Table 5: Mean estimate (and standard error) of 𝜙 using 𝜙 B D 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

0.00−0.00064 (0.2014)0.00017 (0.0060)0.00229 (0.0829)0.00042 (0.0583)−0.00023 (0.0611)−0.00029 (0.0448)−0.00007 (0.0346)0.00008 (0.0312)0.00004 (0.0239)0.00005 (0.0178)
0.010.01578 (0.2745)0.00740 (0.1236)0.01351 (0.0787)0.00868 (0.0630)0.01038 (0.0631)0.01016 (0.0446)0.01012 (0.0344)0.01020 (0.0307)0.01002 (0.0241)0.01000 (0.0179)
0.050.05537 (0.2182)0.05137 (0.1193)0.05045 (0.0823)0.04906 (0.0620)0.04959 (0.0615)0.05004 (0.0423)0.05008 (0.0338)0.04987 (0.0300)0.04982 (0.0236)0.04983 (0.0182)
0.100.10060 (0.2125)0.09994 (0.1087)0.10065 (0.0773)0.10031 (0.0606)0.09990 (0.0688)0.09950 (0.0434)0.09900 (0.0339)0.09925 (0.0299)0.09871 (0.0231)0.09771 (0.0177)
0.200.20554 (0.2037)0.20065 (0.1143)0.19853 (0.0765)0.19771 (0.0574)0.19736 (0.0600)0.19566 (0.0424)0.19334 (0.0308)0.19195 (0.0280)0.18773 (0.0214)0.18065 (0.0154)
0.300.30442 (0.1998)0.30099 (0.1113)0.29682 (0.0754)0.29088 (0.0546)0.29373 (0.0604)0.28762 (0.0390)0.27933 (0.0299)0.27595 (0.0262)0.26320 (0.0184)0.24319 (0.0132)
0.400.39883 (0.2243)0.38977 (0.1152)0.38999 (0.0749)0.38243 (0.0602)0.38611 (0.0628)0.37154 (0.0389)0.35374 (0.0272)0.34521 (0.0240)0.31750 (0.0164)0.28401 (0.0109)
0.500.49941 (0.2300)0.48981 (0.1128)0.48156 (0.0833)0.46832 (0.0528)0.46943 (0.0564)0.44038 (0.0393)0.41736 (0.0253)0.39981 (0.0220)0.35530 (0.0142)0.30366 (0.0093)
0.600.60336 (0.2113)0.58180 (0.1068)0.56500 (0.0712)0.54913 (0.0516)0.54854 (0.0541)0.50988 (0.0337)0.46819 (0.0238)0.44776 (0.0198)0.38563 (0.0130)0.31530 (0.0077)
0.700.69972 (0.2058)0.66768 (0.1121)0.64706 (0.0645)0.60455 (0.0479)0.62207 (0.0503)0.56595 (0.0319)0.50408 (0.0214)0.47675 (0.0176)0.40331 (0.0113)0.31913 (0.0061)
0.800.79011 (0.2568)0.75919 (0.1026)0.71197 (0.0728)0.67057 (0.0437)0.69012 (0.0476)0.61207 (0.0302)0.53082 (0.0190)0.50154 (0.0162)0.40365 (0.0094)0.32837 (0.0049)
0.900.86600 (0.2049)0.83271 (0.0969)0.78390 (0.0627)0.73735 (0.0455)0.75035 (0.0464)0.64749 (0.0269)0.55024 (0.0178)0.51415 (0.0142)0.41282 (0.0079)0.34591 (0.0038)
1.000.95778 (0.2192)0.92254 (0.0996)0.84033 (0.0739)0.77967 (0.0437)0.80391 (0.0458)0.67170 (0.0254)0.56617 (0.0153)0.53203 (0.0134)0.42429 (0.0069)0.36422 (0.0029)
1.101.05198 (0.2011)0.99021 (0.1101)0.90467 (0.0571)0.81670 (0.0410)0.83903 (0.0413)0.69141 (0.0236)0.57224 (0.0140)0.53513 (0.0115)0.43699 (0.0055)0.38981 (0.0021)
1.201.14028 (0.1859)1.05917 (0.0963)0.95848 (0.0551)0.85077 (0.0370)0.86977 (0.0383)0.71457 (0.0213)0.58876 (0.0126)0.54391 (0.0102)0.45929 (0.0045)0.43908 (0.0017)
1.301.24366 (0.2000)1.12319 (0.0973)0.99862 (0.0553)0.88461 (0.0340)0.91884 (0.0386)0.72751 (0.0197)0.59232 (0.0111)0.55751 (0.0091)0.48817 (0.0037)0.60876 (0.0011)
1.401.34106 (0.2180)1.19429 (0.0788)1.04569 (0.0489)0.90048 (0.0337)0.93586 (0.0359)0.74161 (0.0180)0.61512 (0.0100)0.58435 (0.0076)0.51219 (0.0032)0.65896 (0.0010)
1.501.37638 (0.1752)1.25152 (0.0836)1.06724 (0.0460)0.92840 (0.0324)0.98432 (0.0356)0.76259 (0.0177)0.63542 (0.0086)0.59487 (0.0063)0.59138 (0.0027)0.65896 (0.0007)