| A problem encountered in both the biological and psychological sciences is the determination of the tolerance in bioassays or the threshold in psychophysical studies of certain entities for chemical, physical, or sensory stimuli. Researchers in both areas assume that Probit analysis is the appropriate technique for their experimental data. Data are generally analyzed using various computer programs, e.g. SAS, which provide maximum likelihood point estimates. This technique often obtains extremely wide interval estimates as well as being unable to calculate interval estimates under certain conditions. Three new techniques to address this problem were explored: (1) a data smoothing technique (PB), (2) one in which the maximum likelihood estimate is retained (Image), and (3) one generated by selecting the shortest interval from the SAS and the Image intervals (MLC). Simulations were done to examine the properties of the interval estimates using these three techniques and to investigate the use of MLC intervals for hypothesis testing.;Another area of concern to researchers are the properties of threshold estimates obtained from the maximum likelihood method. The properties of the point estimates were examined through the simulation studies.;From the results of the large sample designs drawn from a normal distribution it seems the MLC technique for setting confidence intervals about a threshold value provides a practical solution to the problem of always being able to report a confidence interval with a threshold estimate. It was also determined the MLC confidence intervals can be used as a method of testing one or two sample hypotheses. There was empirical evidence that for some of these deigns the maximum likelihood threshold estimates were biased. However, upon investigation of these designs it was concluded that the bias was a result of including threshold estimates derived through extrapolation or that the magnitude of the bias was so small it was clinically insignificant. |
