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Table 7. Simulation results comparing powers of ratio test to use of fiducial limits to test differences in LD 50s, LD 90s and LD99s in probit regressions.
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| Ratio of slopes |
Ratio test for LD50 rejection rates |
83% CI failure to overlap for LD50 |
Ratio test for LD90 |
83% CI failure to overlap for LD90 |
Ratio test for LD99 rejection rates |
83% CI failure to overlap for LD99 |
| 1.25 |
0.066 |
0.049 |
0.066 |
0.066 |
0.069 |
0.064 |
| 1.50 |
0.076 |
0.062 |
0.136 |
0.130 |
0.166 |
0.156 |
| 1.75 |
0.095 |
0.086 |
0.191 |
0.179 |
0.246 |
0.222 |
| 2.00 |
0.091 |
0.085 |
0.273 |
0.226 |
0.366 |
0.294 |
| 2.25 |
0.118 |
0.101 |
0.341 |
0.274 |
0.442 |
0.348 |
| 2.50 |
0.144 |
0.131 |
0.410 |
0.337 |
0.533 |
0.407 |
| 2.75 |
0.171 |
0.162 |
0.480 |
0.370 |
0.603 |
0.451 |
| 3.00 |
0.197 |
0.184 |
0.531 |
0.391 |
0.664 |
0.463 |
| 3.25 |
0.221 |
0.211 |
0.571 |
0.424 |
0.720 |
0.509 |
| 3.50 |
0.285 |
0.276 |
0.621 |
0.461 |
0.757 |
0.545 |
| 3.75 |
0.314 |
0.308 |
0.697 |
0.525 |
0.813 |
0.606 |
| 4.00 |
0.322 |
0.308 |
0.683 |
0.510 |
0.810 |
0.579 |
| 4.25 |
0.372 |
0.352 |
0.715 |
0.551 |
0.836 |
0.608 |
| 4.50 |
0.380 |
0.369 |
0.742 |
0.531 |
0.863 |
0.586 |
| 4.75 |
0.415 |
0.399 |
0.775 |
0.579 |
0.897 |
0.636 |
| 5.00 |
0.455 |
0.439 |
0.807 |
0.610 |
0.902 |
0.660 |
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These are the results of 1,000 pairs of simulated data sets. An adjustment of  = 0.17 was used in the fiducial limit procedure. Error rates of 0.05 were used for the ratio test. Ratio column refers to the ratio of one probit regression slope to the other probit regression slope. The intercepts of the two regressions are held constant. Large slope ratios reflect large differences in LDs.
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