Identifying effects under a split-plot design structure

Experience shows that in practice very few designs are carried out in a completely randomized fashion, requiring not only that the order of experimentation be random but also that the factor levels in each experiment were reset. The resulting split-plot designs and their properties are well described in the statistical literature but much less so in chemometric journals. In neither of the two, however, can an overview be found of how much is at stake when one decides to leave the safe road of completely randomized designs. This work compares completely randomized designs (CRDs) with designs characterized by different amounts of randomization in terms of type I and type II errors (false positives and false negatives) when using a 2(k) factorial design for screening/identification. It also provides a comparison of the correct statistical analysis based on generalized least squares with the standard ordinary least squares analysis available in most software. Copyright (C) 2005 John Wiley & Sons, Ltd.