Three-Decision Procedures With the Best Control Under Heteroscedasticity

SYNOPTIC ABSTRACT

A design-oriented, two-stage multiple three-decision procedure is proposed to classify a set of test treatments that are better than the best control and that are worse than the best control under heteroscedasticity. A modification of this procedure using a one-stage data analysis technique is also discussed when additional samples for the second stage are not available. The statistical tables of percentage points and the power-related design constants to implement the proposed procedures are given. Both the two-stage and one-stage procedures control Type-III error rate at a prespecified level α. Implementation of both the procedures is demonstrated through a numerical example based on real-life data.

KEY WORDS AND PHRASES:

• Three-decision procedure
• Type III error
• numerical integration
• power of three-decision procedure

Acknowledgments

The authors are thankful to the referees for their suggestions and improvements.