BIRTHDAY SPACINGS TEST, M= 512 N=2**24 LAMBDA= 2.0000 rnd-mcw.bin using bits 1 to 24 p-value= .585787 rnd-mcw.bin using bits 2 to 25 p-value= .637386 rnd-mcw.bin using bits 3 to 26 p-value= .401120 rnd-mcw.bin using bits 4 to 27 p-value= .664948 rnd-mcw.bin using bits 5 to 28 p-value= .348166 rnd-mcw.bin using bits 6 to 29 p-value= .381846 rnd-mcw.bin using bits 7 to 30 p-value= .432308 rnd-mcw.bin using bits 8 to 31 p-value= .707886 rnd-mcw.bin using bits 9 to 32 p-value= .123399 The 9 p-values were .585787 .637386 .401120 .664948 .348166 .381846 .432308 .707886 .123399 A KSTEST for the 9 p-values yields .588871 -------------------------------------------------------------------------------- OPERM5 test for file rnd-mcw.bin chisquare for 99 degrees of freedom= 76.955; p-value= .049211 OPERM5 test for file rnd-mcw.bin chisquare for 99 degrees of freedom= 75.606; p-value= .038649 -------------------------------------------------------------------------------- Binary rank test for rnd-mcw.bin Rank test for 31x31 binary matrices: rows from leftmost 31 bits of each 32-bit integer rank observed expected (o-e)^2/e sum 28 200 211.4 .616651 .617 29 5042 5134.0 1.648981 2.266 30 23224 23103.0 .633235 2.899 31 11534 11551.5 .026586 2.925 chisquare= 2.925 for 3 d. of f.; p-value= .640334 Binary rank test for rnd-mcw.bin Rank test for 32x32 binary matrices: rows from leftmost 32 bits of each 32-bit integer rank observed expected (o-e)^2/e sum 29 228 211.4 1.300562 1.301 30 5068 5134.0 .848723 2.149 31 23193 23103.0 .350238 2.500 32 11511 11551.5 .142165 2.642 chisquare= 2.642 for 3 d. of f.; p-value= .601819 -------------------------------------------------------------------------------- b-rank test for bits 1 to 8 p=1-exp(-SUM/2)= .39798 b-rank test for bits 2 to 9 p=1-exp(-SUM/2)= .06600 b-rank test for bits 3 to 10 p=1-exp(-SUM/2)= .10983 b-rank test for bits 4 to 11 p=1-exp(-SUM/2)= .86145 b-rank test for bits 5 to 12 p=1-exp(-SUM/2)= .92863 b-rank test for bits 6 to 13 p=1-exp(-SUM/2)= .74410 b-rank test for bits 7 to 14 p=1-exp(-SUM/2)= .08282 b-rank test for bits 8 to 15 p=1-exp(-SUM/2)= .71283 b-rank test for bits 9 to 16 p=1-exp(-SUM/2)= .08958 b-rank test for bits 10 to 17 p=1-exp(-SUM/2)= .43973 b-rank test for bits 11 to 18 p=1-exp(-SUM/2)= .42998 b-rank test for bits 12 to 19 p=1-exp(-SUM/2)= .82181 b-rank test for bits 13 to 20 p=1-exp(-SUM/2)= .78128 b-rank test for bits 14 to 21 p=1-exp(-SUM/2)= .42504 b-rank test for bits 15 to 22 p=1-exp(-SUM/2)= .45853 b-rank test for bits 16 to 23 p=1-exp(-SUM/2)= .61229 b-rank test for bits 17 to 24 p=1-exp(-SUM/2)= .67133 b-rank test for bits 18 to 25 p=1-exp(-SUM/2)= .29620 b-rank test for bits 19 to 26 p=1-exp(-SUM/2)= .91823 b-rank test for bits 20 to 27 p=1-exp(-SUM/2)= .66614 b-rank test for bits 21 to 28 p=1-exp(-SUM/2)= .29032 b-rank test for bits 22 to 29 p=1-exp(-SUM/2)= .44780 b-rank test for bits 23 to 30 p=1-exp(-SUM/2)= .29633 b-rank test for bits 24 to 31 p=1-exp(-SUM/2)= .35175 b-rank test for bits 25 to 32 p=1-exp(-SUM/2)= .10322 TEST SUMMARY, 25 tests on 100,000 random 6x8 matrices These should be 25 uniform [0,1] random variables: .397983 .065996 .109827 .861446 .928634 .744097 .082818 .712834 .089578 .439734 .429975 .821810 .781281 .425043 .458534 .612288 .671331 .296197 .918226 .666136 .290320 .447800 .296325 .351753 .103219 brank test summary for rnd-mcw.bin The KS test for those 25 supposed UNI's yields KS p-value= .155148 -------------------------------------------------------------------------------- No. missing words should average 141909. with sigma=428. tst no 1: 141817 missing words, -.22 sigmas from mean, p-value= .41460 tst no 2: 141578 missing words, -.77 sigmas from mean, p-value= .21943 tst no 3: 141527 missing words, -.89 sigmas from mean, p-value= .18585 tst no 4: 142085 missing words, .41 sigmas from mean, p-value= .65926 tst no 5: 141777 missing words, -.31 sigmas from mean, p-value= .37859 tst no 6: 142016 missing words, .25 sigmas from mean, p-value= .59841 tst no 7: 143095 missing words, 2.77 sigmas from mean, p-value= .99720 tst no 8: 142022 missing words, .26 sigmas from mean, p-value= .60382 tst no 9: 141518 missing words, -.91 sigmas from mean, p-value= .18027 tst no 10: 142142 missing words, .54 sigmas from mean, p-value= .70665 tst no 11: 142004 missing words, .22 sigmas from mean, p-value= .58753 tst no 12: 142145 missing words, .55 sigmas from mean, p-value= .70906 tst no 13: 141499 missing words, -.96 sigmas from mean, p-value= .16885 tst no 14: 142742 missing words, 1.95 sigmas from mean, p-value= .97414 tst no 15: 142904 missing words, 2.32 sigmas from mean, p-value= .98994 tst no 16: 142116 missing words, .48 sigmas from mean, p-value= .68541 tst no 17: 142210 missing words, .70 sigmas from mean, p-value= .75882 tst no 18: 141482 missing words, -1.00 sigmas from mean, p-value= .15904 tst no 19: 141772 missing words, -.32 sigmas from mean, p-value= .37416 tst no 20: 140900 missing words, -2.36 sigmas from mean, p-value= .00918 -------------------------------------------------------------------------------- OPSO for rnd-mcw.bin using bits 23 to 32 142016 .368 .6435 OPSO for rnd-mcw.bin using bits 22 to 31 141656 -.874 .1912 OPSO for rnd-mcw.bin using bits 21 to 30 142151 .833 .7977 OPSO for rnd-mcw.bin using bits 20 to 29 142225 1.089 .8618 OPSO for rnd-mcw.bin using bits 19 to 28 141971 .213 .5842 OPSO for rnd-mcw.bin using bits 18 to 27 142048 .478 .6837 OPSO for rnd-mcw.bin using bits 17 to 26 141756 -.529 .2985 OPSO for rnd-mcw.bin using bits 16 to 25 142386 1.644 .9499 OPSO for rnd-mcw.bin using bits 15 to 24 142085 .606 .7277 OPSO for rnd-mcw.bin using bits 14 to 23 142101 .661 .7457 OPSO for rnd-mcw.bin using bits 13 to 22 142481 1.971 .9757 OPSO for rnd-mcw.bin using bits 12 to 21 141935 .089 .5353 OPSO for rnd-mcw.bin using bits 11 to 20 142379 1.620 .9473 OPSO for rnd-mcw.bin using bits 10 to 19 141992 .285 .6122 OPSO for rnd-mcw.bin using bits 9 to 18 142381 1.626 .9481 OPSO for rnd-mcw.bin using bits 8 to 17 141576 -1.149 .1252 OPSO for rnd-mcw.bin using bits 7 to 16 142267 1.233 .8913 OPSO for rnd-mcw.bin using bits 6 to 15 141190 -2.480 .0066 OPSO for rnd-mcw.bin using bits 5 to 14 141660 -.860 .1950 OPSO for rnd-mcw.bin using bits 4 to 13 142059 .516 .6971 OPSO for rnd-mcw.bin using bits 3 to 12 141894 -.053 .4789 OPSO for rnd-mcw.bin using bits 2 to 11 141628 -.970 .1660 OPSO for rnd-mcw.bin using bits 1 to 10 141901 -.029 .4885 OQSO for rnd-mcw.bin using bits 28 to 32 141673 -.801 .2115 OQSO for rnd-mcw.bin using bits 27 to 31 141884 -.086 .4658 OQSO for rnd-mcw.bin using bits 26 to 30 141730 -.608 .2716 OQSO for rnd-mcw.bin using bits 25 to 29 141808 -.343 .3656 OQSO for rnd-mcw.bin using bits 24 to 28 142082 .585 .7208 OQSO for rnd-mcw.bin using bits 23 to 27 141998 .301 .6181 OQSO for rnd-mcw.bin using bits 22 to 26 141794 -.391 .3479 OQSO for rnd-mcw.bin using bits 21 to 25 141362 -1.855 .0318 OQSO for rnd-mcw.bin using bits 20 to 24 141530 -1.286 .0992 OQSO for rnd-mcw.bin using bits 19 to 23 141882 -.093 .4631 OQSO for rnd-mcw.bin using bits 18 to 22 141981 .243 .5960 OQSO for rnd-mcw.bin using bits 17 to 21 142061 .514 .6964 OQSO for rnd-mcw.bin using bits 16 to 20 142415 1.714 .9567 OQSO for rnd-mcw.bin using bits 15 to 19 142435 1.782 .9626 OQSO for rnd-mcw.bin using bits 14 to 18 141809 -.340 .3669 OQSO for rnd-mcw.bin using bits 13 to 17 142145 .799 .7878 OQSO for rnd-mcw.bin using bits 12 to 16 141401 -1.723 .0424 OQSO for rnd-mcw.bin using bits 11 to 15 141917 .026 .5104 OQSO for rnd-mcw.bin using bits 10 to 14 141994 .287 .6130 OQSO for rnd-mcw.bin using bits 9 to 13 141976 .226 .5894 OQSO for rnd-mcw.bin using bits 8 to 12 141983 .250 .5986 OQSO for rnd-mcw.bin using bits 7 to 11 141860 -.167 .4336 OQSO for rnd-mcw.bin using bits 6 to 10 141487 -1.432 .0761 OQSO for rnd-mcw.bin using bits 5 to 9 142373 1.572 .9420 OQSO for rnd-mcw.bin using bits 4 to 8 141616 -.994 .1600 OQSO for rnd-mcw.bin using bits 3 to 7 141497 -1.398 .0811 OQSO for rnd-mcw.bin using bits 2 to 6 141930 .070 .5279 OQSO for rnd-mcw.bin using bits 1 to 5 142404 1.677 .9532 DNA for rnd-mcw.bin using bits 31 to 32 141924 .043 .5173 DNA for rnd-mcw.bin using bits 30 to 31 142128 .645 .7406 DNA for rnd-mcw.bin using bits 29 to 30 142177 .790 .7851 DNA for rnd-mcw.bin using bits 28 to 29 141323 -1.730 .0419 DNA for rnd-mcw.bin using bits 27 to 28 141665 -.721 .2355 DNA for rnd-mcw.bin using bits 26 to 27 141493 -1.228 .1097 DNA for rnd-mcw.bin using bits 25 to 26 141827 -.243 .4041 DNA for rnd-mcw.bin using bits 24 to 25 142041 .388 .6511 DNA for rnd-mcw.bin using bits 23 to 24 141875 -.101 .4597 DNA for rnd-mcw.bin using bits 22 to 23 142434 1.548 .9392 DNA for rnd-mcw.bin using bits 21 to 22 142256 1.023 .8468 DNA for rnd-mcw.bin using bits 20 to 21 141741 -.497 .3098 DNA for rnd-mcw.bin using bits 19 to 20 141449 -1.358 .0872 DNA for rnd-mcw.bin using bits 18 to 19 141366 -1.603 .0545 DNA for rnd-mcw.bin using bits 17 to 18 141853 -.166 .4340 DNA for rnd-mcw.bin using bits 16 to 17 141195 -2.107 .0176 DNA for rnd-mcw.bin using bits 15 to 16 142296 1.141 .8730 DNA for rnd-mcw.bin using bits 14 to 15 141758 -.446 .3277 DNA for rnd-mcw.bin using bits 13 to 14 141631 -.821 .2058 DNA for rnd-mcw.bin using bits 12 to 13 142087 .524 .6999 DNA for rnd-mcw.bin using bits 11 to 12 141666 -.718 .2364 DNA for rnd-mcw.bin using bits 10 to 11 141814 -.281 .3893 DNA for rnd-mcw.bin using bits 9 to 10 141968 .173 .5687 DNA for rnd-mcw.bin using bits 8 to 9 142108 .586 .7211 DNA for rnd-mcw.bin using bits 7 to 8 141892 -.051 .4796 DNA for rnd-mcw.bin using bits 6 to 7 142217 .908 .8180 DNA for rnd-mcw.bin using bits 5 to 6 142054 .427 .6652 DNA for rnd-mcw.bin using bits 4 to 5 141618 -.859 .1951 DNA for rnd-mcw.bin using bits 3 to 4 142013 .306 .6201 DNA for rnd-mcw.bin using bits 2 to 3 141555 -1.045 .1480 DNA for rnd-mcw.bin using bits 1 to 2 141886 -.069 .4726 -------------------------------------------------------------------------------- Test results for rnd-mcw.bin Chi-square with 5^5-5^4=2500 d.of f. for sample size:2560000 chisquare equiv normal p-value Results fo COUNT-THE-1's in successive bytes: byte stream for rnd-mcw.bin 2443.81 -.795 .213394 byte stream for rnd-mcw.bin 2462.52 -.530 .298060 -------------------------------------------------------------------------------- Chi-square with 5^5-5^4=2500 d.of f. for sample size: 256000 chisquare equiv normal p value Results for COUNT-THE-1's in specified bytes: bits 1 to 8 2479.50 -.290 .385935 bits 2 to 9 2388.60 -1.575 .057585 bits 3 to 10 2493.48 -.092 .463262 bits 4 to 11 2487.23 -.181 .428369 bits 5 to 12 2514.09 .199 .578990 bits 6 to 13 2649.81 2.119 .982941 bits 7 to 14 2531.15 .441 .670231 bits 8 to 15 2557.01 .806 .789931 bits 9 to 16 2627.99 1.810 .964852 bits 10 to 17 2480.12 -.281 .389285 bits 11 to 18 2586.78 1.227 .890139 bits 12 to 19 2426.40 -1.041 .148970 bits 13 to 20 2534.64 .490 .687872 bits 14 to 21 2669.95 2.403 .991878 bits 15 to 22 2514.16 .200 .579379 bits 16 to 23 2423.86 -1.077 .140775 bits 17 to 24 2796.78 4.197 .999986 bits 18 to 25 2535.55 .503 .692442 bits 19 to 26 2453.40 -.659 .254957 bits 20 to 27 2373.28 -1.792 .036557 bits 21 to 28 2408.68 -1.291 .098276 bits 22 to 29 2436.10 -.904 .183090 bits 23 to 30 2551.98 .735 .768843 bits 24 to 31 2451.85 -.681 .247975 bits 25 to 32 2601.35 1.433 .924107 -------------------------------------------------------------------------------- CDPARK: result of ten tests on file rnd-mcw.bin Of 12,000 tries, the average no. of successes should be 3523 with sigma=21.9 Successes: 3526 z-score: .137 p-value: .554479 Successes: 3533 z-score: .457 p-value: .676028 Successes: 3509 z-score: -.639 p-value: .261324 Successes: 3514 z-score: -.411 p-value: .340551 Successes: 3502 z-score: -.959 p-value: .168804 Successes: 3526 z-score: .137 p-value: .554479 Successes: 3543 z-score: .913 p-value: .819442 Successes: 3510 z-score: -.594 p-value: .276387 Successes: 3558 z-score: 1.598 p-value: .944998 Successes: 3532 z-score: .411 p-value: .659449 square size avg. no. parked sample sigma 100. 3525.300 16.270 KSTEST for the above 10: p= .114963 -------------------------------------------------------------------------------- This is the MINIMUM DISTANCE test for random integers in the file rnd-mcw.bin Sample no. d^2 avg equiv uni 5 .7291 .8316 .519401 10 .0004 .9285 .000367 15 1.3239 1.0399 .735681 20 .4126 .9613 .339472 25 .1134 .9781 .107705 30 2.5631 1.0939 .923919 35 1.4486 1.0919 .766795 40 1.4254 1.1098 .761303 45 1.0686 1.0968 .658337 50 2.1279 1.0921 .882180 55 .0970 1.1201 .092877 60 .3931 1.0799 .326390 65 .7020 1.0324 .506165 70 1.9481 1.0161 .858842 75 1.2331 .9917 .710400 80 .6360 .9793 .472284 85 .3310 1.0241 .282996 90 .0082 1.0371 .008165 95 .3570 1.0761 .301490 100 .2961 1.0663 .257375 MINIMUM DISTANCE TEST for rnd-mcw.bin Result of KS test on 20 transformed mindist^2's: p-value= .714084 -------------------------------------------------------------------------------- The 3DSPHERES test for file rnd-mcw.bin sample no: 1 r^3= 73.320 p-value= .91319 sample no: 2 r^3= 29.940 p-value= .63139 sample no: 3 r^3= 2.704 p-value= .08618 sample no: 4 r^3= 46.348 p-value= .78667 sample no: 5 r^3= 36.755 p-value= .70629 sample no: 6 r^3= 28.059 p-value= .60753 sample no: 7 r^3= 13.549 p-value= .36340 sample no: 8 r^3= 6.934 p-value= .20636 sample no: 9 r^3= 19.629 p-value= .48019 sample no: 10 r^3= 21.270 p-value= .50786 sample no: 11 r^3= 44.547 p-value= .77347 sample no: 12 r^3= 70.871 p-value= .90580 sample no: 13 r^3= .946 p-value= .03104 sample no: 14 r^3= 32.650 p-value= .66322 sample no: 15 r^3= 1.479 p-value= .04810 sample no: 16 r^3= 25.487 p-value= .57241 sample no: 17 r^3= 18.007 p-value= .45132 sample no: 18 r^3= 4.297 p-value= .13344 sample no: 19 r^3= 2.014 p-value= .06494 sample no: 20 r^3= 23.904 p-value= .54923 3DSPHERES test for file rnd-mcw.bin p-value= .267311 -------------------------------------------------------------------------------- RESULTS OF SQUEEZE TEST FOR rnd-mcw.bin Table of standardized frequency counts ( (obs-exp)/sqrt(exp) )^2 for j taking values <=6,7,8,...,47,>=48: .6 .5 .3 .2 1.1 .9 -1.1 .9 .4 -2.7 -1.3 1.2 .7 -.8 -.4 -1.0 1.3 1.4 -1.8 .1 .6 -.4 2.1 .5 -.5 .1 -.8 -.6 -.7 1.2 -.6 -.7 -.1 2.5 -2.0 .4 .7 -.7 -.4 3.7 -.6 1.0 .8 Chi-square with 42 degrees of freedom: 61.018 z-score= 2.075 p-value= .970982 ______________________________________________________________ -------------------------------------------------------------------------------- Test no. 1 p-value .494861 Test no. 2 p-value .752767 Test no. 3 p-value .824596 Test no. 4 p-value .264183 Test no. 5 p-value .728995 Test no. 6 p-value .296465 Test no. 7 p-value .217794 Test no. 8 p-value .574801 Test no. 9 p-value .430862 Test no. 10 p-value .611641 Results of the OSUM test for rnd-mcw.bin KSTEST on the above 10 p-values: .381084 -------------------------------------------------------------------------------- The RUNS test for file rnd-mcw.bin Up and down runs in a sample of 10000 _________________________________________________ Run test for rnd-mcw.bin : runs up; ks test for 10 p's: .353339 runs down; ks test for 10 p's: .741053 Run test for rnd-mcw.bin : runs up; ks test for 10 p's: .044787 runs down; ks test for 10 p's: .068322 -------------------------------------------------------------------------------- Results of craps test for rnd-mcw.bin No. of wins: Observed Expected 98763 98585.86 Chisq= 14.46 for 20 degrees of freedom, p= .19360 Throws Observed Expected Chisq Sum SUMMARY FOR rnd-mcw.bin p-value for no. of wins: .785900 p-value for throws/game: .193605 Test completed. File rnd-mcw.bin :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::