Design keys, pseudo-factors and general balance

Abstract

Design keys provide an effective way of defining various types of generallybalanced design. This is an important class which coversvirtually all the traditional experimental designs and, inparticular, those with more than one error term (or stratum). They are efficient to analyse and the results arestraightforward to interpret. We describe algorithms that can beused to determine the structure of a design (that is the stratawhere each set of treatment contrasts is estimated and thecorresponding efficiency factors) from the design keys used togenerate the design, and to define the pseudo-factors that maybe necessary to produce the analysis.