Table 1: Mean estimate (and standard error) of 𝜙 using Newton’s unidimensional method, 𝜙 𝑁 , based on 200 simulated contingency tables with a specified value of 𝜙 and 𝑛 = 1 0 0 0 .

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 (0.1160)0.00235 (0.0829)0.00042 (0.0583)−0.00023 (0.0611)−0.00029 (0.0488)−0.00007 (0.0346)0.00008 (0.0312)0.00004 (0.0239)0.00005 (0.0178)
0.010.01617 (0.2765)0.00740 (0.1237)0.01503 (0.0792)0.00868 (0.0631)0.01040 (0.0631)0.01016 (0.0446)0.01012 (0.0344)0.01020 (0.0307)0.01002 (0.0241)0.01000 (0.0179)
0.050.05454 (0.2188)0.05134 (0.1194)0.05046 (0.0824)0.04911 (0.0621)0.04964 (0.0615)0.05009 (0.0424)0.05021 (0.0338)0.04997 (0.0301)0.05001 (0.0236)0.05009 (0.0183)
0.100.10278 (0.2165)0.09998 (0.1089)0.10087 (0.0775)0.10061 (0.0608)0.09994 (0.0690)0.09990 (0.0436)0.09980 (0.0341)0.10006 (0.0301)0.10024 (0.0234)0.10001 (0.0181)
0.200.20473 (0.2048)0.20097 (0.1149)0.19999 (0.0770)0.20010 (0.0580)0.19969 (0.0605)0.19970 (0.0431)0.20021 (0.0317)0.19995 (0.0290)0.20008 (0.0223)0.19995 (0.0165)
0.300.30392 (0.2016)0.30622 (0.1130)0.30312 (0.0770)0.30040 (0.0558)0.30019 (0.0616)0.30022 (0.0404)0.30008 (0.0314)0.30007 (0.0278)0.29995 (0.0202)0.30001 (0.0149)
0.400.40491 (0.2295)0.39656 (0.1170)0.40184 (0.0771)0.40082 (0.0629)0.40079 (0.0649)0.40080 (0.0412)0.40030 (0.0295)0.40001 (0.0263)0.40015 (0.0187)0.40036 (0.0129)
0.500.50762 (0.2353)0.50533 (0.1164)0.50139 (0.0869)0.50326 (0.0564)0.49981 (0.0591)0.49788 (0.0422)0.50018 (0.0284)0.50030 (0.0249)0.50022 (0.0167)0.50025 (0.0113)
0.600.61482 (0.2229)0.60065 (0.1102)0.60149 (0.0751)0.60076 (0.0561)0.59980 (0.0577)0.59945 (0.0373)0.59976 (0.0272)0.60012 (0.0230)0.59999 (0.0156)0.60015 (0.0096)
0.700.71150 (0.2131)0.70272 (0.1175)0.69969 (0.0690)0.70033 (0.0524)0.69953 (0.0547)0.70031 (0.0359)0.70049 (0.0250)0.70026 (0.0209)0.70015 (0.0139)0.69996 (0.0078)
0.800.80482 (0.2773)0.80215 (0.1081)0.79924 (0.0785)0.79978 (0.0485)0.79985 (0.0524)0.80013 (0.0345)0.80002 (0.0226)0.80009 (0.0197)0.79995 (0.0117)0.80038 (0.0066)
0.900.89570 (0.2133)0.89081 (0.1033)0.90338 (0.0687)0.90103 (0.0513)0.89998 (0.0519)0.90018 (0.0314)0.90058 (0.0214)0.89980 (0.0174)0.90041 (0.0102)0.90025 (0.0055)
1.001.01856 (0.2358)0.99917 (0.1074)0.99251 (0.0804)1.00302 (0.0504)0.99954 (0.0517)0.99992 (0.0301)1.00014 (0.0188)0.99983 (0.0167)0.99987 (0.0091)0.99659 (0.0045)
1.101.10279 (0.2169)1.10185 (0.1187)1.10167 (0.0646)1.10041 (0.0472)1.10064 (0.0475)1.10020 (0.0282)1.09998 (0.0174)1.10030 (0.0146)1.10028 (0.0076)1.09676 (0.0035)
1.201.20637 (0.2047)1.20018 (0.1057)1.20161 (0.0626)1.20078 (0.0430)1.20001 (0.0444)1.20077 (0.0260)1.19968 (0.0160)1.19960 (0.0132)1.19975 (0.0066)1.19886 (0.0030)
1.301.32157 (0.2372)1.30192 (0.1100)1.30332 (0.0551)1.30048 (0.0396)1.30092 (0.0452)1.30039 (0.0241)1.29982 (0.0143)1.30007 (0.0121)1.30016 (0.0057)1.28541 (0.0023)
1.401.41818 (0.2433)1.40873 (0.0898)1.40110 (0.0564)1.39902 (0.0395)1.40079 (0.0423)1.40040 (0.0224)1.40003 (0.0132)1.40001 (0.0106)1.39921 (0.0051)1.38124 (0.0021)
1.501.49777 (0.1907)1.50079 (0.0939)1.50105 (0.0531)1.50184 (0.0384)1.49974 (0.0427)1.49900 (0.0223)1.50036 (0.0118)1.50045 (0.0091)1.49371 (0.0045)1.47004 (0.0017)