Comparison Of Various Probit Methods For Analyzing Yes/No Data On A Log Scale

摘要

A study of the various probit methods to analyze biological data was undertakento understand the various methods and to determine the requirements for the input data as to distribution, number, and tightness of data for the desired results. Calculations were run for many data sets, and results were compared. Graphical analysis and the Karber method were used along with the SAS Probit Procedure and EZ-Probit. All four methods provided very close agreement on most data sets, and the EZ-Probit program provided almost identical information to the SAS Probit Procedure. Real biological data sets were used for comparison purposes, and three other data sets were made up to simulate real data (with variations in the number and distribution of data points). Fiducial limits at the 95% confidence level were also calculated and compared. For those data sets which had no fiducial limits with SAS Probit at the 95% confidence interval, 85% confidence levels were calculated with the EZ-Probit method because it is not possible to adjust the confidence levels with SAS Probit. Different data sets were run in an attempt to minimize the amount of additional data points needed for an existing data set to tighten the fiducial limits and to show the correlation with a chi square distribution. Finally, it will be shown that the probability distributions from 0.01 to 0.99 are identical out to four decimal places for the SAS Probit and EZ-Probit and that there are only minor differences in the fiducial limits between the two methods for some data sets. Appendix A contains the program required to run the SAS Probit on a PC computer. The EZ-Probit method is included in Appendix B.