Table 3: Mean estimate (and standard error) of 𝜙 using 𝜙 L o g N I 1 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)−0.00008 (0.1160)0.00299 (0.0829)0.00032 (0.0583)−0.00024 (0.0611)−0.00030 (0.0448)−0.00004 (0.0346)0.00005 (0.0312)0.00006 (0.0239)0.00005 (0.0178)
0.010.01610 (0.2759)0.00633 (0.1234)0.01424 (0.0785)0.00836 (0.0630)0.01029 (0.0631)0.01020 (0.0446)0.01011 (0.0344)0.01021 (0.0307)0.01004 (0.0241)0.01001 (0.0179)
0.050.05446 (0.2187)0.05152 (0.1193)0.05075 (0.0824)0.04922 (0.0620)0.04962 (0.0615)0.05008 (0.0423)0.05016 (0.0338)0.04996 (0.0300)0.04992 (0.0236)0.05000 (0.0182)
0.100.10231 (0.2154)0.09998 (0.1099)0.10078 (0.0773)0.10046 (0.0607)0.09993 (0.0689)0.09975 (0.0434)0.09954 (0.0339)0.09969 (0.0299)0.09964 (0.0231)0.09911 (0.0177)
0.200.20451 (0.2045)0.20025 (0.1145)0.19952 (0.0765)0.19932 (0.0574)0.19893 (0.0600)0.19818 (0.0424)0.19766 (0.0308)0.19676 (0.0281)0.19492 (0.0213)0.19101 (0.0153)
0.300.30337 (0.2007)0.30434 (0.1110)0.29977 (0.0753)0.29721 (0.0546)0.29743 (0.0604)0.29481 (0.0390)0.29092 (0.0297)0.28925 (0.0261)0.28149 (0.0182)0.26891 (0.0129)
0.400.40352 (0.2275)0.39385 (0.1155)0.39791 (0.0749)0.39275 (0.0602)0.39458 (0.0629)0.38791 (0.0388)0.37732 (0.0269)0.37233 (0.0236)0.35294 (0.0159)0.32652 (0.0103)
0.500.50350 (0.2310)0.49954 (0.1134)0.48823 (0.0846)0.48801 (0.0526)0.48693 (0.0563)0.47029 (0.0389)0.45542 (0.0248)0.44396 (0.0214)0.40896 (0.0135)0.36225 (0.0086)
0.600.60742 (0.2165)0.59252 (0.1070)0.58724 (0.0709)0.57402 (0.0516)0.57580 (0.0539)0.55214 (0.0331)0.52330 (0.0231)0.50859 (0.0189)0.45332 (0.0121)0.38300 (0.0070)
0.700.70298 (0.2073)0.69001 (0.1127)0.67442 (0.0644)0.65328 (0.0473)0.66050 (0.0499)0.62525 (0.0311)0.57783 (0.0204)0.55366 (0.0166)0.48359 (0.0104)0.38935 (0.0054)
0.800.79400 (0.2685)0.78320 (0.1027)0.75942 (0.0726)0.73482 (0.0431)0.74372 (0.0469)0.68976 (0.0291)0.62194 (0.0178)0.59053 (0.0151)0.49281 (0.0085)0.39437 (0.0043)
0.900.88478 (0.2076)0.86906 (0.0972)0.84284 (0.0619)0.80984 (0.0446)0.81907 (0.0456)0.74370 (0.0256)0.65549 (0.0165)0.61944 (0.0130)0.50525 (0.0071)0.39864 (0.0034)
1.000.99208 (0.2242)0.95982 (0.1003)0.91896 (0.0711)0.87180 (0.0428)0.88914 (0.0447)0.78265 (0.0240)0.68186 (0.0140)0.64302 (0.0122)0.51164 (0.0061)0.39090 (0.0026)
1.101.07792 (0.2070)1.04284 (0.1102)0.99425 (0.0563)0.93162 (0.0397)0.94721 (0.0399)0.82129 (0.0221)0.69747 (0.0127)0.65111 (0.0103)0.50923 (0.0048)0.38387 (0.0019)
1.201.17866 (0.1918)1.12713 (0.0961)1.06491 (0.0539)0.98924 (0.0355)1.00068 (0.0366)0.85517 (0.0198)0.71206 (0.0114)0.66053 (0.0091)0.51300 (0.0040)0.38100 (0.0016)
1.301.27633 (0.2260)1.20889 (0.0981)1.12928 (0.0542)1.05000 (0.0322)1.05912 (0.0370)0.88164 (0.0181)0.71797 (0.0099)0.67223 (0.0081)0.51028 (0.0033)0.37375 (0.011)
1.401.37037 (0.2244)1.29294 (0.0806)1.19599 (0.0470)1.07872 (0.0317)1.09808 (0.0340)0.90062 (0.0146)0.73551 (0.0089)0.66730 (0.0068)0.50864 (0.0029)0.37198 (0.0011)
1.501.44834 (0.1785)1.37143 (0.0823)1.24810 (0.0439)1.12323 (0.0305)1.14909 (0.0337)0.92568 (0.0161)0.73350 (0.0077)0.66406 (0.0056)0.50923 (0.0025)0.36991 (0.0009)