Table 2: Mean estimate (and standard error) of using based on 200 simulated contingency tables with a specified value of and . The values in bold are where the mean of the 200 values obtained from the Wald test (of the difference between the estimated and true parameter) is significant at the 1% level. The italicised values are significant at the 5% level.

Size of contingency table True 2 × 2 2 × 3 2 × 4 2 × 5 3 × 3 3 × 4 3 × 5 4 × 4 4 × 5 5 × 5 0.00 −0.00068 (0.2014) −0.00026 (0.1161) 0.00350 (0.0828) 0.00019 (0.0583) −0.00023 (0.0611) −0.00030 (0.0448) −0.00003 (0.0346) 0.00002 (0.0312) 0.00006 (0.0239) 0.00005 (0.0178) 0.01 0.01618 (0.2760) 0.00562 (0.1233) 0.01509 (0.0783) 0.00810 (0.0629) 0.01028 (0.0631) 0.01024 (0.0446) 0.01012 (0.0344) 0.01021 (0.0307) 0.01005 (0.0241) 0.01001 (0.0179) 0.05 0.05454 (0.2187) 0.05164 (0.1193) 0.05092 (0.0824) 0.04926 (0.0620) 0.04962 (0.0615) 0.05012 (0.0423) 0.05022 (0.0338) 0.05003 (0.0300) 0.05000 (0.0236) 0.05016 (0.0182) 0.10 0.10278 (0.2163) 0.10001 (0.1088) 0.10092 (0.0773) 0.10061 (0.0607) 0.10010 (0.0689) 0.09997 (0.0434) 0.09989 (0.0339) 0.10008 (0.0299) 0.10034 (0.0231) 0.10018 (0.0177) 0.20 0.20474 (0.2045) 0.20054 (0.1145) 0.20012 (0.0765) 0.20043 (0.0574) 0.19977 (0.0600) 0.19992 (0.0424) 0.20054 (0.0308) 0.19996 (0.0280) 0.20032 (0.0212) 0.20024 (0.0151) 0.30 0.30392 (0.2007) 0.30788 (0.1103) 0.30350 (0.0750) 0.30083 (0.0545) 0.30022 (0.0604) 0.30042 (0.0389) 0.30045 (0.0296) 0.30035 (0.0259) 0.30004 (0.0179) 0.30088 (0.0124) 0.40 0.40491 (0.2281) 0.39618 (0.1155) 0.40358 (0.0748) 0.40355 (0.0598) 0.40126 (0.0629) 0.40262 (0.0386) 0.40080 (0.0265) 0.40078 (0.0232) 0.40167 (0.0151) 0.40312 (0.0092) 0.50 0.50762 (0.2308) 0.50795 (0.1130) 0.49748 (0.0845) 0.50464 (0.0518) 0.50083 (0.0561) 0.49881 (0.0385) 0.50105 (0.0240) 0.50318 (0.0205) 0.50290 (0.0122) 0.50552 (0.0069) 0.60 0.61482 (0.2188) 0.60143 (0.1069) 0.60722 (0.0700) 0.60415 (0.0506) 0.59982 (0.0535) 0.59997 (0.0324) 0.60070 (0.0218) 0.60368 (0.0175) 0.60521 (0.0102) 0.61267 (0.0048) 0.70 0.71150 (0.2063) 0.70642 (0.1128) 0.70040 (0.0639) 0.70262 (0.0463) 0.70007 (0.0493) 0.70457 (0.0298) 0.70614 (0.0185) 0.70520 (0.0145) 0.70790 (0.0079) 0.71631 (0.0029) 0.80 0.80483 (0.2665) 0.80608 (0.1018) 0.80105 (0.0717) 0.79954 (0.0419) 0.74372 (0.0469) 0.80350 (0.0275) 0.80484 (0.0154) 0.80512 (0.0124) 0.81298 (0.0055) 0.82603 (0.0018) 0.90 0.89570 (0.2076) 0.90016 (0.0967) 0.90264 (0.0605) 0.90583 (0.0421) 0.90236 (0.0442) 0.90229 (0.0234) 0.91092 (0.0135) 0.90512 (0.0100) 0.91617 (0.0039) 0.93313 (0.0011) 1.00 1.01857 (0.2247) 0.99812 (0.0995) 0.99674 (0.0698) 1.01016 (0.0394) 1.00154 (0.0429) 1.00645 (0.0209) 1.01148 (0.0105) 1.01483 (0.0085) 1.02763 (0.0028) 1.03001 (0.0006) 1.10 1.10280 (0.2085) 1.09827 (0.1085) 1.10866 (0.0533) 1.10855 (0.0361) 1.10441 (0.0376) 1.11082 (0.0186) 1.11704 (0.0088) 1.12472 (0.0063) 1.13542 (0.0018) 1.12646 (0.0003) 1.20 1.20638 (0.1958) 1.20485 (0.0944) 1.21104 (0.0507) 1.20885 (0.0319) 1.20120 (0.0338) 1.21299 (0.0157) 1.21861 (0.0070) 1.22115 (0.0049) 1.23445 (0.0012) 1.23221 (0.0002) 1.30 1.32158 (0.2227) 1.30226 (0.0970) 1.31646 (0.0494) 1.30883 (0.0286) 1.30870 (0.0334) 1.31479 (0.0137) 1.32367 (0.0053) 1.32639 (0.0039) 1.33670 (0.0008) 1.31161 (0.0001) 1.40 1.41819 (0.2224) 1.40275 (0.0774) 1.40607 (0.0435) 1.41200 (0.0270) 1.41515 (0.0299) 1.41974 (0.0115) 1.43487 (0.0043) 1.43576 (0.0028) 1.42865 (0.0006) 1.36380 (0.0008) 1.50 1.49778 (0.1785) 1.50663 (0.0795) 1.50531 (0.0402) 1.51515 (0.0250) 1.50567 (0.0290) 1.50459 (0.0108) 1.53475 (0.0032) 1.53676 (0.0018) 1.52404 (0.0004) 1.43543 (0.0004)