Table 2: Mean estimate (and standard error) of 𝜙 using 𝜙 L o g N I based on 200 simulated contingency tables with a specified value of 𝜙 and 𝑛 1 0 0 0 . The values in bold are where the mean of the 200 𝑃 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 𝜙 2 × 22 × 32 × 42 × 53 × 33 × 43 × 54 × 44 × 55 × 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)
0.010.01618 (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)
0.050.05454 (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)
0.100.10278 (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)
0.200.20474 (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)
0.300.30392 (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)
0.400.40491 (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)
0.500.50762 (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)
0.600.61482 (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)
0.700.71150 (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)
0.800.80483 (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)
0.900.89570 (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)
1.001.01857 (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)
1.101.10280 (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)
1.201.20638 (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)
1.301.32158 (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)
1.401.41819 (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)
1.501.49778 (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)