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Experimental data are often highly structured due to the use of experimental designs. This does not only simplify the analysis, but it allows for tailored methods of analysis that extract more information from the data than generic methods. One group of three-level experimental designs that are suitable for such tailored methods are orthogonal minimally aliased response surface (OMARS) designs (Núñez Ares and Goos 2020), where all main effects are orthogonal to each other and to all second-order effects. The design based analysis method of Jones and Nachtsheim (2017) has shown significant improvement over existing methods in terms of powers to detect active effects. However, the application of their method is limited to only a small subgroup of OMARS designs known as definitive screening designs (DSDs). In our work, we not only improve upon the Jones and Nachtsheim method for DSDs, but we also generalize their analysis framework to the entire family of OMARS designs. Using extensive simulations, we show that our customized method for analyzing data from OMARS designs is highly effective in identifying active effects when compared to other modern (non-design based) analysis methods, especially in cases where the true model is complex and involves many second-order effects. [ABSTRACT FROM AUTHOR]

In this paper, we present an interactive teaching approach to introduce the concept of optimal design of experiments to students. Our approach is based on the use of spreadsheets. One advantage of this approach is that no complex mathematical theory is needed nor that any design construction algorithm has to be discussed at the introductory stage. Another benefit is that the students build all necessary matrices for concrete examples starting from a sensible initial design. By modifying the initial design by trial and error, they can try to improve the properties of the parameter estimators interactively. For problems in which finding the optimal design is not evident, they can use optimization software which is readily available in the spreadsheet software. (Contains 5 figures.)