SUMMARYFull factorial designs of a significant size are very rarely performed in industry due to the number of trials involved and unavailable time and resources. The data in this paper were obtained from a six-factor full factorial ( 2 6 ) designed experiment that was conducted to determine the optimum operating conditions for a steel milling operation. Fractional-factorial designs 2 623 III (one-eighth) and 2 622 IV (one-fourth, using a fold-over from the one-eighth) are compared with the full 2 6 design. Four of the 2 623 III are de-aliased by adding four more runs. In addition, two 12-run Plackett-Burman experiments and their combination into a fold-over 24-run experiment are considered.Many of the one-eighth fractional-factorial designs reveal some significant effects, but the size of the estimates varies much due to aliasing. Adding four more runs improves the estimation considerably. The one-quarter fraction designs yield satisfactory results, compared to the full factorial, if the 'correct' parameterization is assumed. The Plackett-Burman experiments, estimating all main effects, always perform worse than the equivalent regular designs (which have fewer runs). When considering a reduced model many of the different designs are more or less identical. The paper provides empirical evidence for managers and engineers that the choice of an experimental design is very important and highlights how designs of a minimal size may not always result in productive findings.

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Many scientists believe that small experiments, guided by scientific intuition, are simpler and more efficient than design of experiments. This belief is strong and persists even in the face of data demonstrating that it is clearly wrong. In this paper, we present two powerful teaching examples illustrating the dangers of small experiments guided by scientific intuition. We describe two, simple, two-dimensional spaces. These two spaces give rise to, and at the same time appear to generate supporting data for, scientific intuitions that are deeply flawed or wholly incorrect. We find these spaces useful in unfreezing scientific thinking and challenging the misplaced confidence in scientific intuition.

Our PCR Simulator is a web-based application designed to introduce concepts of multi-factorial experimental design and support teaching of the polymerase chain reaction. Learners select experimental settings and receive results of their simulated reactions quickly, allowing rapid iteration between data generation and analysis. This enables the student to perform complex iterative experimental design strategies within a short teaching session. Here we provide a short overview of the user interface and underpinning model, and describe our experience using this tool in a teaching environment.