Title: Optimal experimental designs for hypothesis testing with multiple factors: maximising power for the biological sciences

Authors: Colin M. Lynch; Douglas C. Montgomery

Addresses: School of Life Science, Arizona State University, Tempe, AZ, 85287, USA ' School of Computing and Augmented Intelligence, Arizona State University, Tempe, AZ, 85287, USA

Abstract: Biologists are facing mounting pressure to perform more complicated experiments with smaller budgets, but the main tool they use to design these experiments - power analyses - are often only calculated for a single factor. When an experiment includes multiple factors, then the spread of points among those factors influences power. Research into the design of experiments has uncovered many useful designs, but because they are not usually described in terms of power, they tend to be ignored by biologists. Here, we show the utility of these designs by calculating their power in two different experimental contexts. We find that various screening experiments provide comparable levels of power; however, they do so for differing numbers of factors. Definitive screening designs maintain high power levels for the largest number of factors. We also find that A-efficient designs (especially central composite designs) maximise power for experiments which characterise a nonlinear response surface.

Keywords: power; experimental designs; hypothesis testing; classical designs; screening experiments; sample size.

DOI: 10.1504/IJEDPO.2024.140455

International Journal of Experimental Design and Process Optimisation, 2024 Vol.7 No.2, pp.105 - 114

Received: 16 Mar 2023
Accepted: 28 Sep 2023
Published online: 19 Aug 2024 *

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