The data below are 500 observations from a standard bivariate
normal distribution (Z1, Z2), and the same data rounded to the
nearest 0.5 (Z1R, Z2R).
Z1 Z2 Z1R Z2R
-0.83923 -0.09391 -1 0
-0.49464 -0.95089 -0.5 -1
-0.23595 -0.39965 0 -0.5
0.44705 -1.17349 0.5 -1
-0.42167 1.31421 -0.5 1.5
1.35469 1.33031 1.5 1.5
-0.62061 -1.56261 -0.5 -1.5
-0.25408 0.71974 -0.5 0.5
-0.53801 0.50476 -0.5 0.5
-1.21637 0.96843 -1 1
0.27365 -0.58286 0.5 -0.5
1.21251 0.15664 1 0
1.0331 0.02917 1 0
-0.14748 0.19471 0 0
-0.30431 -1.28012 -0.5 -1.5
0.24683 0.14572 0 0
-0.65829 -1.05372 -0.5 -1
-0.38053 -1.3501 -0.5 -1.5
0.66269 0.21829 0.5 0
0.67571 -0.80152 0.5 -1
0.21062 -1.68536 0 -1.5
0.08577 0.55528 0 0.5
-0.40738 -0.04883 -0.5 0
0.05143 -0.89931 0 -1
1.06118 1.32107 1 1.5
-0.74758 0.67432 -0.5 0.5
-1.43717 -1.61477 -1.5 -1.5
-1.25231 -0.02815 -1.5 0
-0.09067 1.04517 0 1
0.25039 -0.91148 0.5 -1
0.6613 0.77343 0.5 1
1.22803 0.1126 1 0
1.12469 -0.47307 1 -0.5
0.19475 -0.2899 0 -0.5
0.67512 -1.11578 0.5 -1
-0.89685 -1.87138 -1 -2
-1.5172 0.86293 -1.5 1
-0.47494 -0.39197 -0.5 -0.5
-0.87316 0.67685 -1 0.5
-1.42553 -0.13581 -1.5 0
-0.39805 -0.42751 -0.5 -0.5
0.97245 -0.05927 1 0
-0.95444 1.2667 -1 1.5
0.13609 -1.22926 0 -1
-0.85676 -0.86458 -1 -1
-0.24265 0.1439 0 0
0.4381 -0.48867 0.5 -0.5
-1.39096 -0.61511 -1.5 -0.5
0.18045 0.5587 0 0.5
1.37408 -0.30767 1.5 -0.5
0.22186 0.72419 0 0.5
-2.21333 1.28144 -2 1.5
-0.13833 0.62542 0 0.5
-0.11853 -1.31327 0 -1.5
0.14929 -0.138 0 0
-0.46957 -1.36145 -0.5 -1.5
-0.30374 1.56878 -0.5 1.5
-1.29146 -0.66162 -1.5 -0.5
-0.10251 0.63672 0 0.5
-0.90341 -1.08297 -1 -1
0.58873 -1.61482 0.5 -1.5
-1.04155 -1.12544 -1 -1
-1.17249 0.1294 -1 0
-0.8139 -2.09742 -1 -2
1.03093 -0.08652 1 0
0.3756 2.3464 0.5 2.5
-0.05537 -0.61873 0 -0.5
0.9783 0.53942 1 0.5
0.07291 -1.48337 0 -1.5
-0.54651 0.27084 -0.5 0.5
1.73751 2.26311 1.5 2.5
1.03986 -0.21985 1 0
-0.09603 0.39158 0 0.5
0.13643 0.01285 0 0
-0.34409 -0.20007 -0.5 0
-1.26187 -0.90585 -1.5 -1
-1.01914 0.80593 -1 1
1.88194 1.36659 2 1.5
0.11 -1.72717 0 -1.5
0.96494 0.20392 1 0
-0.12175 0.16771 0 0
-0.72243 -2.3137 -0.5 -2.5
-0.1085 2.69752 0 2.5
0.52722 -0.45825 0.5 -0.5
0.05286 1.17939 0 1
0.7241 0.34782 0.5 0.5
0.05068 -0.2645 0 -0.5
-0.57489 0.23818 -0.5 0
-1.23839 2.85807 -1 3
0.87664 0.60539 1 0.5
-0.84369 1.93802 -1 2
-0.66355 0.05992 -0.5 0
0.92944 -0.15336 1 0
0.93231 -0.53445 1 -0.5
-0.04084 1.47253 0 1.5
-0.67612 0.26422 -0.5 0.5
0.05593 0.78841 0 1
0.79551 -0.16634 1 0
1.07065 2.48446 1 2.5
-1.16379 -0.55549 -1 -0.5
1.84448 -0.02896 2 0
-2.18686 -0.76049 -2 -1
0.52335 -1.44898 0.5 -1.5
-0.55954 -1.69263 -0.5 -1.5
1.44006 -0.00894 1.5 0
1.68497 -0.42991 1.5 -0.5
0.57403 -1.43375 0.5 -1.5
0.09486 1.23333 0 1
1.28009 -0.28609 1.5 -0.5
0.21224 0.64307 0 0.5
-0.03078 0.54087 0 0.5
-0.03684 0.03606 0 0
-0.20487 0.50097 0 0.5
2.03516 -1.047 2 -1
0.29331 -0.37429 0.5 -0.5
0.4749 -0.93028 0.5 -1
0.79727 0.38099 1 0.5
0.72747 -0.3235 0.5 -0.5
-0.38941 -1.481 -0.5 -1.5
-0.4705 0.01902 -0.5 0
-1.26544 0.32978 -1.5 0.5
0.79352 -1.75012 1 -2
0.82211 1.53733 1 1.5
-1.97999 -1.2086 -2 -1
-0.34535 1.06208 -0.5 1
0.19895 0.18177 0 0
-0.59027 0.47999 -0.5 0.5
1.30063 0.76941 1.5 1
-0.49645 0.01614 -0.5 0
-1.58716 -1.01374 -1.5 -1
-1.93846 -0.30585 -2 -0.5
0.28291 -0.54277 0.5 -0.5
-1.76362 -2.91363 -2 -3
-0.6076 -0.83189 -0.5 -1
1.36177 0.35216 1.5 0.5
-0.86324 0.24513 -1 0
1.43334 0.65636 1.5 0.5
0.16174 0.11187 0 0
-1.08357 0.14578 -1 0
1.00601 0.39705 1 0.5
0.40758 0.1921 0.5 0
-0.3509 2.39253 -0.5 2.5
-0.45712 0.21539 -0.5 0
0.51714 1.99743 0.5 2
-1.52599 -0.20017 -1.5 0
0.27263 0.78923 0.5 1
-0.72043 -1.45046 -0.5 -1.5
0.16691 -1.61404 0 -1.5
0.34877 -0.76969 0.5 -1
0.62209 1.2616 0.5 1.5
1.14888 -0.28222 1 -0.5
-0.24222 1.19026 0 1
0.15555 -0.29243 0 -0.5
-0.07651 0.70799 0 0.5
-0.25234 0.0246 -0.5 0
-0.8252 -1.27742 -1 -1.5
-0.49577 0.62342 -0.5 0.5
0.22238 0.01564 0 0
-0.55647 -1.15517 -0.5 -1
0.26963 -0.02483 0.5 0
-1.42648 1.0688 -1.5 1
-0.327 1.36039 -0.5 1.5
-1.08762 0.36972 -1 0.5
0.73543 0.97459 0.5 1
-1.40554 0.10215 -1.5 0
-0.57707 -0.52993 -0.5 -0.5
0.07803 -0.2251 0 0
0.46341 0.45946 0.5 0.5
-1.14903 -0.78162 -1 -1
1.19073 -1.53621 1 -1.5
-0.23702 0.53257 0 0.5
-0.64456 -1.61081 -0.5 -1.5
0.0938 -2.09564 0 -2
0.35282 0.67811 0.5 0.5
0.14282 1.47449 0 1.5
-0.45862 1.00169 -0.5 1
-0.74588 0.12307 -0.5 0
-0.85469 -0.26391 -1 -0.5
-1.31295 -1.53767 -1.5 -1.5
0.01298 0.08927 0 0
-1.09878 -0.30831 -1 -0.5
-1.29807 1.65062 -1.5 1.5
0.55373 0.25348 0.5 0.5
0.18626 0.49346 0 0.5
-1.38172 0.56953 -1.5 0.5
-0.48629 -1.1132 -0.5 -1
-0.86531 -0.08554 -1 0
-0.02449 -0.76973 0 -1
0.08408 0.66393 0 0.5
0.30049 0.24879 0.5 0
-1.25116 -0.53349 -1.5 -0.5
-0.21718 -0.11345 0 0
0.27523 0.63025 0.5 0.5
0.35504 0.95636 0.5 1
-0.02258 -0.26877 0 -0.5
0.40322 1.47887 0.5 1.5
1.3534 -0.57817 1.5 -0.5
-0.72446 -0.08481 -0.5 0
-0.15096 0.10538 0 0
-1.57548 -0.64715 -1.5 -0.5
2.00104 1.50434 2 1.5
-1.04345 0.77693 -1 1
-0.33871 -0.56161 -0.5 -0.5
1.44942 -0.78595 1.5 -1
-0.30356 1.03383 -0.5 1
0.01883 0.89863 0 1
-1.6691 -0.56662 -1.5 -0.5
-0.22177 -0.21425 0 0
-0.51618 -2.27183 -0.5 -2.5
0.374 1.00806 0.5 1
-0.07299 0.02687 0 0
0.56669 -1.35082 0.5 -1.5
-0.49301 -1.65673 -0.5 -1.5
0.59224 -1.30601 0.5 -1.5
0.77803 -2.06616 1 -2
0.88635 -0.03595 1 0
-0.9174 0.77231 -1 1
-2.62362 -2.10632 -2.5 -2
-0.17428 1.0995 0 1
0.53098 -0.46645 0.5 -0.5
-0.94324 0.45252 -1 0.5
-0.4827 -1.69258 -0.5 -1.5
0.55596 -2.77229 0.5 -3
2.44118 -1.05486 2.5 -1
-0.44261 -0.21645 -0.5 0
-0.06786 -0.30839 0 -0.5
-0.28461 0.27105 -0.5 0.5
-0.48295 0.33199 -0.5 0.5
-0.63247 -1.71857 -0.5 -1.5
1.2382 0.03357 1 0
-0.60499 -0.03977 -0.5 0
-0.13669 0.76919 0 1
-1.07371 1.25907 -1 1.5
0.17415 0.46011 0 0.5
-0.91289 0.06301 -1 0
-0.98523 0.3233 -1 0.5
1.37251 -2.02153 1.5 -2
1.0587 1.20236 1 1
1.33604 -0.40126 1.5 -0.5
1.56775 1.1402 1.5 1
-1.00689 -0.52358 -1 -0.5
-0.69846 0.42705 -0.5 0.5
0.75232 -0.48049 1 -0.5
0.98731 0.80917 1 1
-0.54487 0.68481 -0.5 0.5
2.42775 -1.07753 2.5 -1
-0.79568 2.34162 -1 2.5
-0.21408 0.82038 0 1
1.73189 0.49944 1.5 0.5
-0.97531 -0.15255 -1 0
0.09933 -0.35326 0 -0.5
-1.63868 0.83319 -1.5 1
0.09231 -0.93534 0 -1
2.02096 -0.21261 2 0
-0.66843 -0.53735 -0.5 -0.5
-1.29457 0.17651 -1.5 0
0.36675 0.14074 0.5 0
0.60132 -0.36157 0.5 -0.5
0.36942 -0.83107 0.5 -1
1.65642 1.36686 1.5 1.5
-1.43419 0.9038 -1.5 1
-1.32502 0.08426 -1.5 0
0.9966 -2.77243 1 -3
-1.23901 1.55453 -1 1.5
-0.55563 0.05355 -0.5 0
1.10341 1.33308 1 1.5
-0.1095 -1.48798 0 -1.5
1.78356 0.42122 2 0.5
-1.5692 -1.81232 -1.5 -2
0.26939 -1.00433 0.5 -1
-0.72661 1.7504 -0.5 2
0.59848 -0.00141 0.5 0
0.8614 0.83071 1 1
-0.58098 -0.31779 -0.5 -0.5
1.55127 0.17456 1.5 0
0.704 0.10165 0.5 0
0.91973 -0.15606 1 0
0.32473 1.04472 0.5 1
0.324 -1.94339 0.5 -2
-1.16547 -1.70802 -1 -1.5
0.68656 -0.71633 0.5 -0.5
-0.48955 1.78405 -0.5 2
0.26155 1.90968 0.5 2
-1.03941 0.70633 -1 0.5
0.56967 -1.3517 0.5 -1.5
-0.84587 -1.81205 -1 -2
1.02339 -1.26772 1 -1.5
1.37746 -1.45659 1.5 -1.5
0.81853 0.36666 1 0.5
-1.55103 0.63584 -1.5 0.5
-0.72666 -0.73557 -0.5 -0.5
-1.65144 1.67792 -1.5 1.5
0.34706 -1.15054 0.5 -1
0.25586 1.44317 0.5 1.5
0.17897 0.11481 0 0
0.31091 -0.52782 0.5 -0.5
2.018 0.99973 2 1
0.61671 1.39871 0.5 1.5
-1.02286 -0.29839 -1 -0.5
-1.3529 0.53331 -1.5 0.5
0.17739 1.72446 0 1.5
0.79353 0.33198 1 0.5
-0.25011 0.97193 -0.5 1
0.34829 -1.39581 0.5 -1.5
-0.70871 -0.10874 -0.5 0
1.90621 -0.06681 2 0
0.06176 -1.15397 0 -1
-0.79579 -1.31625 -1 -1.5
1.64081 0.27916 1.5 0.5
0.09179 0.38898 0 0.5
-1.88559 0.07052 -2 0
0.23353 0.59404 0 0.5
-0.45008 0.5662 -0.5 0.5
0.11973 -0.74598 0 -0.5
1.70526 -1.53801 1.5 -1.5
-0.56856 0.84917 -0.5 1
-0.03196 -1.25203 0 -1.5
0.7281 -2.67556 0.5 -2.5
-0.12495 1.43233 0 1.5
0.55407 1.39083 0.5 1.5
0.02032 0.00048 0 0
-1.35446 -1.19419 -1.5 -1
-1.70206 1.82669 -1.5 2
-0.98194 0.55519 -1 0.5
1.69498 0.92862 1.5 1
-1.46957 0.42241 -1.5 0.5
-1.10591 0.08208 -1 0
0.72891 0.56398 0.5 0.5
-1.94145 1.43857 -2 1.5
1.51427 -0.1166 1.5 0
1.51246 -0.19083 1.5 0
1.20592 0.51918 1 0.5
-1.11051 0.52753 -1 0.5
0.37874 -0.97686 0.5 -1
0.68075 -1.51167 0.5 -1.5
-0.11659 -0.54346 0 -0.5
1.07632 -1.42893 1 -1.5
2.8306 -0.31956 3 -0.5
1.35135 0.08376 1.5 0
2.06294 -0.64638 2 -0.5
-1.0355 -0.17861 -1 0
1.02651 -1.21504 1 -1
0.32574 -1.15734 0.5 -1
-1.0877 1.49014 -1 1.5
0.43139 0.23931 0.5 0
-0.25985 1.6997 -0.5 1.5
0.63304 -1.28454 0.5 -1.5
3.05221 -0.89812 3 -1
0.78454 -1.24542 1 -1
1.01676 1.82532 1 2
0.42322 0.63288 0.5 0.5
0.75769 -0.93924 1 -1
0.54907 -0.49096 0.5 -0.5
-1.86653 1.03292 -2 1
-0.78443 -1.30161 -1 -1.5
0.65158 -0.65392 0.5 -0.5
-0.03752 0.26295 0 0.5
-1.44412 0.12359 -1.5 0
1.34638 -0.12993 1.5 0
0.32049 -0.5246 0.5 -0.5
1.31605 -2.53583 1.5 -2.5
0.34207 0.74992 0.5 0.5
0.15116 -0.5222 0 -0.5
-0.12031 1.32943 0 1.5
-0.17409 -0.38358 0 -0.5
-0.7247 -0.64442 -0.5 -0.5
0.07383 0.72742 0 0.5
0.65539 -0.43668 0.5 -0.5
0.29549 -1.36966 0.5 -1.5
0.42063 0.09356 0.5 0
-0.29958 0.90413 -0.5 1
-1.38486 0.09106 -1.5 0
-1.17443 -1.05509 -1 -1
0.39475 2.28522 0.5 2.5
-1.56378 0.13773 -1.5 0
0.78106 -0.57944 1 -0.5
-0.23633 -0.29939 0 -0.5
-2.46887 -1.10493 -2.5 -1
0.2432 0.95752 0 1
-1.17685 -0.18723 -1 0
-0.87421 1.57601 -1 1.5
0.13451 1.45095 0 1.5
1.30804 -0.19011 1.5 0
-0.33474 0.46294 -0.5 0.5
-0.2019 -0.17617 0 0
1.21101 -1.40174 1 -1.5
0.68958 0.01745 0.5 0
-0.37379 -1.49588 -0.5 -1.5
-0.787 0.656 -1 0.5
-0.86297 -0.19319 -1 0
0.61641 -0.73194 0.5 -0.5
2.05304 0.68991 2 0.5
-1.33063 -0.87794 -1.5 -1
-1.36443 2.42907 -1.5 2.5
-0.29668 -1.22439 -0.5 -1
-0.49331 -0.83516 -0.5 -1
0.02861 0.03971 0 0
1.12641 -1.61266 1 -1.5
0.47845 -1.47755 0.5 -1.5
-0.17544 0.60136 0 0.5
0.48128 0.11637 0.5 0
0.67158 0.37892 0.5 0.5
1.5482 -0.33739 1.5 -0.5
1.37694 -0.60209 1.5 -0.5
-0.54218 -0.74479 -0.5 -0.5
0.56447 0.05115 0.5 0
-0.1569 -1.19264 0 -1
-1.06894 -0.29597 -1 -0.5
-0.87353 0.24715 -1 0
0.2843 0.81108 0.5 1
-0.15475 -0.66776 0 -0.5
0.62018 1.45681 0.5 1.5
-0.19368 0.35033 0 0.5
-2.13082 0.16927 -2 0
1.70768 -0.46884 1.5 -0.5
-1.13194 0.13359 -1 0
0.54065 -0.8705 0.5 -1
-0.88448 -0.23824 -1 0
-0.03459 0.99946 0 1
0.08899 -1.99588 0 -2
-0.46626 0.27096 -0.5 0.5
-1.6777 -2.00483 -1.5 -2
-0.89314 0.36 -1 0.5
1.50449 -1.12499 1.5 -1
0.70809 0.26912 0.5 0.5
0.63178 -2.02946 0.5 -2
-1.34499 -0.20882 -1.5 0
-0.81521 0.22555 -1 0
-1.21837 0.09416 -1 0
1.50608 0.65857 1.5 0.5
-1.787 0.86357 -2 1
-0.46712 -0.1314 -0.5 0
-0.45099 0.26447 -0.5 0.5
0.88644 -1.44413 1 -1.5
0.47531 -0.91205 0.5 -1
0.0508 -0.43914 0 -0.5
-0.50034 -0.4972 -0.5 -0.5
-0.54933 0.25893 -0.5 0.5
0.31603 -1.64562 0.5 -1.5
0.25979 -0.51174 0.5 -0.5
-0.60526 0.6894 -0.5 0.5
0.02025 -0.34678 0 -0.5
2.00778 0.38757 2 0.5
-0.24822 -1.21143 0 -1
-0.45123 -0.29589 -0.5 -0.5
-1.43938 0.64016 -1.5 0.5
0.6672 -0.5121 0.5 -0.5
-0.74528 0.42949 -0.5 0.5
-1.25678 0.59949 -1.5 0.5
-1.04576 0.57642 -1 0.5
0.20178 -0.63275 0 -0.5
0.40595 0.16456 0.5 0
-1.48354 -0.24532 -1.5 0
0.07453 0.18382 0 0
1.30282 -0.02479 1.5 0
1.14598 1.22364 1 1
-0.7352 -0.20082 -0.5 0
-0.86552 1.35383 -1 1.5
1.69558 -1.49131 1.5 -1.5
0.85103 0.60433 1 0.5
1.90973 -0.0736 2 0
1.38344 -0.27122 1.5 -0.5
0.19104 -0.33259 0 -0.5
0.56846 -0.60506 0.5 -0.5
-1.36335 -0.51691 -1.5 -0.5
1.08008 1.30303 1 1.5
-1.59111 1.33524 -1.5 1.5
-0.34228 0.23561 -0.5 0
-1.0312 0.237 -1 0
3.25243 -1.2618 3.5 -1.5
-0.67701 -1.39735 -0.5 -1.5
-0.30032 0.10879 -0.5 0
0.01894 -1.50338 0 -1.5
0.45615 0.32547 0.5 0.5
0.5451 -0.29107 0.5 -0.5
2.43877 -0.92612 2.5 -1
-1.2262 -0.49503 -1 -0.5
0.54511 -0.20587 0.5 0
0.11714 0.32982 0 0.5
0.36569 -0.60391 0.5 -0.5
0.18518 1.3243 0 1.5
0.89489 -0.73772 1 -0.5
0.50039 -0.5803 0.5 -0.5
0.5697 -0.65244 0.5 -0.5
0.24674 0.20534 0 0
-0.31076 -1.47136 -0.5 -1.5
-1.03153 2.28986 -1 2.5
0.19908 2.05305 0 2
-1.62274 -0.57912 -1.5 -0.5
0.91676 -1.37155 1 -1.5
0.27658 0.31466 0.5 0.5
-0.17893 -0.11501 0 0
2.51982 -0.26678 2.5 -0.5
0.47119 -0.10023 0.5 0
1.22729 0.14822 1 0
-0.27938 0.20605 -0.5 0
-0.1217 0.70996 0 0.5
0.13685 0.80333 0 1
0.53197 0.84236 0.5 1
-0.15209 -0.66379 0 -0.5