Table 4: Mean estimate (and standard error) of 𝜙 using 𝜙 L o g N I 2 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)−0.00020 (0.1161)0.00331 (0.0828)0.00026 (0.0583)−0.00023 (0.0611)−0.00030 (0.0448)−0.00003 (0.0346)0.00003 (0.0312)0.00006 (0.0239)0.00005 (0.0178)
0.010.01617 (0.2760)0.00587 (0.1233)0.01482 (0.0783)0.00818 (0.0629)0.01028 (0.0631)0.01022 (0.0446)0.01012 (0.0344)0.01021 (0.0307)0.01005 (0.0241)0.01001 (0.0179)
0.050.05454 (0.2187)0.05161 (0.1193)0.05075 (0.0824)0.04925 (0.0620)0.04962 (0.0615)0.05011 (0.0423)0.05021 (0.0338)0.05002 (0.0300)0.05000 (0.0236)0.05014 (0.0182)
0.100.10271 (0.2162)0.10001 (0.1088)0.10089 (0.0773)0.10061 (0.0607)0.10007 (0.0689)0.09996 (0.0434)0.09987 (0.0339)0.10007 (0.0299)0.10029 (0.0231)0.10012 (0.0177)
0.200.20473 (0.2045)0.20054 (0.1145)0.20012 (0.0765)0.20036 (0.0574)0.19974 (0.0600)0.19982 (0.0424)0.20031 (0.0308)0.19976 (0.0280)0.19977 (0.0212)0.19881 (0.0152)
0.300.30391 (0.2007)0.30672 (0.1106)0.30252 (0.0752)0.30051 (0.0545)0.30013 (0.0604)0.30002 (0.0389)0.29933 (0.0296)0.29895 (0.0259)0.29652 (0.0179)0.29131 (0.0125)
0.400.40486 (0.2281)0.39614 (0.1155)0.40305 (0.0748)0.40154 (0.0599)0.40072 (0.0629)0.40021 (0.0386)0.39647 (0.0266)0.39431 (0.0233)0.38530 (0.0154)0.36861 (0.0097)
0.500.50682 (0.2309)0.50599 (0.1131)0.49682 (0.0845)0.50235 (0.0521)0.49920 (0.0561)0.49339 (0.0386)0.48907 (0.0242)0.48343 (0.0208)0.46052 (0.0128)0.42230 (0.0079)
0.600.61277 (0.2177)0.60066 (0.1069)0.60309 (0.0704)0.59827 (0.0509)0.59648 (0.0540)0.58824 (0.0326)0.57337 (0.0223)0.56490 (0.0181)0.52303 (0.0112)0.45747 (0.0062)
0.700.70991 (0.2067)0.70403 (0.1126)0.69708 (0.0640)0.69114 (0.0466)0.69288 (0.0494)0.67813 (0.0302)0.64850 (0.0193)0.63058 (0.0155)0.56907 (0.0094)0.47393 (0.0046)
0.800.80340 (0.2670)0.80302 (0.1021)0.79317 (0.0719)0.78409 (0.0422)0.78794 (0.0462)0.76014 (0.0281)0.71204 (0.0166)0.68449 (0.0139)0.59183 (0.0075)0.48567 (0.0036)
0.900.89526 (0.2076)0.89665 (0.0968)0.88885 (0.0610)0.87568 (0.0431)0.87881 (0.0447)0.83495 (0.0243)0.76251 (0.0152)0.73009 (0.0118)0.61468 (0.0061)0.49547 (0.0027)
1.001.01160 (0.2247)0.99328 (0.0996)0.97792 (0.0701)0.95673 (0.0410)0.96469 (0.0435)0.89309 (0.0225)0.80583 (0.0126)0.76616 (0.0108)0.62836 (0.0051)0.48938 (0.0020)
1.101.09777 (0.2076)1.08835 (0.1090)1.07277 (0.0546)1.03428 (0.0379)1.04616 (0.0384)0.94742 (0.0205)0.83311 (0.0113)0.78539 (0.0090)0.63087 (0.0040)0.48327 (0.0015)
1.201.20275 (0.1938)1.18780 (0.0948)1.16055 (0.0520)1.10968 (0.0337)1.11730 (0.0350)1.00053 (0.0181)0.85947 (0.0099)0.80448 (0.0078)0.63668 (0.0032)0.48174 (0.0012)
1.301.31224 (0.2236)1.28023 (0.0971)1.24276 (0.0517)1.18733 (0.0305)1.19350 (0.0351)1.04284 (0.0164)0.87401 (0.0085)0.82342 (0.0068)0.63865 (0.0026)0.47549 (0.0008)
1.401.41026 (0.2230)1.37640 (0.0786)1.32384 (0.0451)1.23586 (0.0297)1.25046 (0.0320)1.07434 (0.0146)0.90116 (0.0075)0.82417 (0.0057)0.63906 (0.0023)0.47335 (0.0008)
1.501.49244 (0.1784)1.46870 (0.0806)1.39468 (0.0420)1.29823 (0.0282)1.31951 (0.0314)1.10946 (0.0142)0.90476 (0.0064)0.82555 (0.0045)0.64242 (0.0019)0.47224 (0.0006)