The Use and Analysis of Staggered Nested Factorial Designs

Often the experimental designs used for accumulating data to estimate variance components are nested or hierarchical. The classical nested design calls for balanced replication at each level of the hierarchy, thus distributing the degrees of freedom unequally so that the factor at the top of the hierarchy has relatively few degrees of freedom. A partially replicated, unbalanced nested design, called a staggered nested design, alleviates this problem. More evenly distributed information in the staggered design usually results overall in an experiment smaller than the classical nested design. This idea is extended to the case where some factors have a factorial relationship and others are nested within the factorial combinations or in levels of other factors. Theory for factorial designs is combined with theory of staggered nested designs to develop sums of squares and expected mean squares for three specific staggered nested factorial designs. An example is also given.