Minimal \(2^ n\) connected factorial experiments (Q1071455)

In a \(2^ n\) factorial experiment as the number of factors increases the number of treatment combinations required in a full experiment becomes so large that the experiment may not be feasible. Our primary concern in this paper is to provide all competing designs which lead to the same information relative to the estimability of the main effects in \(2^ n\) factorial experiments with a minimal number of observations when none of the interactions are present in the model. In order to investigate the estimability of main effects in \(2^ n\) factorial experiments, we provide a simple algorithm. At the outset of this algorithm, we are able to provide a selected number of minimally connected designs for \(n\leq 9\). A catalogue of such designs is furnished. We also give a method of generating all minimally connected designs which can easily be programmed for electronic computers.