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Table 1 Comparison of 95% confidence intervals for three location quotients (LQ1, LQ2, LQ3) using three methods (D = delta, F = Fieller, P = Profile-likelihood). Varying incidence rates (p 1, p 2, p 3) were used along with 3 sets of population size configurations (a) n 1 = 50, n 2 = 80, n 3 = 60 (b) n 1 = 500, n 2 = 900, n 3 = 100 (c) n 1 = 2000, n 2 = 2500, n 3 = 1500. A total of 1000 simulated data sets were used to generate "benchmark" limits (designated as "S" under method)

From: Methods for confidence interval estimation of a ratio parameter with application to location quotients

  p 1 p 2 p 3 Method
(a) 0.25 0.3 0.2 S 0.5903 1.3959 0.8787 1.4844 0.4332 1.1237
     D 0.5789 1.3905 0.8860 1.4679 0.4380 1.1155
     F 0.5664 1.4043 0.8815 1.4824 0.4239 1.1234
     P 0.5715 1.4995 0.8109 1.5950 0.4375 1.2183
  0.2 0.4 0.7 S 0.2249 0.6926 0.7125 1.0744 1.3548 1.8404
     D 0.2235 0.6776 0.7168 1.0909 1.3309 1.8413
     F 0.2156 0.6758 0.7126 1.0918 1.3464 1.8651
     P 0.2409 0.7287 0.6719 1.1505 1.3096 1.8251
  0.9 0.1 0.5 S 1.8387 2.3249 0.0956 0.3765 0.9383 1.3492
     D 1.7335 2.3942 0.0901 0.3640 0.9040 1.3841
     F 1.7718 2.4478 0.0846 0.3624 0.9044 1.3910
     P 1.8297 2.2054 0.1088 0.4035 0.8607 1.4280
  0.02 0.01 0.1 S 0.0000 1.6889 0.0000 1.0037 1.2667 3.1667
     D -0.1536 1.1816 -0.0924 0.6015 1.4479 3.3499
     F -0.5404 1.5539 -0.3073 0.7883 1.0254 4.2516
     P 0.3015 1.0973 0.1272 0.6214 1.9683 3.1071
(b) 0.25 0.3 0.2 S 0.7924 1.0245 1.0156 1.1439 0.4483 1.0191
     D 0.7917 1.0197 1.0167 1.1489 0.4517 1.0012
     F 0.7911 1.0199 1.0167 1.1493 0.4504 1.0017
     P 0.7731 1.0476 0.9765 1.1932 0.4736 1.0343
  0.2 0.4 0.7 S 0.4766 0.6536 1.0807 1.1854 1.7154 2.2426
     D 0.4789 0.6537 1.0755 1.1865 1.7326 2.2467
     F 0.4781 0.6533 1.0757 1.1870 1.7370 2.2525
     P 0.4715 0.6698 1.0411 1.2225 1.7240 2.2265
  0.9 0.1 0.5 S 2.2140 2.3684 0.2129 0.2938 1.0390 1.5164
     D 2.1557 2.4273 0.2084 0.2971 1.0277 1.5079
     F 2.1629 2.4354 0.2078 0.2967 1.0281 1.5093
     P 2.2196 2.3530 0.2060 0.3053 1.022 1.5138
  0.02 0.01 0.1 S 0.5071 1.5517 0.2381 0.8333 2.5862 7.9550
     D 0.5212 1.5436 0.2396 0.7928 2.6717 7.7130
     F 0.4819 1.5835 0.2174 0.8136 2.5448 7.9803
     P 0.5205 1.8078 0.2494 0.9322 2.6765 8.8046
(c) 0.25 0.3 0.2 S 0.9113 1.0322 1.1066 1.2119 0.7077 0.8480
     D 0.9089 1.0296 1.1088 1.2115 0.7043 0.8439
     F 0.9088 1.0296 1.1089 1.2117 0.7041 0.8438
     P 0.8970 1.0440 1.0914 1.2305 0.6977 0.8544
  0.2 0.4 0.7 S 0.4518 0.5288 0.9424 1.0115 1.6636 1.7688
     D 0.4519 0.5285 0.9427 1.0147 1.6588 1.7717
     F 0.4518 0.5283 0.9427 1.0147 1.6595 1.7726
     P 0.4482 0.5341 0.9319 1.026 1.6577 1.7712
  0.9 0.1 0.5 S 1.8962 1.9663 0.1923 0.2365 1.0271 1.1150
     D 1.8797 1.9797 0.1903 0.2374 1.0237 1.1176
     F 1.8808 1.9808 0.1902 0.2373 1.0237 1.1177
     P 1.9004 1.9567 0.1896 0.2399 1.0165 1.1249
  0.02 0.01 0.1 S 0.4000 0.7184 0.1798 0.3847 2.5421 3.0220
     D 0.4020 0.7094 0.1776 0.3813 2.5418 3.0449
     F 0.4005 0.7106 0.1766 0.3821 2.5428 3.0504
     P 0.4018 0.7441 0.1844 0.4026 2.3876 3.2374