## Abstract

. A single—stage procedure is proposed for selecting the event which has the largest probability in multi—factor multinomial experiments with multiplicativity, i.e., experiments in which the factor—level responses of any one factor are independent of those of all other factors. The procedure is a generalization of one proposed for single—factor multinomial experiments by Bechhofer, Elmaghraby and Morse (B— E—M) (1959). Tables necessary to implement the procedure are provided, and properties of the procedure are obtained. It is shown that if independence holds it is much more efficient in terms of minimizing total sample size to conduct the experiment as a factorial experiment rather than as independent single—factor experiments. Specifically, if an f—factor (f > 2) experiment is conducted, and certain symmetry conditions hold, the factorial experiment requires 1/f as many observations to guarantee the same indifference—zone probability requirement, as do f independent single-factor experiments. If multiplicability does not hold the experimenter can use the original B-E-M single-stage, single-factor procedure but for a different goal and probability requirement than the one employed for the 2-factor problem.

Original language | English |
---|---|

Pages (from-to) | 31-61 |

Number of pages | 31 |

Journal | Communications in Statistics - Simulation and Computation |

Volume | 18 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 1989 |

### Bibliographical note

Funding Information:This research was partially supported by the U.S. Army Research Office through the iviathematicai Sciences Institute of Cornell University and by U.S. Army Research Office Contract DAAL03-86-Ic-0046 at Cornell University. The writers are indebted to Professor Santner for his constructive comnents. We also wish to thank Ms. Katliy King for her expertise in typing this manuscript.

Copyright:

Copyright 2015 Elsevier B.V., All rights reserved.

## Keywords

- market research sampling
- multinomial selection problem
- multiplicative probability matrix
- ranking procedures
- selection procedures
- single—stage procedures

## ASJC Scopus subject areas

- Statistics and Probability
- Modelling and Simulation