A Link Between the E-Value and the Robustness of Block Designs

ABSTRACT

This article investigates the robustness of binary incomplete block designs against giving rise to a disconnected design in the event of observation loss. A link is established between the E-value of a planned design and the extent of observation loss that can be experienced while still guaranteeing an eventual design from which all treatment contrasts can be estimated. Patterns of missing observations covered include loss of entire blocks and loss of individual observations. Simple bounds are provided enabling practitioners to easily assess the robustness of a planned design.

KEYWORDS:

• Breakdown number
• Connectivity
• Eigenvalue
• Information matrix

Acknowledgments

The author is grateful to suggestions from two referees and an associate editor which have improved the clarity and final presentation of the article.