RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-24_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.85 5.9798 0.006680 2 to 25 16.10 14.4188 0.362733 3 to 26 15.92 7.6351 0.026260 4 to 27 15.68 21.8828 0.810733 5 to 28 15.93 9.9068 0.092527 6 to 29 15.76 11.7140 0.182860 7 to 30 15.71 28.9723 0.965218 8 to 31 15.83 22.0143 0.815829 9 to 32 15.74 9.3454 0.071202 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.053717 Tough bday spacings test for dh-ranFile-2015-06-24_09:31: 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 67 94 101 83 60 30 12 7 3 (O-E)^2/E 0.1 0.1 0.5 0.1 0.1 0.3 1.2 0.0 0.6 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 3.369, p= 0.029 RESULTS OF GCD FOR dh-ranFile-2015-06-24_09:31 Euclid's algorithm: p-value, steps to gcd: 0.768308 p-value, dist. of gcd's: 0.078769 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-24_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.214 0.792 0.359 0.492 0.905 0.570 0.442 0.812 Bits 8 to 15---> 0.773 0.014 0.129 0.080 0.442 0.750 0.892 0.254 Bits 16 to 23---> 0.888 0.491 0.551 0.507 0.813 0.391 0.484 0.805 Bits 24 to 31---> 0.385 0.213 0.949 0.522 0.276 0.299 0.998 0.068 KS test for the above 32 p values: 0.111 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-24_09:31, p-values for 5 runs: 0.3386, 0.2995, 0.1089, 0.4643, 0.3917 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-24_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5165 5134.0 0.187 0.279 r= 30 23197 23103.0 0.382 0.661 r= 31 11431 11551.5 1.257 1.919 chi-square = 1.919 with df = 3; p-value = 0.411 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-24_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5204 5134.0 0.954 1.009 r= 31 23077 23103.0 0.029 1.039 r= 32 11511 11551.5 0.142 1.181 chi-square = 1.181 with df = 3; p-value = 0.242 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-24_09:31 b-rank test for bits 1 to 8, p=0.27457 b-rank test for bits 2 to 9, p=0.33820 b-rank test for bits 3 to 10, p=0.68660 b-rank test for bits 4 to 11, p=0.92893 b-rank test for bits 5 to 12, p=0.83523 b-rank test for bits 6 to 13, p=0.96837 b-rank test for bits 7 to 14, p=0.96237 b-rank test for bits 8 to 15, p=0.59893 b-rank test for bits 9 to 16, p=0.26917 b-rank test for bits 10 to 17, p=0.97663 b-rank test for bits 11 to 18, p=0.88384 b-rank test for bits 12 to 19, p=0.26437 b-rank test for bits 13 to 20, p=0.58662 b-rank test for bits 14 to 21, p=0.18760 b-rank test for bits 15 to 22, p=0.78942 b-rank test for bits 16 to 23, p=0.81770 b-rank test for bits 17 to 24, p=0.47357 b-rank test for bits 18 to 25, p=0.54774 b-rank test for bits 19 to 26, p=0.06780 b-rank test for bits 20 to 27, p=0.55151 b-rank test for bits 21 to 28, p=0.19129 b-rank test for bits 22 to 29, p=0.33413 b-rank test for bits 23 to 30, p=0.21891 b-rank test for bits 24 to 31, p=0.01059 b-rank test for bits 25 to 32, p=0.46347 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 = 0.782133 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-24_09:31 (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 142409 1.17 0.878486 2 141320 -1.38 0.084266 3 142221 0.73 0.766755 4 141614 -0.69 0.245090 5 142117 0.49 0.686236 6 142445 1.25 0.894636 7 141314 -1.39 0.082119 8 141606 -0.71 0.239251 9 141870 -0.09 0.463392 10 141593 -0.74 0.229927 11 141631 -0.65 0.257748 12 142210 0.70 0.758816 13 141809 -0.23 0.407331 14 141278 -1.48 0.070097 15 142597 1.61 0.945941 16 141187 -1.69 0.045736 17 141792 -0.27 0.391990 18 141891 -0.04 0.482920 19 142169 0.61 0.727977 20 141908 -0.00 0.498760 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-24_09:31 Bits used No. missing words z-score p-value 23 to 32 141611 -1.0287 0.151805 22 to 31 142560 2.2437 0.987574 21 to 30 142026 0.4023 0.656272 20 to 29 141598 -1.0736 0.141512 19 to 28 141977 0.2333 0.592253 18 to 27 142297 1.3368 0.909355 17 to 26 141877 -0.1115 0.455617 16 to 25 142022 0.3885 0.651183 15 to 24 141911 0.0058 0.502297 14 to 23 142176 0.9196 0.821097 13 to 22 142186 0.9540 0.829967 12 to 21 142117 0.7161 0.763036 11 to 20 142146 0.8161 0.792780 10 to 19 141761 -0.5115 0.304507 9 to 18 141884 -0.0873 0.465199 8 to 17 141722 -0.6460 0.259151 7 to 16 141832 -0.2667 0.394867 6 to 15 141826 -0.2873 0.386924 5 to 14 141986 0.2644 0.604256 4 to 13 142015 0.3644 0.642213 3 to 12 142254 1.1885 0.882685 2 to 11 141685 -0.7736 0.219598 1 to 10 141704 -0.7080 0.239462 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-24_09:31 Bits used No. missing words z-score p-value 28 to 32 142010 0.3413 0.633544 27 to 31 142277 1.2463 0.893680 26 to 30 142025 0.3921 0.652509 25 to 29 142021 0.3785 0.647486 24 to 28 141858 -0.1740 0.430933 23 to 27 141609 -1.0181 0.154323 22 to 26 142276 1.2429 0.893057 21 to 25 142203 0.9955 0.840251 20 to 24 142168 0.8768 0.809715 19 to 23 141593 -1.0723 0.141792 18 to 22 142169 0.8802 0.810635 17 to 21 141878 -0.1062 0.457711 16 to 20 141738 -0.5808 0.280695 15 to 19 142092 0.6192 0.732114 14 to 18 141754 -0.5265 0.299256 13 to 17 141465 -1.5062 0.066008 12 to 16 141847 -0.2113 0.416331 11 to 15 142103 0.6565 0.744252 10 to 14 142190 0.9514 0.829305 9 to 13 141362 -1.8554 0.031773 8 to 12 142007 0.3311 0.629710 7 to 11 141645 -0.8960 0.185117 6 to 10 141896 -0.0452 0.481979 5 to 9 141740 -0.5740 0.282984 4 to 8 141695 -0.7265 0.233753 3 to 7 141842 -0.2282 0.409731 2 to 6 142287 1.2802 0.899769 1 to 5 142029 0.4057 0.657504 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-24_09:31 Bits used No. missing words z-score p-value 31 to 32 141780 -0.3815 0.351415 30 to 31 141398 -1.5083 0.065733 29 to 30 141850 -0.1750 0.430534 28 to 29 141729 -0.5319 0.297381 27 to 28 141686 -0.6588 0.255015 26 to 27 141690 -0.6470 0.258819 25 to 26 141652 -0.7591 0.223901 24 to 25 142342 1.2763 0.899078 23 to 24 142358 1.3235 0.907167 22 to 23 141886 -0.0688 0.472566 21 to 22 141405 -1.4877 0.068415 20 to 21 142313 1.1908 0.883127 19 to 20 141233 -1.9951 0.023017 18 to 19 141569 -1.0039 0.157708 17 to 18 141769 -0.4140 0.339454 16 to 17 142336 1.2586 0.895915 15 to 16 141565 -1.0157 0.154881 14 to 15 142062 0.4504 0.673772 13 to 14 141738 -0.5054 0.306640 12 to 13 142448 1.5890 0.943969 11 to 12 141080 -2.4464 0.007215 10 to 11 142743 2.4592 0.993038 9 to 10 142088 0.5271 0.700921 8 to 9 141878 -0.0924 0.463183 7 to 8 141991 0.2409 0.595189 6 to 7 142134 0.6627 0.746253 5 to 6 141931 0.0639 0.525484 4 to 5 141923 0.0403 0.516083 3 to 4 141705 -0.6027 0.273340 2 to 3 141958 0.1436 0.557080 1 to 2 141475 -1.2812 0.100060 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-24_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2505.44 0.077 0.530636 Test results for specific bytes for dh-ranFile-2015-06-24_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2533.04 0.467 0.679864 2 to 9 2412.94 -1.231 0.109126 3 to 10 2580.32 1.136 0.872012 4 to 11 2690.77 2.698 0.996511 5 to 12 2599.34 1.405 0.919976 6 to 13 2436.19 -0.902 0.183403 7 to 14 2469.58 -0.430 0.333519 8 to 15 2371.39 -1.819 0.034465 9 to 16 2473.24 -0.379 0.352529 10 to 17 2480.00 -0.283 0.388636 11 to 18 2385.76 -1.616 0.053089 12 to 19 2437.99 -0.877 0.190253 13 to 20 2514.66 0.207 0.582145 14 to 21 2369.61 -1.844 0.032594 15 to 22 2495.19 -0.068 0.472870 16 to 23 2430.29 -0.986 0.162107 17 to 24 2551.12 0.723 0.765141 18 to 25 2561.25 0.866 0.806827 19 to 26 2527.49 0.389 0.651274 20 to 27 2515.48 0.219 0.586644 21 to 28 2481.73 -0.258 0.398085 22 to 29 2436.67 -0.896 0.185230 23 to 30 2434.42 -0.927 0.176864 24 to 31 2521.52 0.304 0.619547 25 to 32 2409.93 -1.274 0.101365 CDPARK for dh-ranFile-2015-06-24_09:31: 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 3481 -1.9178 0.027568 3534 0.5023 0.692266 3546 1.0502 0.853193 3550 1.2329 0.891189 3532 0.4110 0.659449 3479 -2.0091 0.022262 3527 0.1826 0.572463 3542 0.8676 0.807188 3535 0.5479 0.708135 3537 0.6393 0.738676 Square side=100, avg. no. parked=3526.30 sample std.=24.02 p-value of the KSTEST for those 10 p-values: 0.140023 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-24_09:31 0.3351,0.4872,0.5110,0.6657,0.2563,0.3712,0.0078,0.3021,0.8963,0.6946, The KS test for those 10 p-values: 0.664780 The 3DSPHERES test for dh-ranFile-2015-06-24_09:31 sample no r^3 equiv. uni. 1 40.918 0.744350 2 75.957 0.920493 3 7.235 0.214277 4 11.257 0.312863 5 25.716 0.575653 6 8.784 0.253837 7 45.716 0.782129 8 37.249 0.711091 9 17.059 0.433707 10 39.659 0.733386 11 56.183 0.846300 12 7.082 0.210273 13 89.973 0.950168 14 41.642 0.750447 15 90.076 0.950340 16 50.875 0.816551 17 14.836 0.390152 18 55.164 0.840994 19 60.253 0.865800 20 32.126 0.657293 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.028724 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-24_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -2.0 -0.8 1.9 0.9 1.3 -1.6 -0.7 1.3 -0.6 -0.1 -0.6 -1.1 0.2 1.0 -1.0 -1.3 -0.5 0.9 0.8 -0.2 0.1 2.6 1.1 -0.8 0.1 0.0 0.4 1.1 -0.6 -1.2 0.2 -0.4 -0.4 -1.4 -0.7 -0.7 -0.8 -1.3 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:42.793947 z-score=0.086627, p-value=0.563085 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-24_09:31 Test no p-value 1 0.004993 2 0.083091 3 0.008194 4 0.273720 5 0.626902 6 0.035503 7 0.048374 8 0.135276 9 0.896094 10 0.265606 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000835 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-24_09:31: (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 66974 1.42 66451 0.70 3 25000.00 24824 1.24 25121 0.59 4 6666.67 6621 0.31 6721 0.44 5 1388.89 1316 3.83 1391 0.00 6 238.10 227 0.52 272 4.83 7 34.72 33 0.09 40 0.80 8 4.96 4 0.19 3 0.77 p=0.72965 p=0.77161 Number of rngs required: 688201, p-value: 0.408 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-24_09:31 No. of wins: Observed Expected 98985 98585.9 z-score= 1.785, pvalue=0.96289 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66783 66666.7 0.203 0.203 2 37707 37654.3 0.074 0.277 3 26840 26954.7 0.488 0.765 4 19275 19313.5 0.077 0.842 5 13874 13851.4 0.037 0.878 6 9944 9943.5 0.000 0.878 7 7266 7145.0 2.048 2.927 8 5140 5139.1 0.000 2.927 9 3646 3699.9 0.784 3.711 10 2658 2666.3 0.026 3.737 11 1865 1923.3 1.769 5.506 12 1363 1388.7 0.477 5.983 13 979 1003.7 0.609 6.592 14 723 726.1 0.014 6.605 15 464 525.8 7.272 13.877 16 375 381.2 0.099 13.976 17 287 276.5 0.396 14.372 18 234 200.8 5.479 19.850 19 164 146.0 2.223 22.073 20 101 106.2 0.256 22.330 21 312 287.1 2.157 24.487 Chisq= 24.49 for 20 degrees of freedom, p= 0.77822 SUMMARY of craptest p-value for no. of wins: 0.962885 p-value for throws/game: 0.778217 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-24_09:31 No. of wins: Observed Expected 98796 98585.9 z-score= 0.940, pvalue=0.82636 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66778 66666.7 0.186 0.186 2 37725 37654.3 0.133 0.319 3 26807 26954.7 0.810 1.128 4 19330 19313.5 0.014 1.142 5 13841 13851.4 0.008 1.150 6 9919 9943.5 0.061 1.211 7 7209 7145.0 0.573 1.784 8 5188 5139.1 0.466 2.249 9 3697 3699.9 0.002 2.252 10 2632 2666.3 0.441 2.693 11 1876 1923.3 1.165 3.858 12 1381 1388.7 0.043 3.901 13 1009 1003.7 0.028 3.929 14 706 726.1 0.559 4.487 15 505 525.8 0.826 5.313 16 378 381.2 0.026 5.339 17 286 276.5 0.324 5.662 18 189 200.8 0.697 6.359 19 154 146.0 0.440 6.799 20 99 106.2 0.490 7.290 21 291 287.1 0.053 7.342 Chisq= 7.34 for 20 degrees of freedom, p= 0.00460 SUMMARY of craptest p-value for no. of wins: 0.826359 p-value for throws/game: 0.004597 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0046,0.0050,0.0067,0.0072,0.0078,0.0082,0.0106,0.0142,0.0223, 0.0230,0.0263,0.0276,0.0286,0.0287,0.0318,0.0326,0.0345,0.0355,0.0457, 0.0484,0.0531,0.0537,0.0657,0.0660,0.0678,0.0678,0.0684,0.0701,0.0712, 0.0788,0.0797,0.0821,0.0831,0.0843,0.0925,0.1001,0.1014,0.1089,0.1091, 0.1115,0.1290,0.1353,0.1400,0.1415,0.1418,0.1518,0.1543,0.1549,0.1577, 0.1621,0.1769,0.1829,0.1834,0.1851,0.1852,0.1876,0.1903,0.1913,0.2103, 0.2135,0.2135,0.2143,0.2189,0.2196,0.2239,0.2299,0.2338,0.2393,0.2395, 0.2424,0.2451,0.2538,0.2540,0.2550,0.2563,0.2577,0.2588,0.2592,0.2644, 0.2656,0.2692,0.2733,0.2737,0.2746,0.2757,0.2807,0.2830,0.2974,0.2993, 0.2994,0.2995,0.3021,0.3045,0.3066,0.3129,0.3335,0.3341,0.3351,0.3382, 0.3386,0.3395,0.3514,0.3525,0.3586,0.3627,0.3712,0.3852,0.3869,0.3886, 0.3902,0.3915,0.3917,0.3920,0.3949,0.3981,0.4073,0.4081,0.4097,0.4106, 0.4163,0.4305,0.4309,0.4337,0.4424,0.4424,0.4556,0.4577,0.4632,0.4634, 0.4635,0.4643,0.4652,0.4726,0.4729,0.4736,0.4820,0.4829,0.4835,0.4872, 0.4905,0.4918,0.4988,0.5023,0.5066,0.5110,0.5161,0.5221,0.5255,0.5306, 0.5477,0.5508,0.5515,0.5571,0.5631,0.5702,0.5725,0.5757,0.5821,0.5866, 0.5866,0.5923,0.5952,0.5989,0.6043,0.6195,0.6269,0.6297,0.6335,0.6422, 0.6475,0.6512,0.6513,0.6525,0.6563,0.6573,0.6575,0.6594,0.6648,0.6657, 0.6738,0.6799,0.6862,0.6866,0.6923,0.6946,0.7009,0.7081,0.7111,0.7280, 0.7297,0.7321,0.7334,0.7387,0.7443,0.7444,0.7463,0.7502,0.7504,0.7588, 0.7630,0.7651,0.7668,0.7683,0.7716,0.7731,0.7782,0.7821,0.7821,0.7894, 0.7921,0.7928,0.8046,0.8068,0.8072,0.8097,0.8106,0.8107,0.8116,0.8132, 0.8158,0.8166,0.8177,0.8211,0.8264,0.8293,0.8300,0.8352,0.8403,0.8410, 0.8463,0.8532,0.8658,0.8720,0.8785,0.8827,0.8831,0.8838,0.8881,0.8912, 0.8916,0.8931,0.8937,0.8946,0.8959,0.8961,0.8963,0.8991,0.8998,0.9049, 0.9072,0.9094,0.9200,0.9205,0.9289,0.9440,0.9459,0.9487,0.9502,0.9503, 0.9624,0.9629,0.9652,0.9684,0.9766,0.9876,0.9930,0.9965,0.9977, Overall p-value after applying KStest on 269 p-values = 0.305032 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.