Guido Giani, Klaus Straßburger, and Helmut Finner (Deutsches Diabetes-Forschungsinstitut an der Heinrich-Heine-Universität Düsseldorf, Germany)

Separate - A Program Package for Multiple Comparisons

Separate is a menu-driven software package devoted to designing and analysing experiments for multiple comparisons with the "best" and with a control. In addition, support is given in certain problems of testing for equivalence and for difference. For normally distributed data three designs, the one-way layout, the randomized bock design, and the crossover design without carry-over effects, are supported by the program. For each of the two options of determining sample sizes (option I) and calculating probability levels of correct decisions being achieved with given sample sizes (option II), the experimenter has to specify threshold values to characterize treatments as good, bad, or equivalent to the control. To cover the unknown variance case, the treatment qualities good, bad, or equivalent are defined in terms of standardized mean differences from the best or the control. Besides the classical indifference zone approach of Bechhofer (1954), the subset selection formulation of Gupta (1956) supplemented by additional power requirements, and further related approaches, the problem of discriminating between good and bad treatments and, if intended, those being equivalent to the control is dealt with. Option I facilitates simultaneous as well as seperated control of all the kinds of multiple errors at designated levels, whereas under option II the respective minimum multiple error probabilities being achieved for given sample sizes are numerically calculated (Giani and Straßburger 1997, 2000). For most of the implemented decision rules the program also gives the least favorable parameter configuration at which the minimum probability of correct selection or correct discrimination is attained. For the discrimination problems this configuration is the solution of a complex optimization task and depends in general on the parameters of the underlying procedure and all the specifications made in advance. Finally, it should be mentioned that also single-step and step-down procedures are implemented for various subset selection objectives. Besides this, the software offers facilities to handle the described discrimination problems under distribution models with scale parameter. At the present, for the one-way layout procedures for discriminating with respect to variances under the normal model and with respect to incidences in exponentially distributed data are available.

- References:Bechhofer, R.E. (1954): A Single-Sample Multiple Decision Procedure for Ranking Means of Normal Populations With Known Variances. Annals of Mathematical Statistics 25, 16-39.
- Gupta, S.S. (1965): On Some Multiple Decision (Selection and Ranking) Rules. Technometrics 7, 225-245.
- Giani, G., Straßburger, K. (1997): Optimum Partition Procedures for Separating Good and Bad Treatments. Journal of the American Statistical Association 92, 291-298.

Giani, G., Straßburger, K. (2000): Multiple Comparison Procedures for Optimally Discriminating Between Good, Equivalent, and Bad Treatments With Respect to a Control. Journal of Statistical Planning and Inference 83, 413-440.