3992,0.4045,0.4076,0.4086,0.4167,0.4202,0.4216,0.4243,0.4309, 0.4327,0.4329,0.4387,0.4500,0.4528,0.4579,0.4643,0.4673,0.4773,0.4775, 0.4818,0.4830,0.4833,0.4874,0.4896,0.4913,0.4985,0.5009,0.5036,0.5144, 0.5173,0.5279,0.5431,0.5490,0.5499,0.5544,0.5562,0.5582,0.5650,0.5656, 0.5688,0.5849,0.5862,0.5933,0.5959,0.5980,0.6187,0.6333,0.6351,0.6357, 0.6386,0.6457,0.6480,0.6539,0.6594,0.6609,0.6609,0.6610,0.6625,0.6631, 0.6653,0.6697,0.6714,0.6748,0.6895,0.6952,0.7052,0.7058,0.7081,0.7093, 0.7133,0.7179,0.7214,0.7231,0.7276,0.7299,0.7338,0.7344,0.7359,0.7403, 0.7421,0.7439,0.7443,0.7443,0.7451,0.7693,0.7703,0.7738,0.7767,0.7777, 0.7787,0.7806,0.7848,0.7893,0.8231,0.8268,0.8343,0.8510,0.8527,0.8550, 0.8634,0.8674,0.8686,0.8703,0.8781,0.8831,0.8839,0.8891,0.8895,0.8916, 0.8921,0.8923,0.8968,0.8980,0.9046,0.9067,0.9107,0.9256,0.9261,0.9305, 0.9337,0.9342,0.9371,0.9381,0.9392,0.9397,0.9447,0.9475,0.9539,0.9632, 0.9644,0.9668,0.9770,0.9817,0.9840,0.9905,0.9907,0.9939,0.9953, Overall p-value after applying KStest on 269 p-values = 0.029755 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.