Bitruns test results
The following is an example of the output of
`bbctl --bit-runs` taken from one of the long-term
test machines we've been running. This test counts the number of runs
of consecutive 0's and 1's of every length.
The source field shows where the samples were taken from
and in most cases it is simply the serial number of device being tested.
The Kernel and Pool sources correspond to the
QA points indicated in this diagram for
the output pool and entropy that we feed to the kernel.
The /dev/random source shows statistics obtained by reading
bits from that device and analysing its output too.
The first column is the length of the run. The second and third columns
show the number of runs of that length for zeros and ones respectively.
The fourth column is the ratio of runs of zeros to runs of ones of that
length. The fifth column is the expected number of runs of that length
based on the total number of bits that have been analysed so far. The
sixth and seventh columns show the percentage error in the observed
number of runs compared to the expected number. The last two columns
show the normalised χ2 statistic for zeros and ones of
that run length (which is the square of the error divided by the
expected number).
The final line after the tabulated data shows the total number of
zeros and ones observed, their ratio, the overall χ2
statistic (which includes all runs where the expected number is
greater than 5), its p-value, and the number of degrees of freedom
used to calculate it.
The relatively large difference in the totals between some of the
devices is mainly because they weren't all placed into this machine
at the same time. Some of them were hotplugged after the initial test
first started running. And yes, some of them really had output around
2 terabits of data for analysis at the time this was run, this is testing
the raw bits directly out of each source
This test can be quite good at giving an early warning for streams
that will subsequently begin showing statistically significant failures
in other tests, but it's not always 100% reliable in that respect.
The χ2 statistic for it can be quite volatile, and on a
good random source it is expected to swing between the fullest extremes
of probability over time, so looking at individual results without
watching how they evolve over time (potentially quite a long time as
the number of samples gets large), and watching what other tests are
indicating, can be initially misleading sometimes.
source: /dev/random
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 141037634207 141037875000 0.999998 141037467500.250 0.0001 0.0003 0.20 1.18
2: 70518987521 70518816789 1.000002 70518733750.062 0.0004 0.0001 0.91 0.10
3: 35259381018 35259347374 1.000001 35259366875.000 0.0000 -0.0001 0.01 0.01-
4: 17629565438 17629772945 0.999988 17629683437.484 -0.0007 0.0005 0.79- 0.45
5: 8814859729 8814712601 1.000017 8814841718.734 0.0002 -0.0015 0.04 1.89-
6: 4407513281 4407323658 1.000043 4407420859.363 0.0021 -0.0022 1.94 2.14-
7: 2203670940 2203707677 0.999983 2203710429.680 -0.0018 -0.0001 0.71- 0.00-
8: 1101844834 1101852693 0.999993 1101855214.839 -0.0009 -0.0002 0.10- 0.01-
9: 550892962 550936670 0.999921 550927607.419 -0.0063 0.0016 2.18- 0.15
10: 275466050 275460422 1.000020 275463803.709 0.0008 -0.0012 0.02 0.04-
11: 137743296 137732747 1.000077 137731901.854 0.0083 0.0006 0.94 0.01
12: 68854765 68869145 0.999791 68865950.927 -0.0162 0.0046 1.82- 0.15
13: 34432695 34433716 0.999970 34432975.464 -0.0008 0.0022 0.00- 0.02
14: 17212339 17220343 0.999535 17216487.732 -0.0241 0.0224 1.00- 0.86
15: 8611015 8609619 1.000162 8608243.866 0.0322 0.0160 0.89 0.22
16: 4302777 4303488 0.999835 4304121.933 -0.0312 -0.0147 0.42- 0.09-
17: 2155632 2152646 1.001387 2152060.966 0.1659 0.0272 5.93 0.16
18: 1074741 1076704 0.998177 1076030.483 -0.1198 0.0626 1.55- 0.42
19: 537575 536754 1.001530 538015.242 -0.0818 -0.2344 0.36- 2.96-
20: 269593 268670 1.003435 269007.621 0.2176 -0.1255 1.27 0.42-
21: 134371 134759 0.997121 134503.810 -0.0987 0.1897 0.13- 0.48
22: 67058 67442 0.994306 67251.905 -0.2883 0.2827 0.56- 0.54
23: 33562 33516 1.001372 33625.953 -0.1902 -0.3270 0.12- 0.36-
24: 16721 16815 0.994410 16812.976 -0.5471 0.0120 0.50- 0.00
25: 8470 8408 1.007374 8406.488 0.7555 0.0180 0.48 0.00
26: 4246 4237 1.002124 4203.244 1.0172 0.8031 0.43 0.27
27: 2155 2150 1.002326 2101.622 2.5398 2.3019 1.36 1.11
28: 1083 1071 1.011204 1050.811 3.0633 1.9213 0.99 0.39
29: 528 506 1.043478 525.406 0.4938 -3.6934 0.01 0.72-
30: 250 276 0.905797 262.703 -4.8354 5.0617 0.61- 0.67
31: 132 130 1.015385 131.351 0.4938 -1.0288 0.00 0.01-
32: 63 69 0.913043 65.676 -4.0741 5.0617 0.11- 0.17
33: 32 32 1.000000 32.838 -2.5515 -2.5515 0.02- 0.02-
34: 16 24 0.666667 16.419 -2.5515 46.1728 0.01- 3.50
35: 8 4 2.000000 8.209 -2.5515 -51.2757 0.01- 2.16-
36: 3 8 0.375000 4.105 -26.9136 94.8971 0.30- 3.70
37: 1 1 1.000000 2.052 -51.2757 -51.2757 0.54- 0.54-
38: 1 0 inf 1.026 -2.5515 -100.0000 0.00- 1.03-
total: 564150094474 564149645526 1.000001 χ2 = 48.098160 (p = 0.973874), k = 69
source: G2SD3I
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 116429997775 116430052305 1.000000 116430077500.250 -0.0001 -0.0000 0.05- 0.01-
2: 58215151556 58215064690 1.000001 58215038750.062 0.0002 0.0000 0.22 0.01
3: 29107229824 29107734307 0.999983 29107519375.000 -0.0010 0.0007 2.88- 1.59
4: 14553828290 14553646963 1.000012 14553759687.484 0.0005 -0.0008 0.32 0.87-
5: 7276911380 7276812472 1.000014 7276879843.734 0.0004 -0.0009 0.14 0.62-
6: 3638381907 3638372755 1.000003 3638439921.863 -0.0016 -0.0018 0.93- 1.24-
7: 1819307508 1819216503 1.000050 1819219960.930 0.0048 -0.0002 4.21 0.01-
8: 909613142 909583182 1.000033 909609980.464 0.0003 -0.0029 0.01 0.79-
9: 454816096 454797028 1.000042 454804990.231 0.0024 -0.0018 0.27 0.14-
10: 227424829 227386787 1.000167 227402495.115 0.0098 -0.0069 2.19 1.09-
11: 113706316 113706116 1.000002 113701247.558 0.0045 0.0043 0.23 0.21
12: 56859486 56860700 0.999979 56850623.779 0.0156 0.0177 1.38 1.79
13: 28430400 28429153 1.000044 28425311.889 0.0179 0.0135 0.91 0.52
14: 14217550 14218160 0.999957 14212655.945 0.0344 0.0387 1.69 2.13
15: 7104688 7106444 0.999753 7106327.972 -0.0231 0.0016 0.38- 0.00
16: 3556690 3551770 1.001385 3553163.986 0.0992 -0.0392 3.50 0.55-
17: 1778261 1775808 1.001381 1776581.993 0.0945 -0.0436 1.59 0.34-
18: 889143 888525 1.000696 888290.997 0.0959 0.0263 0.82 0.06
19: 444139 444703 0.998732 444145.498 -0.0015 0.1255 0.00- 0.70
20: 221839 221760 1.000356 222072.749 -0.1053 -0.1408 0.25- 0.44-
21: 111273 111637 0.996739 111036.375 0.2131 0.5409 0.50 3.25
22: 55567 55477 1.001622 55518.187 0.0879 -0.0742 0.04 0.03-
23: 27324 27845 0.981289 27759.094 -1.5674 0.3095 6.82- 0.27
24: 14041 13934 1.007679 13879.547 1.1632 0.3923 1.88 0.21
25: 7045 6993 1.007436 6939.773 1.5163 0.7670 1.60 0.41
26: 3508 3488 1.005734 3469.887 1.0984 0.5220 0.42 0.09
27: 1711 1724 0.992459 1734.943 -1.3801 -0.6308 0.33- 0.07-
28: 858 884 0.970588 867.472 -1.0919 1.9053 0.10- 0.31
29: 424 437 0.970252 433.736 -2.2446 0.7526 0.22- 0.02
30: 228 228 1.000000 216.868 5.1331 5.1331 0.57 0.57
31: 94 111 0.846847 108.434 -13.3113 2.3665 1.92- 0.06
32: 51 69 0.739130 54.217 -5.9335 27.2664 0.19- 4.03
33: 25 26 0.961538 27.108 -7.7780 -4.0891 0.16- 0.05-
34: 25 9 2.777778 13.554 84.4441 -33.6001 9.67 1.53-
35: 3 6 0.500000 6.777 -55.7334 -11.4668 2.11- 0.09-
36: 3 1 3.000000 3.389 -11.4668 -70.4889 0.04- 1.68-
37: 1 3 0.333333 1.694 -40.9779 77.0663 0.28- 1.01
38: 3 1 3.000000 0.847 254.1327 18.0442 5.47 0.03
39: 0 0 -nan 0.424 -100.0000 -100.0000 0.42- 0.42-
40: 1 0 inf 0.212 372.1770 -100.0000 2.93 0.21-
total: 465721002665 465719617335 1.000003 χ2 = 72.580046 (p = 0.360851), k = 69
source: G2SJDD
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 116442118992 116441990085 1.000001 116442267500.250 -0.0001 -0.0002 0.19- 0.66-
2: 58221085812 58221019901 1.000001 58221133750.062 -0.0001 -0.0002 0.04- 0.22-
3: 29110619549 29110483326 1.000005 29110566875.000 0.0002 -0.0003 0.10 0.24-
4: 14555264414 14555600234 0.999977 14555283437.484 -0.0001 0.0022 0.02- 6.90
5: 7277733081 7277616804 1.000016 7277641718.734 0.0013 -0.0003 1.15 0.09-
6: 3638810755 3638764726 1.000013 3638820859.363 -0.0003 -0.0015 0.03- 0.87-
7: 1819375025 1819412658 0.999979 1819410429.680 -0.0019 0.0001 0.69- 0.00
8: 909692844 909778908 0.999905 909705214.839 -0.0014 0.0081 0.17- 5.97
9: 454839960 454827948 1.000026 454852607.419 -0.0028 -0.0054 0.35- 1.34-
10: 227415293 227438693 0.999897 227426303.709 -0.0048 0.0054 0.53- 0.67
11: 113703181 113714643 0.999899 113713151.854 -0.0088 0.0013 0.87- 0.02
12: 56851835 56854418 0.999955 56856575.927 -0.0083 -0.0038 0.40- 0.08-
13: 28427913 28433536 0.999802 28428287.964 -0.0013 0.0185 0.00- 0.97
14: 14217394 14216365 1.000072 14214143.982 0.0229 0.0156 0.74 0.35
15: 7104887 7105513 0.999912 7107071.991 -0.0307 -0.0219 0.67- 0.34-
16: 3551404 3548759 1.000745 3553535.995 -0.0600 -0.1344 1.28- 6.42-
17: 1773743 1779694 0.996656 1776767.998 -0.1703 0.1647 5.15- 4.82
18: 888639 888441 1.000223 888383.999 0.0287 0.0064 0.07 0.00
19: 444210 444359 0.999665 444191.999 0.0041 0.0376 0.00 0.06
20: 221554 221467 1.000393 222096.000 -0.2440 -0.2832 1.32- 1.78-
21: 110980 111115 0.998785 111048.000 -0.0612 0.0603 0.04- 0.04
22: 55525 55302 1.004032 55524.000 0.0018 -0.3998 0.00 0.89-
23: 27640 27868 0.991819 27762.000 -0.4394 0.3818 0.54- 0.40
24: 13940 13934 1.000431 13881.000 0.4250 0.3818 0.25 0.20
25: 6918 6926 0.998845 6940.500 -0.3242 -0.2089 0.07- 0.03-
26: 3497 3427 1.020426 3470.250 0.7708 -1.2463 0.21 0.54-
27: 1784 1726 1.033604 1735.125 2.8168 -0.5259 1.38 0.05-
28: 901 885 1.018079 867.562 3.8542 2.0099 1.29 0.35
29: 429 413 1.038741 433.781 -1.1022 -4.7907 0.05- 1.00-
30: 225 227 0.991189 216.891 3.7389 4.6610 0.30 0.47
31: 105 123 0.853659 108.445 -3.1770 13.4212 0.11- 1.95
32: 54 61 0.885246 54.223 -0.4106 12.4991 0.00- 0.85
33: 28 30 0.933333 27.111 3.2779 10.6549 0.03 0.31
34: 7 10 0.700000 13.556 -48.3611 -26.2301 3.17- 0.93-
35: 8 5 1.600000 6.778 18.0318 -26.2301 0.22 0.47-
36: 5 2 2.500000 3.389 47.5398 -40.9841 0.77 0.57-
37: 1 1 1.000000 1.694 -40.9841 -40.9841 0.28- 0.28-
38: 1 1 1.000000 0.847 18.0318 18.0318 0.03 0.03
39: 0 0 -nan 0.424 -100.0000 -100.0000 0.42- 0.42-
40: 0 0 -nan 0.212 -100.0000 -100.0000 0.21- 0.21-
41: 0 0 -nan 0.106 -100.0000 -100.0000 0.11- 0.11-
42: 1 0 inf 0.053 1788.5028 -100.0000 16.94 0.05-
total: 465768482310 465769657690 0.999997 χ2 = 61.718883 (p = 0.720980), k = 69
source: G2SJEZ
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 116945901912 116946088110 0.999998 116945715000.250 0.0002 0.0003 0.30 1.19
2: 58472934792 58472329041 1.000010 58472857500.062 0.0001 -0.0009 0.10 4.78-
3: 29236562623 29236478191 1.000003 29236428750.000 0.0005 0.0002 0.61 0.08
4: 14618028325 14618237027 0.999986 14618214374.984 -0.0013 0.0002 2.37- 0.04
5: 7308990718 7309281224 0.999960 7309107187.484 -0.0016 0.0024 1.86- 4.14
6: 3654514372 3654578573 0.999982 3654553593.738 -0.0011 0.0007 0.42- 0.17
7: 1827288054 1827269801 1.000010 1827276796.867 0.0006 -0.0004 0.07 0.03-
8: 913671630 913642654 1.000032 913638398.433 0.0036 0.0005 1.21 0.02
9: 456822714 456793741 1.000063 456819199.216 0.0008 -0.0056 0.03 1.42-
10: 228415568 228432598 0.999925 228409599.608 0.0026 0.0101 0.16 2.32
11: 114192893 114196368 0.999970 114204799.804 -0.0104 -0.0074 1.24- 0.62-
12: 57111987 57102021 1.000175 57102399.902 0.0168 -0.0007 1.61 0.00-
13: 28543083 28553509 0.999635 28551199.951 -0.0284 0.0081 2.31- 0.19
14: 14277857 14274726 1.000219 14275599.975 0.0158 -0.0061 0.36 0.05-
15: 7138952 7140253 0.999818 7137799.988 0.0161 0.0344 0.19 0.84
16: 3568313 3566187 1.000596 3568899.994 -0.0164 -0.0760 0.10- 2.06-
17: 1785896 1784785 1.000622 1784449.997 0.0810 0.0188 1.17 0.06
18: 891167 891355 0.999789 892224.998 -0.1186 -0.0975 1.25- 0.85-
19: 445614 446915 0.997089 446112.499 -0.1117 0.1799 0.56- 1.44
20: 222998 222501 1.002234 223056.250 -0.0261 -0.2489 0.02- 1.38-
21: 111773 111340 1.003889 111528.125 0.2196 -0.1687 0.54 0.32-
22: 55752 55546 1.003709 55764.062 -0.0216 -0.3910 0.00- 0.85-
23: 27819 28138 0.988663 27882.031 -0.2261 0.9180 0.14- 2.35
24: 13886 14056 0.987906 13941.016 -0.3946 0.8248 0.22- 0.95
25: 7024 7017 1.000998 6970.508 0.7674 0.6670 0.41 0.31
26: 3396 3435 0.988646 3485.254 -2.5609 -1.4419 2.29- 0.72-
27: 1775 1697 1.045963 1742.627 1.8577 -2.6183 0.60 1.19-
28: 875 900 0.972222 871.313 0.4231 3.2923 0.02 0.94
29: 408 450 0.906667 435.657 -6.3483 3.2923 1.76- 0.47
30: 221 231 0.956710 217.828 1.4560 6.0468 0.05 0.80
31: 95 104 0.913462 108.914 -12.7754 -4.5120 1.78- 0.22-
32: 54 52 1.038462 54.457 -0.8394 -4.5120 0.00- 0.11-
33: 26 22 1.181818 27.229 -4.5120 -19.2024 0.06- 1.00-
34: 13 15 0.866667 13.614 -4.5120 10.1785 0.03- 0.14
35: 8 9 0.888889 6.807 17.5237 32.2142 0.21 0.71
36: 3 4 0.750000 3.404 -11.8572 17.5237 0.05- 0.10
37: 0 0 -nan 1.702 -100.0000 -100.0000 1.70- 1.70-
38: 1 0 inf 0.851 17.5237 -100.0000 0.03 0.85-
39: 0 2 0.000000 0.425 -100.0000 370.0949 0.43- 5.83
40: 1 0 inf 0.213 370.0949 -100.0000 2.91 0.21-
total: 467782391008 467783328992 0.999998 χ2 = 56.788263 (p = 0.853237), k = 69
source: G2SJHO
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 119695631203 119695895212 0.999998 119695670000.250 -0.0000 0.0002 0.01- 0.42
2: 59848336762 59847937541 1.000007 59847835000.062 0.0008 0.0002 4.21 0.18
3: 29923760639 29923691124 1.000002 29923917500.000 -0.0005 -0.0008 0.82- 1.71-
4: 14961855459 14962063452 0.999986 14961958749.984 -0.0007 0.0007 0.71- 0.73
5: 7481079850 7480851334 1.000031 7480979374.984 0.0013 -0.0017 1.35 2.19-
6: 3740489764 3740577527 0.999977 3740489687.488 0.0000 0.0023 0.00 2.06
7: 1870210060 1870191201 1.000010 1870244843.742 -0.0019 -0.0029 0.65- 1.54-
8: 935070367 935206243 0.999855 935122421.870 -0.0056 0.0090 2.90- 7.51
9: 467558284 467572802 0.999969 467561210.935 -0.0006 0.0025 0.02- 0.29
10: 233769931 233744082 1.000111 233780605.467 -0.0046 -0.0156 0.49- 5.71-
11: 116876947 116887749 0.999908 116890302.733 -0.0114 -0.0022 1.53- 0.06-
12: 58446217 58460025 0.999764 58445151.367 0.0018 0.0254 0.02 3.79
13: 29221673 29219711 1.000067 29222575.683 -0.0031 -0.0098 0.03- 0.28-
14: 14609605 14610375 0.999947 14611287.842 -0.0115 -0.0062 0.19- 0.06-
15: 7308781 7311305 0.999655 7305643.921 0.0429 0.0775 1.35 4.39
16: 3652266 3656571 0.998823 3652821.960 -0.0152 0.1026 0.08- 3.85
17: 1825282 1828161 0.998425 1826410.980 -0.0618 0.0958 0.70- 1.68
18: 913712 912510 1.001317 913205.490 0.0555 -0.0762 0.28 0.53-
19: 457313 455875 1.003154 456602.745 0.1556 -0.1594 1.10 1.16-
20: 228078 228823 0.996744 228301.373 -0.0978 0.2285 0.22- 1.19
21: 113614 113753 0.998778 114150.686 -0.4702 -0.3484 2.52- 1.39-
22: 56768 57340 0.990024 57075.343 -0.5385 0.4637 1.66- 1.23
23: 28543 28690 0.994876 28537.672 0.0187 0.5338 0.00 0.81
24: 14426 14385 1.002850 14268.836 1.1015 0.8141 1.73 0.95
25: 7293 7161 1.018433 7134.418 2.2228 0.3726 3.52 0.10
26: 3492 3490 1.000573 3567.209 -2.1083 -2.1644 1.59- 1.67-
27: 1809 1737 1.041451 1783.604 1.4238 -2.6129 0.36 1.22-
28: 906 903 1.003322 891.802 1.5920 1.2556 0.23 0.14
29: 475 431 1.102088 445.901 6.5259 -3.3418 1.90 0.50-
30: 221 238 0.928571 222.951 -0.8749 6.7501 0.02- 1.02
31: 114 120 0.950000 111.475 2.2648 7.6472 0.06 0.65
32: 62 51 1.215686 55.738 11.2354 -8.4999 0.70 0.40-
33: 32 25 1.280000 27.869 14.8237 -10.2940 0.61 0.30-
34: 10 12 0.833333 13.934 -28.2352 -13.8823 1.11- 0.27-
35: 7 9 0.777778 6.967 0.4707 29.1766 0.00 0.59
36: 3 2 1.500000 3.484 -13.8822 -42.5882 0.07- 0.63-
37: 3 1 3.000000 1.742 72.2355 -42.5882 0.91 0.32-
38: 0 1 0.000000 0.871 -100.0000 14.8236 0.87- 0.02
39: 0 0 -nan 0.435 -100.0000 -100.0000 0.44- 0.44-
40: 0 0 -nan 0.218 -100.0000 -100.0000 0.22- 0.22-
41: 0 0 -nan 0.109 -100.0000 -100.0000 0.11- 0.11-
42: 0 0 -nan 0.054 -100.0000 -100.0000 0.05- 0.05-
43: 1 0 inf 0.027 3574.3092 -100.0000 34.77 0.03-
total: 478782328523 478783031477 0.999999 χ2 = 83.205572 (p = 0.116851), k = 69
source: G2SPON
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 119711985479 119711659141 1.000003 119712577500.250 -0.0005 -0.0008 2.93- 7.05-
2: 59856340724 59856163443 1.000003 59856288750.062 0.0001 -0.0002 0.05 0.26-
3: 29928316947 29928417825 0.999997 29928144375.000 0.0006 0.0009 1.00 2.50
4: 14963962702 14964148928 0.999988 14964072187.484 -0.0007 0.0005 0.80- 0.39
5: 7482030807 7482128092 0.999987 7482036093.734 -0.0001 0.0012 0.00- 1.13
6: 3741027852 3741037911 0.999997 3741018046.863 0.0003 0.0005 0.03 0.11
7: 1870441227 1870555587 0.999939 1870509023.430 -0.0036 0.0025 2.46- 1.16
8: 935235821 935222888 1.000014 935254511.714 -0.0020 -0.0034 0.37- 1.07-
9: 467633167 467628481 1.000010 467627255.856 0.0013 0.0003 0.07 0.00
10: 233805473 233841232 0.999847 233813627.928 -0.0035 0.0118 0.28- 3.26
11: 116914788 116894932 1.000170 116906813.964 0.0068 -0.0102 0.54 1.21-
12: 58458969 58456539 1.000042 58453406.982 0.0095 0.0054 0.53 0.17
13: 29235268 29225417 1.000337 29226703.491 0.0293 -0.0044 2.51 0.06-
14: 14611173 14613409 0.999847 14613351.745 -0.0149 0.0004 0.32- 0.00
15: 7306287 7310350 0.999444 7306675.873 -0.0053 0.0503 0.02- 1.85
16: 3653449 3654900 0.999603 3653337.936 0.0030 0.0428 0.00 0.67
17: 1825975 1825366 1.000334 1826668.968 -0.0380 -0.0713 0.26- 0.93-
18: 912848 913800 0.998958 913334.484 -0.0533 0.0510 0.26- 0.24
19: 455706 456867 0.997459 456667.242 -0.2105 0.0437 2.02- 0.09
20: 228338 228694 0.998443 228333.621 0.0019 0.1578 0.00 0.57
21: 114593 113946 1.005678 114166.811 0.3733 -0.1934 1.59 0.43-
22: 56540 56754 0.996229 57083.405 -0.9519 -0.5771 5.17- 1.90-
23: 28419 28339 1.002823 28541.703 -0.4299 -0.7102 0.53- 1.44-
24: 14155 14185 0.997885 14270.851 -0.8118 -0.6016 0.94- 0.52-
25: 7128 7015 1.016108 7135.426 -0.1041 -1.6877 0.01- 2.03-
26: 3675 3570 1.029412 3567.713 3.0072 0.0641 3.23 0.00
27: 1810 1752 1.033105 1783.856 1.4656 -1.7858 0.38 0.57-
28: 869 824 1.054612 891.928 -2.5706 -7.6159 0.59- 5.17-
29: 450 432 1.041667 445.964 0.9050 -3.1312 0.04 0.44-
30: 228 231 0.987013 222.982 2.2504 3.5958 0.11 0.29
31: 114 109 1.045872 111.491 2.2504 -2.2343 0.06 0.06-
32: 53 62 0.854839 55.746 -4.9251 11.2197 0.14- 0.70
33: 24 34 0.705882 27.873 -13.8944 21.9829 0.54- 1.35
34: 14 16 0.875000 13.936 0.4565 14.8074 0.00 0.31
35: 7 5 1.400000 6.968 0.4565 -28.2453 0.00 0.56-
36: 2 2 1.000000 3.484 -42.5963 -42.5963 0.63- 0.63-
37: 0 2 0.000000 1.742 -100.0000 14.8075 1.74- 0.04
38: 2 3 0.666667 0.871 129.6148 244.4222 1.46 5.20
39: 0 0 -nan 0.436 -100.0000 -100.0000 0.44- 0.44-
40: 1 1 1.000000 0.218 359.2296 359.2296 2.81 2.81
total: 478849468282 478851151718 0.999996 χ2 = 66.233282 (p = 0.572115), k = 69
source: GC1WOV
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 250589081501 250588731601 1.000001 250588495000.250 0.0002 0.0001 1.37 0.22
2: 125294300055 125294558382 0.999998 125294247500.062 0.0000 0.0002 0.02 0.77
3: 62647096788 62647392727 0.999995 62647123750.000 -0.0000 0.0004 0.01- 1.15
4: 31323555169 31323476474 1.000003 31323561874.984 -0.0000 -0.0003 0.00- 0.23-
5: 15661623668 15661945588 0.999979 15661780937.484 -0.0010 0.0011 1.58- 1.73
6: 7830859998 7830653565 1.000026 7830890468.738 -0.0004 -0.0030 0.12- 7.17-
7: 3915448388 3915340510 1.000028 3915445234.367 0.0001 -0.0027 0.00 2.80-
8: 1957724324 1957686504 1.000019 1957722617.183 0.0001 -0.0018 0.00 0.67-
9: 978891139 978879038 1.000012 978861308.591 0.0030 0.0018 0.91 0.32
10: 489451807 489416245 1.000073 489430654.295 0.0043 -0.0029 0.91 0.42-
11: 244742473 244703016 1.000161 244715327.147 0.0111 -0.0050 3.01 0.62-
12: 122343478 122358339 0.999879 122357663.574 -0.0116 0.0006 1.64- 0.00
13: 61185001 61178924 1.000099 61178831.787 0.0101 0.0002 0.62 0.00
14: 30595970 30582602 1.000437 30589415.893 0.0214 -0.0223 1.40 1.52-
15: 15296641 15296498 1.000009 15294707.947 0.0126 0.0117 0.24 0.21
16: 7647676 7645421 1.000295 7647353.973 0.0042 -0.0253 0.01 0.49-
17: 3822795 3825710 0.999238 3823676.987 -0.0231 0.0532 0.20- 1.08
18: 1913365 1912591 1.000405 1911838.493 0.0798 0.0394 1.22 0.30
19: 955774 956035 0.999727 955919.247 -0.0152 0.0121 0.02- 0.01
20: 478419 477380 1.002176 477959.623 0.0961 -0.1213 0.44 0.70-
21: 239832 238589 1.005210 238979.812 0.3566 -0.1635 3.04 0.64-
22: 119769 118695 1.009048 119489.906 0.2336 -0.6652 0.65 5.29-
23: 59724 59268 1.007694 59744.953 -0.0351 -0.7983 0.01- 3.81-
24: 29767 29808 0.998625 29872.476 -0.3531 -0.2158 0.37- 0.14-
25: 14816 14878 0.995833 14936.238 -0.8050 -0.3899 0.97- 0.23-
26: 7388 7550 0.978543 7468.119 -1.0728 1.0964 0.86- 0.90
27: 3850 3742 1.028862 3734.060 3.1049 0.2126 3.60 0.02
28: 1902 1849 1.028664 1867.030 1.8730 -0.9657 0.66 0.17-
29: 951 917 1.037077 933.515 1.8730 -1.7691 0.33 0.29-
30: 474 505 0.938614 466.757 1.5517 8.1932 0.11 3.13
31: 249 239 1.041841 233.379 6.6935 2.4087 1.05 0.14
32: 117 101 1.158416 116.689 0.2662 -13.4454 0.00 2.11-
33: 61 59 1.033898 58.345 4.5511 1.1232 0.12 0.01
34: 32 20 1.600000 29.172 9.6929 -31.4419 0.27 2.88-
35: 28 14 2.000000 14.586 91.9627 -4.0187 12.34 0.02-
36: 4 8 0.500000 7.293 -45.1535 9.6929 1.49- 0.07
37: 2 2 1.000000 3.647 -45.1535 -45.1535 0.74- 0.74-
38: 3 2 1.500000 1.823 64.5394 9.6930 0.76 0.02
39: 1 1 1.000000 0.912 9.6929 9.6929 0.01 0.01
40: 1 1 1.000000 0.456 119.3858 119.3858 0.65 0.65
41: 0 1 0.000000 0.228 -100.0000 338.7716 0.23- 2.62
total: 1002354485640 1002353474360 1.000001 χ2 = 79.885210 (p = 0.220046), k = 71
source: GC1WPW
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 250024778172 250024186135 1.000002 250024295000.250 0.0002 -0.0000 0.93 0.05-
2: 125011939995 125012008473 0.999999 125012147500.062 -0.0002 -0.0001 0.34- 0.15-
3: 62506164014 62506241919 0.999999 62506073750.000 0.0001 0.0003 0.13 0.45
4: 31252901040 31253071493 0.999995 31253036874.984 -0.0004 0.0001 0.59- 0.04
5: 15626403365 15626598287 0.999988 15626518437.484 -0.0007 0.0005 0.85- 0.41
6: 7813143370 7813185046 0.999995 7813259218.738 -0.0015 -0.0009 1.72- 0.70-
7: 3906644753 3906637300 1.000002 3906629609.367 0.0004 0.0002 0.06 0.02
8: 1953333512 1953368446 0.999982 1953314804.683 0.0010 0.0027 0.18 1.47
9: 976660578 976629868 1.000031 976657402.341 0.0003 -0.0028 0.01 0.78-
10: 488341965 488337537 1.000009 488328701.170 0.0027 0.0018 0.36 0.16
11: 244151296 244176932 0.999895 244164350.585 -0.0053 0.0052 0.70- 0.65
12: 122071887 122096768 0.999796 122082175.292 -0.0084 0.0120 0.87- 1.74
13: 61062968 61043162 1.000324 61041087.646 0.0358 0.0034 7.84 0.07
14: 30516512 30533399 0.999447 30520543.823 -0.0132 0.0421 0.53- 5.41
15: 15259302 15260784 0.999903 15260271.912 -0.0064 0.0034 0.06- 0.02
16: 7631987 7629149 1.000372 7630135.956 0.0243 -0.0129 0.45 0.13-
17: 3814313 3814039 1.000072 3815067.978 -0.0198 -0.0270 0.15- 0.28-
18: 1908544 1908357 1.000098 1907533.989 0.0529 0.0431 0.53 0.36
19: 954151 954927 0.999187 953766.994 0.0403 0.1216 0.15 1.41
20: 476521 476601 0.999832 476883.497 -0.0760 -0.0592 0.28- 0.17-
21: 238741 238676 1.000272 238441.749 0.1255 0.0982 0.38 0.23
22: 119629 118953 1.005683 119220.874 0.3423 -0.2247 1.40 0.60-
23: 59699 59641 1.000972 59610.437 0.1486 0.0513 0.13 0.02
24: 29676 29934 0.991381 29805.219 -0.4335 0.4321 0.56- 0.56
25: 14897 15076 0.988127 14902.609 -0.0376 1.1635 0.00- 2.02
26: 7476 7352 1.016866 7451.305 0.3314 -1.3327 0.08 1.32-
27: 3645 3732 0.976688 3725.652 -2.1648 0.1704 1.75- 0.01
28: 1828 1842 0.992400 1862.826 -1.8695 -1.1180 0.65- 0.23-
29: 980 942 1.040340 931.413 5.2165 1.1367 2.53 0.12
30: 456 471 0.968153 465.707 -2.0843 1.1367 0.20- 0.06
31: 213 246 0.865854 232.853 -8.5261 5.6459 1.69- 0.74
32: 115 119 0.966387 116.427 -1.2254 2.2103 0.02- 0.06
33: 56 51 1.098039 58.213 -3.8021 -12.3912 0.08- 0.89-
34: 29 30 0.966667 29.107 -0.3664 3.0692 0.00- 0.03
35: 16 14 1.142857 14.553 9.9405 -3.8021 0.14 0.02-
36: 5 6 0.833333 7.277 -31.2872 -17.5446 0.71- 0.22-
37: 3 3 1.000000 3.638 -17.5446 -17.5446 0.11- 0.11-
38: 2 1 2.000000 1.819 9.9405 -45.0298 0.02 0.37-
39: 2 1 2.000000 0.910 119.8810 9.9405 1.31 0.01
40: 0 1 0.000000 0.455 -100.0000 119.8807 0.45- 0.65
41: 1 0 inf 0.227 339.7615 -100.0000 2.63 0.23-
total: 1000096115367 1000098244633 0.999998 χ2 = 48.668487 (p = 0.980269), k = 71
source: GC1WQX
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 250524862191 250525312422 0.999998 250524860000.250 0.0000 0.0002 0.00 0.82
2: 125262014572 125261957818 1.000000 125262430000.062 -0.0003 -0.0004 1.38- 1.78-
3: 62631419316 62631375495 1.000001 62631215000.000 0.0003 0.0003 0.67 0.41
4: 31315851753 31315396982 1.000015 31315607499.984 0.0008 -0.0007 1.91 1.42-
5: 15657761485 15657627119 1.000009 15657803749.984 -0.0003 -0.0011 0.11- 1.99-
6: 7828974781 7828978388 1.000000 7828901874.988 0.0009 0.0010 0.68 0.75
7: 3914309929 3914517207 0.999947 3914450937.492 -0.0036 0.0017 5.08- 1.12
8: 1957268279 1957253589 1.000008 1957225468.745 0.0022 0.0014 0.94 0.40
9: 978607118 978597285 1.000010 978612734.372 -0.0006 -0.0016 0.03- 0.24-
10: 489285647 489373534 0.999820 489306367.186 -0.0042 0.0137 0.88- 9.22
11: 244675597 244640936 1.000142 244653183.593 0.0092 -0.0050 2.05 0.61-
12: 122324083 122329177 0.999958 122326591.796 -0.0021 0.0021 0.05- 0.05
13: 61163602 61154097 1.000155 61163295.898 0.0005 -0.0150 0.00 1.38-
14: 30579200 30583400 0.999863 30581647.949 -0.0080 0.0057 0.20- 0.10
15: 15291770 15284930 1.000447 15290823.975 0.0062 -0.0385 0.06 2.27-
16: 7643323 7647115 0.999504 7645411.987 -0.0273 0.0223 0.57- 0.38
17: 3822882 3823906 0.999732 3822705.994 0.0046 0.0314 0.01 0.38
18: 1909476 1911045 0.999179 1911352.997 -0.0982 -0.0161 1.84- 0.05-
19: 957202 955772 1.001496 955676.498 0.1596 0.0100 2.44 0.01
20: 477723 479044 0.997242 477838.249 -0.0241 0.2523 0.03- 3.04
21: 238968 239058 0.999624 238919.125 0.0205 0.0581 0.01 0.08
22: 119211 120255 0.991318 119459.562 -0.2081 0.6659 0.52- 5.30
23: 59936 59822 1.001906 59729.781 0.3453 0.1544 0.71 0.14
24: 30377 29775 1.020218 29864.891 1.7148 -0.3010 8.78 0.27-
25: 14678 14841 0.989017 14932.445 -1.7040 -0.6124 4.34- 0.56-
26: 7533 7455 1.010463 7466.223 0.8944 -0.1503 0.60 0.02-
27: 3713 3823 0.971227 3733.111 -0.5387 2.4079 0.11- 2.16
28: 1878 1851 1.014587 1866.556 0.6131 -0.8334 0.07 0.13-
29: 909 893 1.017917 933.278 -2.6014 -4.3157 0.63- 1.74-
30: 462 516 0.895349 466.639 -0.9941 10.5780 0.05- 5.22
31: 224 225 0.995556 233.319 -3.9943 -3.5657 0.37- 0.30-
32: 100 137 0.729927 116.660 -14.2806 17.4356 2.38- 3.55
33: 56 58 0.965517 58.330 -3.9943 -0.5655 0.09- 0.00-
34: 25 26 0.961538 29.165 -14.2806 -10.8518 0.59- 0.34-
35: 15 15 1.000000 14.582 2.8633 2.8633 0.01 0.01
36: 5 9 0.555556 7.291 -31.4245 23.4359 0.72- 0.40
37: 4 5 0.800000 3.646 9.7208 37.1510 0.03 0.50
38: 1 0 inf 1.823 -45.1396 -100.0000 0.37- 1.82-
39: 3 2 1.500000 0.911 229.1625 119.4417 4.79 1.30
40: 1 1 1.000000 0.456 119.4417 119.4417 0.65 0.65
41: 0 0 -nan 0.228 -100.0000 -100.0000 0.23- 0.23-
42: 0 0 -nan 0.114 -100.0000 -100.0000 0.11- 0.11-
43: 0 1 0.000000 0.057 -100.0000 1655.5255 0.06- 15.61
total: 1002099693742 1002099186258 1.000001 χ2 = 85.551041 (p = 0.114778), k = 71
source: GD135W
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 250754965570 250755396337 0.999998 250755022500.250 -0.0000 0.0001 0.01- 0.56
2: 125377970986 125377363672 1.000005 125377511250.062 0.0004 -0.0001 1.69 0.17-
3: 62688653395 62688642600 1.000000 62688755625.000 -0.0002 -0.0002 0.17- 0.20-
4: 31344337691 31344502635 0.999995 31344377812.484 -0.0001 0.0004 0.05- 0.50
5: 15672308687 15672154902 1.000010 15672188906.234 0.0008 -0.0002 0.92 0.07-
6: 7836071593 7836032558 1.000005 7836094453.113 -0.0003 -0.0008 0.07- 0.49-
7: 3917947532 3918054587 0.999973 3918047226.555 -0.0025 0.0002 2.54- 0.01
8: 1958979637 1959077280 0.999950 1959023613.276 -0.0022 0.0027 0.99- 1.47
9: 979512489 979497478 1.000015 979511806.638 0.0001 -0.0015 0.00 0.21-
10: 489732747 489774517 0.999915 489755903.319 -0.0047 0.0038 1.09- 0.71
11: 244880813 244851151 1.000121 244877951.659 0.0012 -0.0109 0.03 2.93-
12: 122440748 122442726 0.999984 122438975.830 0.0014 0.0031 0.03 0.11
13: 61219429 61232100 0.999793 61219487.915 -0.0001 0.0206 0.00- 2.60
14: 30606639 30617808 0.999635 30609743.957 -0.0101 0.0263 0.31- 2.12
15: 15309135 15304749 1.000287 15304871.979 0.0279 -0.0008 1.19 0.00-
16: 7657973 7651684 1.000822 7652435.989 0.0724 -0.0098 4.01 0.07-
17: 3825849 3827821 0.999485 3826217.995 -0.0096 0.0419 0.04- 0.67
18: 1911893 1911834 1.000031 1913108.997 -0.0636 -0.0666 0.77- 0.85-
19: 957837 956869 1.001012 956554.499 0.1341 0.0329 1.72 0.10
20: 479073 478060 1.002119 478277.249 0.1664 -0.0454 1.32 0.10-
21: 239952 238457 1.006269 239138.625 0.3401 -0.2850 2.77 1.94-
22: 119640 118922 1.006038 119569.312 0.0591 -0.5414 0.04 3.50-
23: 59462 60008 0.990901 59784.656 -0.5397 0.3736 1.74- 0.83
24: 30038 29878 1.005355 29892.328 0.4873 -0.0479 0.71 0.01-
25: 14784 15092 0.979592 14946.164 -1.0850 0.9757 1.76- 1.42
26: 7411 7415 0.999461 7473.082 -0.8307 -0.7772 0.52- 0.45-
27: 3755 3724 1.008324 3736.541 0.4940 -0.3356 0.09 0.04-
28: 1873 1801 1.039978 1868.271 0.2531 -3.6007 0.01 2.42-
29: 1007 985 1.022335 934.135 7.8002 5.4451 5.68 2.77
30: 494 469 1.053305 467.068 5.7663 0.4137 1.55 0.01
31: 252 224 1.125000 233.534 7.9073 -4.0824 1.46 0.39-
32: 103 119 0.865546 116.767 -11.7901 1.9124 1.62- 0.04
33: 60 69 0.869565 58.383 2.7688 18.1842 0.04 1.93
34: 20 31 0.645161 29.192 -31.4874 6.1945 2.89- 0.11
35: 17 16 1.062500 14.596 16.4714 9.6201 0.40 0.14
36: 3 6 0.500000 7.298 -58.8925 -17.7849 2.53- 0.23-
37: 1 5 0.200000 3.649 -72.5950 37.0251 1.92- 0.50
38: 2 2 1.000000 1.824 9.6201 9.6201 0.02 0.02
39: 0 0 -nan 0.912 -100.0000 -100.0000 0.91- 0.91-
40: 1 0 inf 0.456 119.2401 -100.0000 0.65 0.46-
41: 0 0 -nan 0.228 -100.0000 -100.0000 0.23- 0.23-
42: 0 0 -nan 0.114 -100.0000 -100.0000 0.11- 0.11-
43: 1 0 inf 0.057 1653.9244 -100.0000 15.60 0.06-
total: 1003019857495 1003020322505 1.000000 χ2 = 70.971837 (p = 0.478619), k = 71
source: GDD3H9
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 251500880828 251500864171 1.000000 251501017500.250 -0.0001 -0.0001 0.07- 0.09-
2: 125750358735 125750994524 0.999995 125750508750.062 -0.0001 0.0004 0.18- 1.88
3: 62875188073 62875137961 1.000001 62875254375.000 -0.0001 -0.0002 0.07- 0.22-
4: 31437899069 31437625046 1.000009 31437627187.484 0.0009 -0.0000 2.35 0.00-
5: 15718909568 15718783188 1.000008 15718813593.734 0.0006 -0.0002 0.59 0.06-
6: 7859481872 7859286035 1.000025 7859406796.863 0.0010 -0.0015 0.72 1.86-
7: 3929652235 3929645570 1.000002 3929703398.430 -0.0013 -0.0015 0.67- 0.85-
8: 1964811924 1964867956 0.999971 1964851699.214 -0.0020 0.0008 0.81- 0.13
9: 982428302 982404412 1.000024 982425849.606 0.0002 -0.0022 0.01 0.47-
10: 491247855 491224714 1.000047 491212924.803 0.0071 0.0024 2.48 0.28
11: 245583202 245618513 0.999856 245606462.401 -0.0095 0.0049 2.20- 0.59
12: 122789044 122781263 1.000063 122803231.201 -0.0116 -0.0179 1.64- 3.93-
13: 61413414 61398211 1.000248 61401615.600 0.0192 -0.0055 2.27 0.19-
14: 30701401 30707519 0.999801 30700807.800 0.0019 0.0219 0.01 1.47
15: 15343627 15345769 0.999860 15350403.900 -0.0441 -0.0302 2.99- 1.40-
16: 7676647 7682305 0.999264 7675201.950 0.0188 0.0925 0.27 6.57
17: 3839822 3839204 1.000161 3837600.975 0.0579 0.0418 1.29 0.67
18: 1917140 1919315 0.998867 1918800.488 -0.0865 0.0268 1.44- 0.14
19: 960165 958598 1.001635 959400.244 0.0797 -0.0836 0.61 0.67-
20: 480469 479530 1.001958 479700.122 0.1603 -0.0355 1.23 0.06-
21: 239794 240049 0.998938 239850.061 -0.0234 0.0829 0.01- 0.17
22: 120255 119908 1.002894 119925.030 0.2751 -0.0142 0.91 0.00-
23: 59850 59780 1.001171 59962.515 -0.1876 -0.3044 0.21- 0.56-
24: 30228 30234 0.999802 29981.258 0.8230 0.8430 2.03 2.13
25: 15100 14875 1.015126 14990.629 0.7296 -0.7713 0.80 0.89-
26: 7464 7655 0.975049 7495.314 -0.4178 2.1305 0.13- 3.40
27: 3823 3651 1.047110 3747.657 2.0104 -2.5791 1.51 2.49-
28: 1805 1770 1.019774 1873.829 -3.6732 -5.5410 2.53- 5.75-
29: 958 911 1.051592 936.914 2.2505 -2.7659 0.47 0.72-
30: 464 494 0.939271 468.457 -0.9515 5.4525 0.04- 1.39
31: 231 238 0.970588 234.229 -1.3784 1.6101 0.04- 0.06
32: 117 116 1.008621 117.114 -0.0976 -0.9515 0.00- 0.01-
33: 67 49 1.367347 58.557 14.4181 -16.3211 1.22 1.56-
34: 21 30 0.700000 29.279 -28.2752 2.4640 2.34- 0.02
35: 16 14 1.142857 14.639 9.2949 -4.3669 0.13 0.03-
36: 7 12 0.583333 7.320 -4.3669 63.9424 0.01- 2.99
37: 3 4 0.750000 3.660 -18.0288 9.2950 0.12- 0.03
38: 2 4 0.500000 1.830 9.2949 118.5899 0.02 2.57
39: 2 0 inf 0.915 118.5900 -100.0000 1.29 0.91-
40: 0 1 0.000000 0.457 -100.0000 118.5897 0.46- 0.64
total: 1006004853924 1006003286076 1.000002 χ2 = 77.979900 (p = 0.266604), k = 71
source: GDYXTH
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 250013514811 250013185684 1.000001 250013547500.250 -0.0000 -0.0001 0.00- 0.52-
2: 125006709555 125006782616 0.999999 125006773750.062 -0.0001 0.0000 0.03- 0.00
3: 62503310553 62503180188 1.000002 62503386875.000 -0.0001 -0.0003 0.09- 0.68-
4: 31251595022 31251834665 0.999992 31251693437.484 -0.0003 0.0005 0.31- 0.64
5: 15625888808 15626149884 0.999983 15625846718.734 0.0003 0.0019 0.11 5.88
6: 7812947026 7812900064 1.000006 7812923359.363 0.0003 -0.0003 0.07 0.07-
7: 3906461186 3906468694 0.999998 3906461679.680 -0.0000 0.0002 0.00- 0.01
8: 1953209891 1953202550 1.000004 1953230839.839 -0.0011 -0.0014 0.22- 0.41-
9: 976610092 976612186 0.999998 976615419.919 -0.0005 -0.0003 0.03- 0.01-
10: 488302644 488283742 1.000039 488307709.959 -0.0010 -0.0049 0.05- 1.18-
11: 244167145 244152268 1.000061 244153854.979 0.0054 -0.0006 0.72 0.01-
12: 122084688 122069981 1.000120 122076927.490 0.0064 -0.0057 0.49 0.40-
13: 61049803 61035032 1.000242 61038463.745 0.0186 -0.0056 2.11 0.19-
14: 30525595 30518079 1.000246 30519231.872 0.0208 -0.0038 1.33 0.04-
15: 15258228 15256135 1.000137 15259615.936 -0.0091 -0.0228 0.13- 0.79-
16: 7624787 7631370 0.999137 7629807.968 -0.0658 0.0205 3.30- 0.32
17: 3815785 3814411 1.000360 3814903.984 0.0231 -0.0129 0.20 0.06-
18: 1908198 1905380 1.001479 1907451.992 0.0391 -0.1086 0.29 2.25-
19: 953413 953403 1.000010 953725.996 -0.0328 -0.0339 0.10- 0.11-
20: 476689 477291 0.998739 476862.998 -0.0365 0.0898 0.06- 0.38
21: 237934 239205 0.994687 238431.499 -0.2087 0.3244 1.04- 2.51
22: 119758 119083 1.005668 119215.750 0.4548 -0.1114 2.47 0.15-
23: 59821 59313 1.008565 59607.875 0.3575 -0.4947 0.76 1.46-
24: 29452 29641 0.993624 29803.937 -1.1808 -0.5467 4.16- 0.89-
25: 14933 14980 0.996862 14901.969 0.2082 0.5236 0.06 0.41
26: 7543 7464 1.010584 7450.984 1.2349 0.1747 1.14 0.02
27: 3694 3801 0.971850 3725.492 -0.8453 2.0268 0.27- 1.53
28: 1917 1852 1.035097 1862.746 2.9126 -0.5769 1.58 0.06-
29: 900 928 0.969828 931.373 -3.3685 -0.3622 1.06- 0.01-
30: 467 453 1.030905 465.687 0.2821 -2.7243 0.00 0.35-
31: 246 245 1.004082 232.843 5.6505 5.2210 0.74 0.63
32: 146 124 1.177419 116.422 25.4062 6.5094 7.51 0.49
33: 43 65 0.661538 58.211 -26.1306 11.6631 3.97- 0.79
34: 26 21 1.238095 29.105 -10.6695 -27.8485 0.33- 2.26-
35: 11 16 0.687500 14.553 -24.4127 9.9452 0.87- 0.14
36: 7 6 1.166667 7.276 -3.7979 -17.5411 0.01- 0.22-
37: 8 6 1.333333 3.638 119.8904 64.9178 5.23 1.53
38: 3 0 inf 1.819 64.9178 -100.0000 0.77 1.82-
39: 0 2 0.000000 0.910 -100.0000 119.8904 0.91- 1.31
40: 0 1 0.000000 0.455 -100.0000 119.8904 0.45- 0.65
41: 0 0 -nan 0.227 -100.0000 -100.0000 0.23- 0.23-
42: 0 0 -nan 0.114 -100.0000 -100.0000 0.11- 0.11-
43: 0 0 -nan 0.057 -100.0000 -100.0000 0.06- 0.06-
44: 0 0 -nan 0.028 -100.0000 -100.0000 0.03- 0.03-
45: 1 0 inf 0.014 6936.3073 -100.0000 68.38 0.01-
total: 1000053884411 1000054495589 0.999999 χ2 = 61.549441 (p = 0.780726), k = 71
source: GEFSTF
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 244764041358 244764348857 0.999999 244763525000.250 0.0002 0.0003 1.09 2.77
2: 122381764640 122381614283 1.000001 122381762500.062 0.0000 -0.0001 0.00 0.18-
3: 61191168210 61190592322 1.000009 61190881250.000 0.0005 -0.0005 1.35 1.36-
4: 30595483264 30595348378 1.000004 30595440624.984 0.0001 -0.0003 0.06 0.28-
5: 15297554494 15297934433 0.999975 15297720312.484 -0.0011 0.0014 1.80- 3.00
6: 7648840786 7648911325 0.999991 7648860156.238 -0.0003 0.0007 0.05- 0.34
7: 3824300327 3824338519 0.999990 3824430078.117 -0.0034 -0.0024 4.40- 2.19-
8: 1912158626 1912211235 0.999972 1912215039.058 -0.0030 -0.0002 1.66- 0.01-
9: 956126835 956114036 1.000013 956107519.528 0.0020 0.0007 0.39 0.04
10: 478062886 478053056 1.000021 478053759.764 0.0019 -0.0001 0.17 0.00-
11: 239038018 239049712 0.999951 239026879.882 0.0047 0.0096 0.52 2.18
12: 119514156 119526993 0.999893 119513439.941 0.0006 0.0113 0.00 1.54
13: 59748250 59762151 0.999767 59756719.970 -0.0142 0.0091 1.20- 0.49
14: 29880928 29881494 0.999981 29878359.985 0.0086 0.0105 0.22 0.33
15: 14942058 14935501 1.000439 14939179.993 0.0193 -0.0246 0.55 0.91-
16: 7470171 7470555 0.999949 7469589.996 0.0078 0.0129 0.05 0.12
17: 3733192 3733204 0.999997 3734794.998 -0.0429 -0.0426 0.69- 0.68-
18: 1867532 1865068 1.001321 1867397.499 0.0072 -0.1247 0.01 2.91-
19: 931685 932824 0.998779 933698.750 -0.2157 -0.0937 4.34- 0.82-
20: 466977 467743 0.998362 466849.375 0.0273 0.1914 0.03 1.71
21: 232816 233492 0.997105 233424.687 -0.2608 0.0288 1.59- 0.02
22: 116225 116969 0.993639 116712.344 -0.4176 0.2199 2.03- 0.56
23: 58217 58508 0.995026 58356.172 -0.2385 0.2602 0.33- 0.40
24: 28877 29242 0.987518 29178.086 -1.0319 0.2190 3.11- 0.14
25: 14402 14513 0.992352 14589.043 -1.2821 -0.5212 2.40- 0.40-
26: 7194 7531 0.955252 7294.521 -1.3780 3.2419 1.39- 7.67
27: 3583 3698 0.968902 3647.261 -1.7619 1.3912 1.13- 0.71
28: 1749 1800 0.971667 1823.630 -4.0924 -1.2958 3.05- 0.31-
29: 857 870 0.985057 911.815 -6.0117 -4.5859 3.30- 1.92-
30: 471 481 0.979210 455.908 3.3104 5.5038 0.50 1.38
31: 201 203 0.990148 227.954 -11.8242 -10.9469 3.19- 2.73-
32: 108 112 0.964286 113.977 -5.2440 -1.7345 0.31- 0.03-
33: 52 50 1.040000 56.988 -8.7534 -12.2629 0.44- 0.86-
34: 34 28 1.214286 28.494 19.3224 -1.7345 1.06 0.01-
35: 15 17 0.882353 14.247 5.2845 19.3224 0.04 0.53
36: 12 4 3.000000 7.124 68.4552 -43.8483 3.34 1.37-
37: 4 3 1.333333 3.562 12.3035 -15.7724 0.05 0.09-
38: 2 2 1.000000 1.781 12.3035 12.3035 0.03 0.03
39: 0 0 -nan 0.890 -100.0000 -100.0000 0.89- 0.89-
40: 1 1 1.000000 0.445 124.6070 124.6070 0.69 0.69
41: 1 0 inf 0.223 349.2141 -100.0000 2.71 0.22-
total: 979053614231 979054585769 0.999999 χ2 = 86.685361 (p = 0.099357), k = 71
source: GEH88D
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 250743965810 250743843513 1.000000 250744340000.250 -0.0001 -0.0002 0.56- 0.98-
2: 125371689727 125372590873 0.999993 125372170000.062 -0.0004 0.0003 1.84- 1.41
3: 62685884888 62685880556 1.000000 62686085000.000 -0.0003 -0.0003 0.64- 0.67-
4: 31343386105 31342898484 1.000016 31343042499.984 0.0011 -0.0005 3.77 0.66-
5: 15671760126 15671491732 1.000017 15671521249.984 0.0015 -0.0002 3.64 0.06-
6: 7835689991 7835701568 0.999999 7835760624.988 -0.0009 -0.0008 0.64- 0.45-
7: 3917898590 3917909711 0.999997 3917880312.492 0.0005 0.0008 0.09 0.22
8: 1958959598 1958923005 1.000019 1958940156.245 0.0010 -0.0009 0.19 0.15-
9: 979499010 979485245 1.000014 979470078.122 0.0030 0.0015 0.85 0.23
10: 489757459 489769506 0.999975 489735039.061 0.0046 0.0070 1.03 2.43
11: 244863712 244858728 1.000020 244867519.530 -0.0016 -0.0036 0.06- 0.32-
12: 122439357 122435882 1.000028 122433759.765 0.0046 0.0017 0.26 0.04
13: 61214710 61228623 0.999773 61216879.883 -0.0035 0.0192 0.08- 2.25
14: 30606768 30610503 0.999878 30608439.941 -0.0055 0.0067 0.09- 0.14
15: 15303283 15298395 1.000320 15304219.971 -0.0061 -0.0381 0.06- 2.22-
16: 7650449 7645402 1.000660 7652109.985 -0.0217 -0.0877 0.36- 5.88-
17: 3827468 3823889 1.000936 3826054.993 0.0369 -0.0566 0.52 1.23-
18: 1912317 1913285 0.999494 1913027.496 -0.0371 0.0135 0.26- 0.03
19: 956814 957558 0.999223 956513.748 0.0314 0.1092 0.09 1.14
20: 477721 478406 0.998568 478256.874 -0.1120 0.0312 0.60- 0.05
21: 239250 238352 1.003768 239128.437 0.0508 -0.3247 0.06 2.52-
22: 118975 119418 0.996290 119564.219 -0.4928 -0.1223 2.90- 0.18-
23: 60118 59801 1.005301 59782.109 0.5619 0.0316 1.89 0.01
24: 29925 29792 1.004464 29891.055 0.1136 -0.3314 0.04 0.33-
25: 14981 14869 1.007532 14945.527 0.2373 -0.5120 0.08 0.39-
26: 7448 7449 0.999866 7472.764 -0.3314 -0.3180 0.08- 0.08-
27: 3662 3730 0.981769 3736.382 -1.9907 -0.1708 1.48- 0.01-
28: 1862 1854 1.004315 1868.191 -0.3314 -0.7596 0.02- 0.11-
29: 971 977 0.993859 934.095 3.9508 4.5932 1.46 1.97
30: 456 456 1.000000 467.048 -2.3654 -2.3654 0.26- 0.26-
31: 240 225 1.066667 233.524 2.7732 -3.6501 0.18 0.31-
32: 113 127 0.889764 116.762 -3.2219 8.7683 0.12- 0.90
33: 67 53 1.264151 58.381 14.7634 -9.2170 1.27 0.50-
34: 21 24 0.875000 29.190 -28.0587 -17.7814 2.30- 0.92-
35: 16 14 1.142857 14.595 9.6248 -4.0783 0.14 0.02-
36: 5 8 0.625000 7.298 -31.4845 9.6248 0.72- 0.07
37: 2 1 2.000000 3.649 -45.1876 -72.5938 0.75- 1.92-
38: 0 2 0.000000 1.824 -100.0000 9.6248 1.82- 0.02
39: 1 0 inf 0.912 9.6247 -100.0000 0.01 0.91-
40: 2 1 2.000000 0.456 338.4994 119.2497 5.23 0.65
total: 1002978274143 1002976445857 1.000002 χ2 = 57.748000 (p = 0.871402), k = 71
source: GEZ63J
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 250866898369 250866772825 1.000001 250866367500.250 0.0002 0.0002 1.12 0.65
2: 125432721965 125433018643 0.999998 125433183750.062 -0.0004 -0.0001 1.70- 0.22-
3: 62716642625 62716620059 1.000000 62716591875.000 0.0001 0.0000 0.04 0.01
4: 31358346177 31358503356 0.999995 31358295937.484 0.0002 0.0007 0.08 1.37
5: 15679065156 15679159797 0.999994 15679147968.734 -0.0005 0.0001 0.44- 0.01
6: 7839766954 7839404823 1.000046 7839573984.363 0.0025 -0.0022 4.75 3.65-
7: 3919742516 3919769811 0.999993 3919786992.180 -0.0011 -0.0004 0.50- 0.08-
8: 1959860205 1959910759 0.999974 1959893496.089 -0.0017 0.0009 0.57- 0.15
9: 979981132 979927052 1.000055 979946748.044 0.0035 -0.0020 1.21 0.40-
10: 489962915 489933504 1.000060 489973374.022 -0.0021 -0.0081 0.22- 3.24-
11: 244984101 244970924 1.000054 244986687.011 -0.0011 -0.0064 0.03- 1.01-
12: 122510024 122494995 1.000123 122493343.505 0.0136 0.0013 2.27 0.02
13: 61249363 61247305 1.000034 61246671.753 0.0044 0.0010 0.12 0.01
14: 30628663 30628567 1.000003 30623335.876 0.0174 0.0171 0.93 0.89
15: 15314229 15306439 1.000509 15311667.938 0.0167 -0.0342 0.43 1.79-
16: 7656631 7657834 0.999843 7655833.969 0.0104 0.0261 0.08 0.52
17: 3829693 3829680 1.000003 3827916.985 0.0464 0.0461 0.82 0.81
18: 1911794 1914299 0.998691 1913958.492 -0.1131 0.0178 2.45- 0.06
19: 956185 956433 0.999741 956979.246 -0.0830 -0.0571 0.66- 0.31-
20: 477330 479197 0.996104 478489.623 -0.2424 0.1478 2.81- 1.05
21: 239426 239191 1.000982 239244.812 0.0757 -0.0225 0.14 0.01-
22: 119386 119084 1.002536 119622.406 -0.1976 -0.4501 0.47- 2.42-
23: 59787 59660 1.002129 59811.203 -0.0405 -0.2528 0.01- 0.38-
24: 29776 30009 0.992236 29905.601 -0.4334 0.3457 0.56- 0.36
25: 15015 14937 1.005222 14952.801 0.4160 -0.1057 0.26 0.02-
26: 7464 7571 0.985867 7476.400 -0.1659 1.2653 0.02- 1.20
27: 3667 3780 0.970106 3738.200 -1.9047 1.1182 1.36- 0.47
28: 1811 1900 0.953158 1869.100 -3.1085 1.6532 1.81- 0.51
29: 988 941 1.049947 934.550 5.7193 0.6902 3.06 0.04
30: 481 447 1.076063 467.275 2.9372 -4.3390 0.40 0.88-
31: 243 254 0.956693 233.638 4.0073 8.7154 0.38 1.77
32: 138 148 0.932432 116.819 18.1317 26.6920 3.84 8.32
33: 69 49 1.408163 58.409 18.1317 -16.1094 1.92 1.52-
34: 26 29 0.896552 29.205 -10.9732 -0.7009 0.35- 0.00-
35: 16 11 1.454545 14.602 9.5714 -24.6696 0.13 0.89-
36: 5 5 1.000000 7.301 -31.5178 -31.5178 0.73- 0.73-
37: 1 7 0.142857 3.651 -72.6071 91.7500 1.92- 3.07
38: 0 1 0.000000 1.825 -100.0000 -45.2143 1.83- 0.37-
39: 1 1 1.000000 0.913 9.5714 9.5714 0.01 0.01
40: 0 0 -nan 0.456 -100.0000 -100.0000 0.46- 0.46-
41: 0 1 0.000000 0.228 -100.0000 338.2851 0.23- 2.61
total: 1003466082423 1003464857577 1.000001 χ2 = 72.431108 (p = 0.430466), k = 71
source: GEZ64G
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 250157058448 250156778022 1.000001 250157070000.250 -0.0000 -0.0001 0.00- 0.34-
2: 125078509258 125078336229 1.000001 125078535000.062 -0.0000 -0.0002 0.01- 0.32-
3: 62538832209 62539455269 0.999990 62539267500.000 -0.0007 0.0003 3.03- 0.56
4: 31269698161 31269587916 1.000004 31269633749.984 0.0002 -0.0001 0.13 0.07-
5: 15634800711 15634976233 0.999989 15634816874.984 -0.0001 0.0010 0.02- 1.62
6: 7817585346 7817423775 1.000021 7817408437.488 0.0023 0.0002 4.00 0.03
7: 3908621156 3908741331 0.999969 3908704218.742 -0.0021 0.0009 1.77- 0.35
8: 1954398065 1954264416 1.000068 1954352109.370 0.0024 -0.0045 1.08 3.93-
9: 977189311 977146855 1.000043 977176054.685 0.0014 -0.0030 0.18 0.87-
10: 488597337 488579384 1.000037 488588027.342 0.0019 -0.0018 0.18 0.15-
11: 244290353 244306701 0.999933 244294013.671 -0.0015 0.0052 0.05- 0.66
12: 122153882 122157607 0.999970 122147006.835 0.0056 0.0087 0.39 0.92
13: 61088754 61061535 1.000446 61073503.418 0.0250 -0.0196 3.81 2.35-
14: 30529407 30544267 0.999513 30536751.709 -0.0241 0.0246 1.77- 1.85
15: 15270718 15268686 1.000133 15268375.854 0.0153 0.0020 0.36 0.01
16: 7631583 7632613 0.999865 7634187.927 -0.0341 -0.0206 0.89- 0.32-
17: 3820107 3815685 1.001159 3817093.964 0.0789 -0.0369 2.38 0.52-
18: 1908714 1906614 1.001101 1908546.982 0.0088 -0.1013 0.01 1.96-
19: 953171 953970 0.999162 954273.491 -0.1155 -0.0318 1.27- 0.10-
20: 478165 478070 1.000199 477136.745 0.2155 0.1956 2.22 1.83
21: 238943 238165 1.003267 238568.373 0.1570 -0.1691 0.59 0.68-
22: 119091 119021 1.000588 119284.186 -0.1620 -0.2206 0.31- 0.58-
23: 59661 59819 0.997359 59642.093 0.0317 0.2966 0.01 0.52
24: 29788 30235 0.985216 29821.047 -0.1108 1.3881 0.04- 5.75
25: 14867 14877 0.999328 14910.523 -0.2919 -0.2248 0.13- 0.08-
26: 7587 7601 0.998158 7455.262 1.7671 1.9548 2.33 2.85
27: 3771 3681 1.024450 3727.631 1.1635 -1.2510 0.50 0.58-
28: 1840 1826 1.007667 1863.815 -1.2778 -2.0289 0.30- 0.77-
29: 919 958 0.959290 931.908 -1.3851 2.7999 0.18- 0.73
30: 483 471 1.025478 465.954 3.6583 1.0830 0.62 0.05
31: 251 249 1.008032 232.977 7.7360 6.8775 1.39 1.10
32: 133 100 1.330000 116.488 14.1744 -14.1546 2.34 2.33-
33: 54 68 0.794118 58.244 -7.2870 16.7498 0.31- 1.63
34: 34 30 1.133333 29.122 16.7498 3.0145 0.82 0.03
35: 15 17 0.882353 14.561 3.0145 16.7498 0.01 0.41
36: 4 7 0.571429 7.281 -45.0589 -3.8531 1.48- 0.01-
37: 4 1 4.000000 3.640 9.8821 -72.5295 0.04 1.91-
38: 2 1 2.000000 1.820 9.8821 -45.0589 0.02 0.37-
39: 2 0 inf 0.910 119.7643 -100.0000 1.31 0.91-
40: 0 1 0.000000 0.455 -100.0000 119.7643 0.46- 0.65
total: 1000628340214 1000628219786 1.000000 χ2 = 71.769958 (p = 0.452117), k = 71
source: GTHJA5
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 244699414116 244699865414 0.999998 244699495000.250 -0.0000 0.0002 0.03- 0.56
2: 122349649199 122349453691 1.000002 122349747500.062 -0.0001 -0.0002 0.08- 0.71-
3: 61175022369 61175111000 0.999999 61174873750.000 0.0002 0.0004 0.36 0.92
4: 30587380330 30587390208 1.000000 30587436874.984 -0.0002 -0.0002 0.10- 0.07-
5: 15293876068 15293702055 1.000011 15293718437.484 0.0010 -0.0001 1.62 0.02-
6: 7646900980 7646735922 1.000022 7646859218.738 0.0005 -0.0016 0.23 1.99-
7: 3823387195 3823397487 0.999997 3823429609.367 -0.0011 -0.0008 0.47- 0.27-
8: 1911753622 1911765643 0.999994 1911714804.683 0.0020 0.0027 0.79 1.35
9: 955809798 955814309 0.999995 955857402.341 -0.0050 -0.0045 2.37- 1.94-
10: 477923558 477913419 1.000021 477928701.170 -0.0011 -0.0032 0.06- 0.49-
11: 238981615 238952276 1.000123 238964350.585 0.0072 -0.0051 1.25 0.61-
12: 119485678 119488310 0.999978 119482175.292 0.0029 0.0051 0.10 0.31
13: 59746221 59740517 1.000095 59741087.646 0.0086 -0.0010 0.44 0.01-
14: 29866719 29877448 0.999641 29870543.823 -0.0128 0.0231 0.49- 1.60
15: 14936986 14937153 0.999989 14935271.912 0.0115 0.0126 0.20 0.24
16: 7471352 7463506 1.001051 7467635.956 0.0498 -0.0553 1.85 2.28-
17: 3736961 3734453 1.000672 3733817.978 0.0842 0.0170 2.65 0.11
18: 1866915 1866785 1.000070 1866908.989 0.0003 -0.0066 0.00 0.01-
19: 932857 932157 1.000751 933454.494 -0.0640 -0.1390 0.38- 1.80-
20: 466090 467606 0.996758 466727.247 -0.1365 0.1883 0.87- 1.65
21: 232851 233433 0.997507 233363.624 -0.2197 0.0297 1.13- 0.02
22: 116900 116358 1.004658 116681.812 0.1870 -0.2775 0.41 0.90-
23: 58736 58309 1.007323 58340.906 0.6772 -0.0547 2.68 0.02-
24: 29215 29152 1.002161 29170.453 0.1527 -0.0633 0.07 0.01-
25: 14654 14667 0.999114 14585.226 0.4715 0.5607 0.32 0.46
26: 7279 7211 1.009430 7292.613 -0.1867 -1.1191 0.03- 0.91-
27: 3702 3612 1.024917 3646.307 1.5274 -0.9409 0.85 0.32-
28: 1897 1890 1.003704 1823.153 4.0505 3.6665 2.99 2.45
29: 971 879 1.104664 911.577 6.5187 -3.5737 3.87 1.16-
30: 447 456 0.980263 455.788 -1.9282 0.0464 0.17- 0.00
31: 258 214 1.205607 227.894 13.2104 -6.0968 3.98 0.85-
32: 122 118 1.033898 113.947 7.0672 3.5568 0.57 0.14
33: 62 64 0.968750 56.974 8.8224 12.3328 0.44 0.87
34: 21 24 0.875000 28.487 -26.2816 -15.7504 1.97- 0.71-
35: 13 14 0.928571 14.243 -8.7296 -1.7088 0.11- 0.00-
36: 10 8 1.250000 7.122 40.4160 12.3328 1.16 0.11
37: 4 3 1.333333 3.561 12.3329 -15.7504 0.05 0.09-
38: 1 1 1.000000 1.780 -43.8336 -43.8336 0.34- 0.34-
39: 1 0 inf 0.890 12.3328 -100.0000 0.01 0.89-
40: 0 1 0.000000 0.445 -100.0000 124.6656 0.45- 0.69
41: 0 1 0.000000 0.223 -100.0000 349.3312 0.22- 2.72
total: 978798866121 978797093879 1.000002 χ2 = 60.948626 (p = 0.796808), k = 71
source: GTHJA7
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 244860908824 244861469986 0.999998 244861172500.250 -0.0001 0.0001 0.28- 0.36
2: 122430930916 122430705236 1.000002 122430586250.062 0.0003 0.0001 0.97 0.12
3: 61215316172 61215341749 1.000000 61215293125.000 0.0000 0.0001 0.01 0.04
4: 30607641318 30607586431 1.000002 30607646562.484 -0.0000 -0.0002 0.00- 0.12-
5: 15303836953 15303815827 1.000001 15303823281.234 0.0001 -0.0000 0.01 0.00-
6: 7652006703 7651869733 1.000018 7651911640.613 0.0012 -0.0005 1.18 0.23-
7: 3825972038 3825880772 1.000024 3825955820.305 0.0004 -0.0020 0.07 1.47-
8: 1912935756 1912950215 0.999992 1912977910.151 -0.0022 -0.0014 0.93- 0.40-
9: 956489186 956446378 1.000045 956488955.075 0.0000 -0.0045 0.00 1.90-
10: 478274731 478238305 1.000076 478244477.537 0.0063 -0.0013 1.91 0.08-
11: 239134819 239125093 1.000041 239122238.769 0.0053 0.0012 0.66 0.03
12: 119548273 119564313 0.999866 119561119.384 -0.0107 0.0027 1.38- 0.09
13: 59782057 59768539 1.000226 59780559.692 0.0025 -0.0201 0.04 2.42-
14: 29883686 29898666 0.999499 29890279.846 -0.0221 0.0281 1.45- 2.35
15: 14940861 14938772 1.000140 14945139.923 -0.0286 -0.0426 1.23- 2.71-
16: 7473972 7473279 1.000093 7472569.961 0.0188 0.0095 0.26 0.07
17: 3737062 3737795 0.999804 3736284.981 0.0208 0.0404 0.16 0.61
18: 1867934 1869805 0.998999 1868142.490 -0.0112 0.0890 0.02- 1.48
19: 932958 934139 0.998736 934071.245 -0.1192 0.0073 1.33- 0.00
20: 466135 466051 1.000180 467035.623 -0.1928 -0.2108 1.74- 2.08-
21: 233427 233889 0.998025 233517.811 -0.0389 0.1590 0.04- 0.59
22: 117441 116365 1.009247 116758.906 0.5842 -0.3374 3.98 1.33-
23: 58804 58150 1.011247 58379.453 0.7272 -0.3930 3.09 0.90-
24: 29245 29525 0.990517 29189.726 0.1894 1.1486 0.10 3.85
25: 14534 14594 0.995889 14594.863 -0.4170 -0.0059 0.25- 0.00-
26: 7254 7255 0.999862 7297.432 -0.5952 -0.5815 0.26- 0.25-
27: 3635 3760 0.966755 3648.716 -0.3759 3.0500 0.05- 3.39
28: 1743 1787 0.975378 1824.358 -4.4595 -2.0477 3.63- 0.76-
29: 912 950 0.960000 912.179 -0.0196 4.1462 0.00- 1.57
30: 462 469 0.985075 456.089 1.2959 2.8307 0.08 0.37
31: 214 215 0.995349 228.045 -6.1588 -5.7203 0.86- 0.75-
32: 125 105 1.190476 114.022 9.6276 -7.9128 1.06 0.71-
33: 59 55 1.072727 57.011 3.4885 -3.5277 0.07 0.07-
34: 28 31 0.903226 28.506 -1.7737 8.7506 0.01- 0.22
35: 14 17 0.823529 14.253 -1.7737 19.2748 0.00- 0.53
36: 7 6 1.166667 7.126 -1.7737 -15.8060 0.00- 0.18-
37: 3 2 1.500000 3.563 -15.8060 -43.8707 0.09- 0.69-
38: 1 4 0.250000 1.782 -43.8707 124.5173 0.34- 2.76
39: 1 0 inf 0.891 12.2586 -100.0000 0.01 0.89-
total: 979445742306 979443637694 1.000002 χ2 = 59.150577 (p = 0.841103), k = 71
source: GTHJA9
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 245426538066 245426544390 1.000000 245426747500.250 -0.0001 -0.0001 0.18- 0.17-
2: 122713623147 122712946929 1.000006 122713373750.062 0.0002 -0.0003 0.51 1.48-
3: 61356859662 61357326258 0.999992 61356686875.000 0.0003 0.0010 0.49 6.66
4: 30678152855 30678442739 0.999991 30678343437.484 -0.0006 0.0003 1.18- 0.32
5: 15339206037 15339260632 0.999996 15339171718.734 0.0002 0.0006 0.08 0.52
6: 7669556641 7669437918 1.000015 7669585859.363 -0.0004 -0.0019 0.11- 2.85-
7: 3834851359 3834838827 1.000003 3834792929.680 0.0015 0.0012 0.89 0.55
8: 1917335152 1917364004 0.999985 1917396464.839 -0.0032 -0.0017 1.96- 0.55-
9: 958715616 958637220 1.000082 958698232.419 0.0018 -0.0064 0.32 3.88-
10: 479344371 479351076 0.999986 479349116.209 -0.0010 0.0004 0.05- 0.01
11: 239635172 239672289 0.999845 239674558.104 -0.0164 -0.0009 6.47- 0.02-
12: 119837022 119831164 1.000049 119837279.052 -0.0002 -0.0051 0.00- 0.31-
13: 59923979 59910877 1.000219 59918639.526 0.0089 -0.0130 0.48 1.01-
14: 29955489 29967858 0.999587 29959319.763 -0.0128 0.0285 0.49- 2.43
15: 14976438 14980816 0.999708 14979659.882 -0.0215 0.0077 0.69- 0.09
16: 7495442 7490532 1.000655 7489829.941 0.0749 0.0094 4.21 0.07
17: 3743686 3743116 1.000152 3744914.970 -0.0328 -0.0480 0.40- 0.86-
18: 1873675 1874051 0.999799 1872457.485 0.0650 0.0851 0.79 1.36
19: 934676 937144 0.997366 936228.743 -0.1659 0.0978 2.58- 0.89
20: 468590 468916 0.999305 468114.371 0.1016 0.1712 0.48 1.37
21: 234272 234317 0.999808 234057.186 0.0918 0.1110 0.20 0.29
22: 117019 116716 1.002596 117028.593 -0.0082 -0.2671 0.00- 0.83-
23: 58494 58786 0.995033 58514.296 -0.0347 0.4643 0.01- 1.26
24: 29085 29282 0.993272 29257.148 -0.5884 0.0849 1.01- 0.02
25: 14619 14787 0.988639 14628.574 -0.0654 1.0830 0.01- 1.72
26: 7193 7149 1.006155 7314.287 -1.6582 -2.2598 2.01- 3.74-
27: 3745 3647 1.026871 3657.144 2.4023 -0.2774 2.11 0.03-
28: 1774 1792 0.989955 1828.572 -2.9844 -2.0000 1.63- 0.73-
29: 903 924 0.977273 914.286 -1.2344 1.0625 0.14- 0.10
30: 432 463 0.933045 457.143 -5.5000 1.2812 1.38- 0.08
31: 217 207 1.048309 228.571 -5.0625 -9.4375 0.59- 2.04-
32: 122 142 0.859155 114.286 6.7500 24.2500 0.52 6.72
33: 67 70 0.957143 57.143 17.2500 22.5000 1.70 2.89
34: 25 16 1.562500 28.571 -12.5000 -44.0000 0.45- 5.53-
35: 21 17 1.235294 14.286 47.0000 19.0000 3.16 0.52
36: 13 2 6.500000 7.143 82.0000 -72.0000 4.80 3.70-
37: 4 2 2.000000 3.571 12.0000 -44.0000 0.05 0.69-
38: 1 2 0.500000 1.786 -44.0000 12.0000 0.35- 0.03
39: 0 1 0.000000 0.893 -100.0000 12.0000 0.89- 0.01
40: 0 1 0.000000 0.446 -100.0000 123.9998 0.45- 0.69
41: 0 1 0.000000 0.223 -100.0000 348.0006 0.22- 2.70
total: 981706657647 981707322353 0.999999 χ2 = 97.661317 (p = 0.019672), k = 71
source: GTHO65
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 244587765359 244587069934 1.000003 244588215000.250 -0.0002 -0.0005 0.83- 5.36-
2: 122293484147 122294457720 0.999992 122294107500.062 -0.0005 0.0003 3.18- 1.00
3: 61147247155 61146929674 1.000005 61147053750.000 0.0003 -0.0002 0.61 0.25-
4: 30573423783 30573351160 1.000002 30573526874.984 -0.0003 -0.0006 0.35- 1.01-
5: 15286852347 15286850108 1.000000 15286763437.484 0.0006 0.0006 0.52 0.49
6: 7643349497 7643437838 0.999988 7643381718.738 -0.0004 0.0007 0.14- 0.41
7: 3821669672 3821730982 0.999984 3821690859.367 -0.0006 0.0010 0.12- 0.42
8: 1910925846 1910880228 1.000024 1910845429.683 0.0042 0.0018 3.38 0.63
9: 955433499 955435140 0.999998 955422714.841 0.0011 0.0013 0.12 0.16
10: 477726765 477742695 0.999967 477711357.420 0.0032 0.0066 0.50 2.06
11: 238840433 238836986 1.000014 238855678.710 -0.0064 -0.0078 0.97- 1.46-
12: 119447920 119430079 1.000149 119427839.355 0.0168 0.0019 3.38 0.04
13: 59710469 59723943 0.999774 59713919.677 -0.0058 0.0168 0.20- 1.68
14: 29862894 29860363 1.000085 29856959.839 0.0199 0.0114 1.18 0.39
15: 14928510 14934724 0.999584 14928479.919 0.0002 0.0418 0.00 2.61
16: 7467966 7465389 1.000345 7464239.960 0.0499 0.0154 1.86 0.18
17: 3732628 3732034 1.000159 3732119.980 0.0136 -0.0023 0.07 0.00-
18: 1866401 1865529 1.000467 1866059.990 0.0183 -0.0285 0.06 0.15-
19: 932947 933474 0.999435 933029.995 -0.0089 0.0476 0.01- 0.21
20: 466472 466051 1.000903 466514.997 -0.0092 -0.0995 0.00- 0.46-
21: 233078 233802 0.996903 233257.499 -0.0770 0.2334 0.14- 1.27
22: 116753 116450 1.002602 116628.749 0.1065 -0.1533 0.13 0.27-
23: 58231 58729 0.991520 58314.375 -0.1430 0.7110 0.12- 2.95
24: 29414 29062 1.012112 29157.187 0.8808 -0.3265 2.26 0.31-
25: 14571 14535 1.002477 14578.594 -0.0521 -0.2990 0.00- 0.13-
26: 7302 7267 1.004816 7289.297 0.1743 -0.3059 0.02 0.07-
27: 3581 3610 0.991967 3644.648 -1.7464 -0.9507 1.11- 0.33-
28: 1752 1843 0.950624 1822.324 -3.8590 1.1346 2.71- 0.23
29: 887 939 0.944622 911.162 -2.6518 3.0552 0.64- 0.85
30: 474 455 1.041758 455.581 4.0430 -0.1275 0.74 0.00-
31: 218 248 0.879032 227.791 -4.2980 8.8720 0.42- 1.79
32: 122 101 1.207921 113.895 7.1160 -11.3220 0.58 1.46-
33: 54 50 1.080000 56.948 -5.1760 -12.2000 0.15- 0.85-
34: 33 41 0.804878 28.474 15.8960 43.9919 0.72 5.51
35: 14 9 1.555556 14.237 -1.6640 -36.7840 0.00- 1.93-
36: 8 6 1.333333 7.118 12.3840 -15.7120 0.11 0.18-
37: 1 4 0.250000 3.559 -71.9040 12.3840 1.84- 0.05
38: 1 1 1.000000 1.780 -43.8080 -43.8080 0.34- 0.34-
39: 1 1 1.000000 0.890 12.3839 12.3839 0.01 0.01
total: 978352512153 978353207847 0.999999 χ2 = 64.460502 (p = 0.695036), k = 71
source: GTHO7J
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 245050142043 245050549078 0.999998 245049915000.250 0.0001 0.0003 0.21 1.64
2: 122524977495 122524875739 1.000001 122524957500.062 0.0000 -0.0001 0.00 0.05-
3: 61262239906 61262474145 0.999996 61262478750.000 -0.0004 -0.0000 0.93- 0.00-
4: 30631274821 30631435262 0.999995 30631239374.984 0.0001 0.0006 0.04 1.25
5: 15315670355 15315477016 1.000013 15315619687.484 0.0003 -0.0009 0.17 1.33-
6: 7657988786 7657622941 1.000048 7657809843.738 0.0023 -0.0024 4.18 4.56-
7: 3828948806 3828833111 1.000030 3828904921.867 0.0011 -0.0019 0.50 1.35-
8: 1914506458 1914472987 1.000017 1914452460.933 0.0028 0.0011 1.52 0.22
9: 957189333 957202905 0.999986 957226230.466 -0.0039 -0.0024 1.42- 0.57-
10: 478589421 478595230 0.999988 478613115.233 -0.0050 -0.0037 1.17- 0.67-
11: 239312088 239299930 1.000051 239306557.616 0.0023 -0.0028 0.13 0.18-
12: 119677803 119659741 1.000151 119653278.808 0.0205 0.0054 5.03 0.35
13: 59819786 59829498 0.999838 59826639.404 -0.0115 0.0048 0.79- 0.14
14: 29903074 29908437 0.999821 29913319.702 -0.0343 -0.0163 3.51- 0.80-
15: 14959072 14957623 1.000097 14956659.851 0.0161 0.0064 0.39 0.06
16: 7474972 7480744 0.999228 7478329.925 -0.0449 0.0323 1.51- 0.78
17: 3737511 3737044 1.000125 3739164.963 -0.0442 -0.0567 0.73- 1.20-
18: 1870315 1872291 0.998945 1869582.481 0.0392 0.1449 0.29 3.92
19: 934873 934918 0.999952 934791.241 0.0087 0.0136 0.01 0.02
20: 468138 466408 1.003709 467395.620 0.1588 -0.2113 1.18 2.09-
21: 233425 233788 0.998447 233697.810 -0.1167 0.0386 0.32- 0.03
22: 117160 117216 0.999522 116848.905 0.2662 0.3142 0.83 1.15
23: 58771 58242 1.009083 58424.453 0.5932 -0.3123 2.06 0.57-
24: 29084 29011 1.002516 29212.226 -0.4389 -0.6888 0.56- 1.39-
25: 14619 14674 0.996252 14606.113 0.0882 0.4648 0.01 0.32
26: 7164 7211 0.993482 7303.057 -1.9041 -1.2605 2.65- 1.16-
27: 3599 3693 0.974546 3651.528 -1.4385 1.1357 0.76- 0.47
28: 1870 1829 1.022417 1825.764 2.4229 0.1772 1.07 0.01
29: 903 955 0.945550 912.882 -1.0825 4.6137 0.11- 1.94
30: 463 439 1.054670 456.441 1.4370 -3.8211 0.09 0.67-
31: 225 229 0.982533 228.221 -1.4111 0.3415 0.05- 0.00
32: 106 110 0.963636 114.110 -7.1074 -3.6020 0.58- 0.15-
33: 57 50 1.140000 57.055 -0.0966 -12.3655 0.00- 0.87-
34: 25 30 0.833333 28.528 -12.3655 5.1614 0.44- 0.08
35: 20 13 1.538462 14.264 40.2153 -8.8601 2.31 0.11-
36: 7 11 0.636364 7.132 -1.8493 54.2368 0.00- 2.10
37: 2 1 2.000000 3.566 -43.9139 -71.9570 0.69- 1.85-
38: 0 3 0.000000 1.783 -100.0000 68.2583 1.78- 0.83
39: 0 1 0.000000 0.891 -100.0000 12.1723 0.89- 0.01
40: 0 1 0.000000 0.446 -100.0000 124.3445 0.45- 0.69
41: 0 1 0.000000 0.223 -100.0000 348.6880 0.22- 2.71
total: 980200957900 980198362100 1.000003 χ2 = 67.723218 (p = 0.588282), k = 71
source: GTHO7Y
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 250976316173 250976596287 0.999999 250976140000.250 0.0001 0.0002 0.12 0.83
2: 125488637948 125487993095 1.000005 125488070000.062 0.0005 -0.0001 2.57 0.05-
3: 62743926143 62743965012 0.999999 62744035000.000 -0.0002 -0.0001 0.19- 0.08-
4: 31371805156 31372155213 0.999989 31372017499.984 -0.0007 0.0004 1.44- 0.60
5: 15685961820 15686131796 0.999989 15686008749.984 -0.0003 0.0008 0.14- 0.97
6: 7843018238 7842825374 1.000025 7843004374.988 0.0002 -0.0023 0.02 4.09-
7: 3921501515 3921427107 1.000019 3921502187.492 -0.0000 -0.0019 0.00- 1.44-
8: 1960737292 1960773156 0.999982 1960751093.745 -0.0007 0.0011 0.10- 0.25
9: 980380004 980376495 1.000004 980375546.872 0.0005 0.0001 0.02 0.00
10: 490189164 490197204 0.999984 490187773.436 0.0003 0.0019 0.00 0.18
11: 245099746 245126708 0.999890 245093886.718 0.0024 0.0134 0.14 4.40
12: 122544449 122545215 0.999994 122546943.359 -0.0020 -0.0014 0.05- 0.02-
13: 61273868 61271002 1.000047 61273471.679 0.0006 -0.0040 0.00 0.10-
14: 30636184 30641379 0.999830 30636735.840 -0.0018 0.0152 0.01- 0.70
15: 15313851 15313916 0.999996 15318367.920 -0.0295 -0.0291 1.33- 1.29-
16: 7655119 7657319 0.999713 7659183.960 -0.0531 -0.0243 2.16- 0.45-
17: 3827229 3830593 0.999122 3829591.980 -0.0617 0.0261 1.46- 0.26
18: 1914930 1914937 0.999996 1914795.990 0.0070 0.0074 0.01 0.01
19: 959025 957518 1.001574 957397.995 0.1699 0.0125 2.76 0.02
20: 478649 477778 1.001823 478698.997 -0.0104 -0.1924 0.01- 1.77-
21: 238681 238436 1.001028 239349.499 -0.2793 -0.3817 1.87- 3.49-
22: 119900 119585 1.002634 119674.749 0.1882 -0.0750 0.42 0.07-
23: 59650 59373 1.004665 59837.375 -0.3131 -0.7761 0.59- 3.60-
24: 29937 29988 0.998299 29918.687 0.0612 0.2317 0.01 0.16
25: 14990 15065 0.995022 14959.344 0.2049 0.7063 0.06 0.75
26: 7399 7490 0.987850 7479.672 -1.0785 0.1381 0.87- 0.01
27: 3777 3789 0.996833 3739.836 0.9937 1.3146 0.37 0.65
28: 1912 1933 0.989136 1869.918 2.2505 3.3735 0.95 2.13
29: 919 955 0.962304 934.959 -1.7069 2.1435 0.27- 0.43
30: 482 485 0.993814 467.479 3.1061 3.7479 0.45 0.66
31: 271 246 1.101626 233.740 15.9409 5.2453 5.94 0.64
32: 127 127 1.000000 116.870 8.6679 8.6679 0.88 0.88
33: 65 42 1.547619 58.435 11.2348 -28.1252 0.74 4.62-
34: 28 25 1.120000 29.217 -4.1669 -14.4347 0.05- 0.61-
35: 20 16 1.250000 14.609 36.9044 9.5235 1.99 0.13
36: 5 6 0.833333 7.304 -31.5478 -17.8574 0.73- 0.23-
37: 3 8 0.375000 3.652 -17.8574 119.0470 0.12- 5.18
38: 2 2 1.000000 1.826 9.5235 9.5235 0.02 0.02
39: 2 0 inf 0.913 119.0470 -100.0000 1.29 0.91-
40: 1 0 inf 0.457 119.0470 -100.0000 0.65 0.46-
41: 1 0 inf 0.228 338.0950 -100.0000 2.61 0.23-
42: 0 1 0.000000 0.114 -100.0000 776.1861 0.11- 6.88
total: 1003904364556 1003904755444 1.000000 χ2 = 65.285892 (p = 0.668819), k = 71
source: Kernel
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 173416872143 173416193065 1.000004 173416435000.250 0.0003 -0.0001 1.10 0.34-
2: 86708081740 86708559735 0.999994 86708217500.062 -0.0002 0.0004 0.21- 1.35
3: 43353923480 43354039385 0.999997 43354108750.000 -0.0004 -0.0002 0.79- 0.11-
4: 21677100747 21677020989 1.000004 21677054374.984 0.0002 -0.0002 0.10 0.05-
5: 10838597865 10838594540 1.000000 10838527187.484 0.0007 0.0006 0.46 0.42
6: 5419147287 5419273445 0.999977 5419263593.738 -0.0021 0.0002 2.50- 0.02
7: 2709508678 2709626603 0.999956 2709631796.867 -0.0045 -0.0002 5.59- 0.01-
8: 1354833100 1354805507 1.000020 1354815898.433 0.0013 -0.0008 0.22 0.08-
9: 677448218 677431826 1.000024 677407949.216 0.0059 0.0035 2.39 0.84
10: 338726606 338697794 1.000085 338703974.608 0.0067 -0.0018 1.51 0.11-
11: 169357280 169356935 1.000002 169351987.304 0.0031 0.0029 0.17 0.14
12: 84678241 84677310 1.000011 84675993.652 0.0027 0.0016 0.06 0.02
13: 42336691 42327241 1.000223 42337996.826 -0.0031 -0.0254 0.04- 2.73-
14: 21163405 21171618 0.999612 21168998.413 -0.0264 0.0124 1.48- 0.32
15: 10586447 10587039 0.999944 10584499.206 0.0184 0.0240 0.36 0.61
16: 5292913 5293851 0.999823 5292249.603 0.0125 0.0303 0.08 0.48
17: 2648475 2648585 0.999958 2646124.802 0.0888 0.0930 2.09 2.29
18: 1322870 1323382 0.999613 1323062.401 -0.0145 0.0242 0.03- 0.08
19: 661806 661524 1.000426 661531.200 0.0415 -0.0011 0.11 0.00-
20: 331235 329615 1.004915 330765.600 0.1419 -0.3479 0.67 4.00-
21: 165389 165225 1.000993 165382.800 0.0037 -0.0954 0.00 0.15-
22: 82874 83007 0.998398 82691.400 0.2208 0.3817 0.40 1.20
23: 41370 41082 1.007010 41345.700 0.0588 -0.6378 0.01 1.68-
24: 20908 20628 1.013574 20672.850 1.1375 -0.2170 2.67 0.10-
25: 10505 10460 1.004302 10336.425 1.6309 1.1955 2.75 1.48
26: 5297 5153 1.027945 5168.213 2.4919 -0.2943 3.21 0.04-
27: 2653 2597 1.021563 2584.106 2.6661 0.4990 1.84 0.06
28: 1222 1280 0.954688 1292.053 -5.4218 -0.9329 3.80- 0.11-
29: 642 682 0.941349 646.027 -0.6233 5.5684 0.03- 2.00
30: 328 336 0.976190 323.013 1.5438 4.0205 0.08 0.52
31: 153 159 0.962264 161.507 -5.2671 -1.5520 0.45- 0.04-
32: 96 73 1.315068 80.753 18.8806 -9.6012 2.88 0.74-
33: 45 39 1.153846 40.377 11.4505 -3.4095 0.53 0.05-
34: 22 22 1.000000 20.188 8.9738 8.9738 0.16 0.16
35: 8 8 1.000000 10.094 -20.7463 -20.7463 0.43- 0.43-
36: 3 5 0.600000 5.047 -40.5597 -0.9329 0.83- 0.00-
37: 1 1 1.000000 2.524 -60.3731 -60.3731 0.92- 0.92-
38: 2 0 inf 1.262 58.5074 -100.0000 0.43 1.26-
39: 0 0 -nan 0.631 -100.0000 -100.0000 0.63- 0.63-
40: 1 0 inf 0.315 217.0145 -100.0000 1.49 0.32-
41: 0 0 -nan 0.158 -100.0000 -100.0000 0.16- 0.16-
42: 0 1 0.000000 0.079 -100.0000 1168.0539 0.08- 10.76
total: 693665154294 693666325706 0.999998 χ2 = 62.833176 (p = 0.744410), k = 71
source: Pool
run of zeros ones bias expect e0 % e1 % e02/e e12/e
1: 694926543098 694926620650 1.000000 694927152500.250 -0.0001 -0.0001 0.53- 0.41-
2: 347464068761 347463112814 1.000003 347463576250.062 0.0001 -0.0001 0.70 0.62-
3: 173731669099 173732244390 0.999997 173731788125.000 -0.0001 0.0003 0.08- 1.20
4: 86865467148 86866038682 0.999993 86865894062.484 -0.0005 0.0002 2.10- 0.24
5: 43432971030 43432778114 1.000004 43432947031.234 0.0001 -0.0004 0.01 0.66-
6: 21716572126 21716383615 1.000009 21716473515.613 0.0005 -0.0004 0.45 0.37-
7: 10858257452 10858328546 0.999993 10858236757.805 0.0002 0.0008 0.04 0.78
8: 5429145234 5429146762 1.000000 5429118378.901 0.0005 0.0005 0.13 0.15
9: 2714491410 2714584608 0.999966 2714559189.450 -0.0025 0.0009 1.69- 0.24
10: 1357280338 1357249172 1.000023 1357279594.725 0.0001 -0.0022 0.00 0.68-
11: 678684315 678647026 1.000055 678639797.362 0.0066 0.0011 2.92 0.08
12: 339324654 339308518 1.000048 339319898.681 0.0014 -0.0034 0.07 0.38-
13: 169671483 169677850 0.999962 169659949.341 0.0068 0.0106 0.78 1.89
14: 84834694 84850454 0.999814 84829974.670 0.0056 0.0241 0.26 4.94
15: 42412526 42413354 0.999980 42414987.335 -0.0058 -0.0039 0.14- 0.06-
16: 21213212 21205692 1.000355 21207493.668 0.0270 -0.0085 1.54 0.15-
17: 10601302 10605657 0.999589 10603746.834 -0.0231 0.0180 0.56- 0.34
18: 5299899 5305398 0.998964 5301873.417 -0.0372 0.0665 0.74- 2.34
19: 2650111 2654180 0.998467 2650936.708 -0.0311 0.1223 0.26- 3.97
20: 1324963 1325140 0.999866 1325468.354 -0.0381 -0.0248 0.19- 0.08-
21: 662956 664200 0.998127 662734.177 0.0335 0.2212 0.07 3.24
22: 330394 330698 0.999081 331367.089 -0.2937 -0.2019 2.86- 1.35-
23: 166087 166776 0.995869 165683.544 0.2435 0.6594 0.98 7.20
24: 83037 82668 1.004464 82841.772 0.2357 -0.2098 0.46 0.36-
25: 41294 41552 0.993791 41420.886 -0.3063 0.3165 0.39- 0.42
26: 20684 20768 0.995955 20710.443 -0.1277 0.2779 0.03- 0.16
27: 10380 10377 1.000289 10355.222 0.2393 0.2103 0.06 0.05
28: 5306 5267 1.007405 5177.611 2.4797 1.7265 3.18 1.54
29: 2587 2689 0.962068 2588.805 -0.0697 3.8703 0.00- 3.88
30: 1292 1280 1.009375 1294.403 -0.1856 -1.1127 0.00- 0.16-
31: 663 641 1.034321 647.201 2.4411 -0.9582 0.39 0.06-
32: 328 340 0.964706 323.601 1.3595 5.0678 0.06 0.83
33: 189 171 1.105263 161.800 16.8106 5.6858 4.57 0.52
34: 77 69 1.115942 80.900 -4.8210 -14.7097 0.19- 1.75-
35: 33 51 0.647059 40.450 -18.4180 26.0813 1.37- 2.75
36: 28 28 1.000000 20.225 38.4422 38.4422 2.99 2.99
37: 11 9 1.222222 10.113 8.7760 -11.0014 0.08 0.12-
38: 7 4 1.750000 5.056 38.4422 -20.8902 0.75 0.22-
39: 2 2 1.000000 2.528 -20.8901 -20.8901 0.11- 0.11-
40: 4 3 1.333333 1.264 216.4394 137.3296 5.92 2.38
total: 2779708103155 2779709116845 1.000000 χ2 = 78.834848 (p = 0.358612), k = 75