Design and analysis of a fractional 413125 split-plot experiment

This paper is a case study on two aspects of constructing mixed factorial experiments: (1) three equally sized fractions of a 2p+ 2 design are combined under a three level factor, yielding a 312p+ 2 experiment; (2) two carefully selected factors from a 2p+ 2 design are combined to obtain a 412p design. We consider both aspects for the design of a 1/8 fraction of a 413125 experiment (48 observations) to investigate a DNA amplification technique. The experiment is of the split-plot type, because the main effects of two factors had to be confounded with runs of a piece of equipment (whole-plots), while the other factors were varied between vials (subplots) contained within the equipment. We confounded an additional effect to avoid the usual difficulty in evaluating the whole-plot effects in unreplicated experiments. Both whole-plot and subplot effects can then be evaluated with half-normal plots. The analysis is illustrated with the results of the experiment.