RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-28_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.94 14.3506 0.357853
2 to 25 15.72 13.4831 0.296708
3 to 26 16.16 12.3092 0.218939
4 to 27 15.68 18.5352 0.644147
5 to 28 15.68 17.4022 0.572546
6 to 29 15.74 28.9111 0.964645
7 to 30 15.42 24.1982 0.885852
8 to 31 15.51 23.3876 0.862948
9 to 32 15.46 36.4508 0.996009
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.137613
Tough bday spacings test for dh-ranFile-2018-06-28_14:31: 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 9 42 69 109 96 77 57 27 6 4 4
(O-E)^2/E 0.0 0.8 0.2 1.3 0.0 0.0 0.5 0.3 5.3 1.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 9.452, p= 0.510
RESULTS OF GCD FOR dh-ranFile-2018-06-28_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.041933
p-value, dist. of gcd's: 0.269298
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-28_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.064 0.968 0.774 0.558 0.904 0.193 0.722 0.696
Bits 8 to 15---> 0.114 0.337 0.391 0.767 0.781 0.425 0.165 0.775
Bits 16 to 23---> 0.663 0.312 0.520 0.610 0.777 0.050 0.362 0.177
Bits 24 to 31---> 0.038 0.997 0.118 0.342 0.343 0.624 0.423 0.295
KS test for the above 32 p values: 0.108
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-28_14:31,
p-values for 5 runs: 0.7176, 0.5054, 0.5471, 0.6874, 0.5049
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-28_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 208 211.4 0.055 0.055
r= 29 5134 5134.0 0.000 0.055
r= 30 23106 23103.0 0.000 0.056
r= 31 11552 11551.5 0.000 0.056
chi-square = 0.056 with df = 3; p-value = 0.003
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-28_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 198 211.4 0.852 0.852
r= 30 5173 5134.0 0.296 1.148
r= 31 23069 23103.0 0.050 1.198
r= 32 11560 11551.5 0.006 1.204
chi-square = 1.204 with df = 3; p-value = 0.248
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-28_14:31
b-rank test for bits 1 to 8, p=0.03161
b-rank test for bits 2 to 9, p=0.42150
b-rank test for bits 3 to 10, p=0.84884
b-rank test for bits 4 to 11, p=0.99329
b-rank test for bits 5 to 12, p=0.64125
b-rank test for bits 6 to 13, p=0.26128
b-rank test for bits 7 to 14, p=0.91470
b-rank test for bits 8 to 15, p=0.96023
b-rank test for bits 9 to 16, p=0.95853
b-rank test for bits 10 to 17, p=0.91930
b-rank test for bits 11 to 18, p=0.09280
b-rank test for bits 12 to 19, p=0.84148
b-rank test for bits 13 to 20, p=0.06001
b-rank test for bits 14 to 21, p=0.21260
b-rank test for bits 15 to 22, p=0.86784
b-rank test for bits 16 to 23, p=0.44499
b-rank test for bits 17 to 24, p=0.85187
b-rank test for bits 18 to 25, p=0.70261
b-rank test for bits 19 to 26, p=0.58737
b-rank test for bits 20 to 27, p=0.27587
b-rank test for bits 21 to 28, p=0.45267
b-rank test for bits 22 to 29, p=0.07460
b-rank test for bits 23 to 30, p=0.27696
b-rank test for bits 24 to 31, p=0.07898
b-rank test for bits 25 to 32, p=0.80945
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 = 0.255172
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-28_14:31
(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 141524 -0.90 0.183979
2 142071 0.38 0.647186
3 141792 -0.27 0.391990
4 141910 0.00 0.500625
5 142094 0.43 0.666937
6 141646 -0.62 0.269193
7 141416 -1.15 0.124529
8 142266 0.83 0.797674
9 141780 -0.30 0.381260
10 141840 -0.16 0.435658
11 141442 -1.09 0.137440
12 141997 0.20 0.581150
13 141951 0.10 0.538780
14 142075 0.39 0.650651
15 141682 -0.53 0.297659
16 141997 0.20 0.581150
17 142109 0.47 0.679578
18 142049 0.33 0.627913
19 142159 0.58 0.720168
20 142151 0.56 0.713844
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-28_14:31
Bits used No. missing words z-score p-value
23 to 32 142054 0.4989 0.691062
22 to 31 141651 -0.8908 0.186520
21 to 30 141293 -2.1253 0.016782
20 to 29 142436 1.8161 0.965323
19 to 28 141974 0.2230 0.588232
18 to 27 141802 -0.3701 0.355653
17 to 26 141793 -0.4011 0.344159
16 to 25 141981 0.2471 0.597599
15 to 24 142228 1.0989 0.864086
14 to 23 141888 -0.0736 0.470684
13 to 22 142032 0.4230 0.663852
12 to 21 141916 0.0230 0.509175
11 to 20 142353 1.5299 0.936979
10 to 19 141821 -0.3046 0.380341
9 to 18 141580 -1.1356 0.128058
8 to 17 142586 2.3333 0.990185
7 to 16 142420 1.7609 0.960875
6 to 15 142361 1.5575 0.940322
5 to 14 141719 -0.6563 0.255812
4 to 13 141942 0.1127 0.544848
3 to 12 142072 0.5609 0.712578
2 to 11 141930 0.0713 0.528411
1 to 10 142154 0.8437 0.800579
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-28_14:31
Bits used No. missing words z-score p-value
28 to 32 142059 0.5074 0.694048
27 to 31 141843 -0.2248 0.411049
26 to 30 141671 -0.8079 0.209575
25 to 29 141931 0.0735 0.529279
24 to 28 142162 0.8565 0.804142
23 to 27 142233 1.0972 0.863720
22 to 26 142236 1.1074 0.865930
21 to 25 142064 0.5243 0.699967
20 to 24 141904 -0.0181 0.492792
19 to 23 141642 -0.9062 0.182414
18 to 22 141992 0.2802 0.610352
17 to 21 142092 0.6192 0.732114
16 to 20 142181 0.9209 0.821453
15 to 19 142223 1.0633 0.856174
14 to 18 142099 0.6429 0.739872
13 to 17 142168 0.8768 0.809715
12 to 16 141987 0.2633 0.603836
11 to 15 141854 -0.1876 0.425611
10 to 14 141452 -1.5503 0.060538
9 to 13 141594 -1.0689 0.142554
8 to 12 141827 -0.2791 0.390090
7 to 11 141764 -0.4926 0.311132
6 to 10 142264 1.2023 0.885371
5 to 9 141527 -1.2960 0.097482
4 to 8 142062 0.5175 0.697605
3 to 7 141947 0.1277 0.550805
2 to 6 141179 -2.4757 0.006649
1 to 5 141957 0.1616 0.564187
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-28_14:31
Bits used No. missing words z-score p-value
31 to 32 141674 -0.6942 0.243782
30 to 31 142034 0.3678 0.643473
29 to 30 142193 0.8368 0.798643
28 to 29 141879 -0.0895 0.464355
27 to 28 142163 0.7483 0.772857
26 to 27 142285 1.1082 0.866106
25 to 26 141937 0.0816 0.532527
24 to 25 141878 -0.0924 0.463183
23 to 24 142177 0.7896 0.785116
22 to 23 141446 -1.3668 0.085851
21 to 22 142117 0.6126 0.729928
20 to 21 142184 0.8102 0.791098
19 to 20 141619 -0.8564 0.195880
18 to 19 141546 -1.0718 0.141912
17 to 18 141638 -0.8004 0.211744
16 to 17 142213 0.8958 0.814815
15 to 16 141415 -1.4582 0.072393
14 to 15 141999 0.2645 0.604308
13 to 14 141898 -0.0334 0.486669
12 to 13 141773 -0.4022 0.343786
11 to 12 142016 0.3147 0.623490
10 to 11 142016 0.3147 0.623490
9 to 10 142786 2.5860 0.995146
8 to 9 142555 1.9046 0.971586
7 to 8 141743 -0.4906 0.311837
6 to 7 141798 -0.3284 0.371302
5 to 6 142260 1.0344 0.849531
4 to 5 141497 -1.2163 0.111933
3 to 4 142100 0.5624 0.713095
2 to 3 141635 -0.8092 0.209191
1 to 2 142314 1.1937 0.883706
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-28_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2612.55 1.592 0.944270
Test results for specific bytes for dh-ranFile-2018-06-28_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2564.61 0.914 0.819575
2 to 9 2582.31 1.164 0.877800
3 to 10 2454.05 -0.650 0.257884
4 to 11 2483.00 -0.240 0.405009
5 to 12 2559.62 0.843 0.800421
6 to 13 2480.96 -0.269 0.393872
7 to 14 2555.33 0.783 0.783047
8 to 15 2391.00 -1.541 0.061601
9 to 16 2514.38 0.203 0.580580
10 to 17 2566.63 0.942 0.826978
11 to 18 2447.91 -0.737 0.230654
12 to 19 2528.54 0.404 0.656762
13 to 20 2292.60 -2.933 0.001678
14 to 21 2523.70 0.335 0.631258
15 to 22 2448.46 -0.729 0.233045
16 to 23 2483.05 -0.240 0.405294
17 to 24 2469.72 -0.428 0.334236
18 to 25 2415.50 -1.195 0.116045
19 to 26 2480.72 -0.273 0.392569
20 to 27 2535.74 0.505 0.693358
21 to 28 2413.89 -1.218 0.111663
22 to 29 2525.34 0.358 0.639989
23 to 30 2471.73 -0.400 0.344632
24 to 31 2571.32 1.009 0.843424
25 to 32 2599.63 1.409 0.920569
CDPARK for dh-ranFile-2018-06-28_14:31: 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
3533 0.4566 0.676028
3582 2.6941 0.996471
3536 0.5936 0.723613
3509 -0.6393 0.261324
3531 0.3653 0.642555
3488 -1.5982 0.055002
3516 -0.3196 0.374623
3554 1.4155 0.921543
3540 0.7763 0.781201
3536 0.5936 0.723613
Square side=100, avg. no. parked=3532.50 sample std.=24.08
p-value of the KSTEST for those 10 p-values: 0.272371
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-28_14:31
0.8063,0.1820,0.3685,0.2888,0.0336,0.2002,0.3141,0.9612,0.2726,0.7410,
The KS test for those 10 p-values: 0.460502
The 3DSPHERES test for dh-ranFile-2018-06-28_14:31
sample no r^3 equiv. uni.
1 16.341 0.419976
2 8.591 0.249022
3 8.793 0.254053
4 18.139 0.453732
5 55.534 0.842942
6 41.673 0.750703
7 4.221 0.131256
8 16.131 0.415904
9 1.221 0.039870
10 35.259 0.691270
11 34.244 0.680652
12 5.598 0.170227
13 64.562 0.883756
14 9.332 0.267327
15 20.066 0.487707
16 28.086 0.607890
17 45.549 0.780920
18 33.895 0.676914
19 25.214 0.568486
20 8.320 0.242210
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.774338
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-28_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.1 1.1 -0.4 -0.9 -0.4
1.0 0.2 -0.4 0.6 -1.0 0.3
1.2 -0.3 0.6 0.0 -0.5 -0.3
0.4 0.0 -0.4 0.6 -0.5 -0.3
-0.6 0.1 -0.1 -0.9 0.1 0.8
1.1 -1.1 0.5 -0.3 -0.4 2.6
-1.6 -1.0 -0.4 -0.1 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:25.214333
z-score=-1.831466, p-value=0.018778
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-28_14:31
Test no p-value
1 0.027026
2 0.340133
3 0.911078
4 0.017382
5 0.631709
6 0.211782
7 0.200820
8 0.346192
9 0.017577
10 0.751357
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.059511
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-28_14:31:
(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 66699 0.02 66646 0.01
3 25000.00 24845 0.96 24941 0.14
4 6666.67 6704 0.21 6727 0.55
5 1388.89 1477 5.59 1397 0.05
6 238.10 232 0.16 256 1.35
7 34.72 36 0.05 29 0.94
8 4.96 6 0.22 3 0.77
p=0.69695 p=0.29659
Number of rngs required: 688739, p-value: 0.651
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-28_14:31
No. of wins: Observed Expected
98480 98585.9
z-score=-0.473, pvalue=0.31794
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66855 66666.7 0.532 0.532
2 37449 37654.3 1.120 1.652
3 26995 26954.7 0.060 1.712
4 19259 19313.5 0.154 1.865
5 13712 13851.4 1.403 3.269
6 9939 9943.5 0.002 3.271
7 7161 7145.0 0.036 3.306
8 5240 5139.1 1.982 5.289
9 3723 3699.9 0.145 5.433
10 2682 2666.3 0.092 5.526
11 1881 1923.3 0.932 6.457
12 1435 1388.7 1.541 7.998
13 1028 1003.7 0.588 8.586
14 725 726.1 0.002 8.588
15 467 525.8 6.583 15.171
16 377 381.2 0.045 15.216
17 301 276.5 2.164 17.380
18 222 200.8 2.232 19.611
19 151 146.0 0.172 19.784
20 104 106.2 0.046 19.830
21 294 287.1 0.165 19.995
Chisq= 19.99 for 20 degrees of freedom, p= 0.54175
SUMMARY of craptest
p-value for no. of wins: 0.317942
p-value for throws/game: 0.541748
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-28_14:31
No. of wins: Observed Expected
98090 98585.9
z-score=-2.218, pvalue=0.01329
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66492 66666.7 0.458 0.458
2 37595 37654.3 0.093 0.551
3 26942 26954.7 0.006 0.557
4 19486 19313.5 1.541 2.098
5 13770 13851.4 0.479 2.577
6 9982 9943.5 0.149 2.726
7 7179 7145.0 0.162 2.887
8 5189 5139.1 0.485 3.372
9 3712 3699.9 0.040 3.412
10 2688 2666.3 0.177 3.589
11 1867 1923.3 1.650 5.239
12 1363 1388.7 0.477 5.716
13 1030 1003.7 0.688 6.404
14 724 726.1 0.006 6.410
15 576 525.8 4.786 11.196
16 391 381.2 0.255 11.450
17 275 276.5 0.009 11.459
18 179 200.8 2.373 13.832
19 143 146.0 0.061 13.893
20 113 106.2 0.433 14.326
21 304 287.1 0.993 15.319
Chisq= 15.32 for 20 degrees of freedom, p= 0.24215
SUMMARY of craptest
p-value for no. of wins: 0.013285
p-value for throws/game: 0.242152
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0017,0.0034,0.0066,0.0133,0.0168,0.0174,0.0176,0.0188,0.0270,0.0316,
0.0336,0.0378,0.0399,0.0419,0.0498,0.0550,0.0595,0.0600,0.0605,0.0616,
0.0644,0.0724,0.0746,0.0790,0.0859,0.0928,0.0975,0.1080,0.1117,0.1119,
0.1137,0.1160,0.1183,0.1245,0.1281,0.1313,0.1374,0.1376,0.1419,0.1426,
0.1646,0.1702,0.1773,0.1820,0.1824,0.1840,0.1865,0.1931,0.1959,0.2002,
0.2008,0.2092,0.2096,0.2117,0.2118,0.2126,0.2189,0.2307,0.2330,0.2422,
0.2422,0.2438,0.2480,0.2490,0.2541,0.2552,0.2558,0.2579,0.2613,0.2613,
0.2673,0.2692,0.2693,0.2724,0.2726,0.2759,0.2770,0.2888,0.2945,0.2966,
0.2967,0.2977,0.3111,0.3118,0.3124,0.3141,0.3179,0.3342,0.3369,0.3401,
0.3419,0.3426,0.3438,0.3442,0.3446,0.3462,0.3557,0.3579,0.3615,0.3685,
0.3713,0.3746,0.3803,0.3813,0.3901,0.3911,0.3920,0.3926,0.3939,0.4050,
0.4053,0.4110,0.4159,0.4200,0.4215,0.4229,0.4252,0.4256,0.4357,0.4450,
0.4527,0.4537,0.4605,0.4632,0.4644,0.4707,0.4867,0.4877,0.4928,0.5006,
0.5049,0.5054,0.5092,0.5102,0.5195,0.5284,0.5293,0.5325,0.5388,0.5417,
0.5448,0.5471,0.5508,0.5583,0.5642,0.5685,0.5725,0.5806,0.5812,0.5812,
0.5874,0.5882,0.5976,0.6038,0.6043,0.6079,0.6100,0.6104,0.6235,0.6235,
0.6242,0.6279,0.6313,0.6317,0.6400,0.6413,0.6426,0.6435,0.6441,0.6472,
0.6506,0.6507,0.6568,0.6625,0.6639,0.6669,0.6760,0.6769,0.6796,0.6807,
0.6874,0.6911,0.6913,0.6934,0.6940,0.6964,0.6970,0.6976,0.7000,0.7026,
0.7126,0.7131,0.7138,0.7176,0.7202,0.7217,0.7236,0.7236,0.7299,0.7321,
0.7399,0.7410,0.7507,0.7514,0.7674,0.7729,0.7741,0.7743,0.7748,0.7769,
0.7808,0.7809,0.7812,0.7830,0.7851,0.7911,0.7977,0.7986,0.8004,0.8006,
0.8041,0.8063,0.8094,0.8097,0.8148,0.8196,0.8215,0.8270,0.8415,0.8429,
0.8434,0.8488,0.8495,0.8519,0.8562,0.8629,0.8637,0.8641,0.8659,0.8661,
0.8678,0.8778,0.8837,0.8838,0.8854,0.8859,0.9044,0.9111,0.9147,0.9193,
0.9206,0.9215,0.9370,0.9403,0.9443,0.9585,0.9602,0.9609,0.9612,0.9646,
0.9653,0.9678,0.9716,0.9902,0.9933,0.9951,0.9960,0.9965,0.9967,
Overall p-value after applying KStest on 269 p-values = 0.908984
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.