Designed experiments for ANOVA studies are ubiquitous across all areas of scientific endeavor. An important decision facing experimenter is that of the experiment run size. Often the run size is chosen to meet a desired level of statistical power. The conventional approach in doing so uses the lower bound on statistical power for a given experiment design. However, this minimum power specification is conservative and frequently calls for larger experiments than needed in many settings. At the very least, it does not give the experimenter the entire picture of power across competing arrangements of the factor effects. In this paper, we propose to view the unknown effects as random variables, thereby inducing a distribution on statistical power for an experimental design. The power distribution can then be used as a new way to assess experimental designs. It turns out that using the proposed expected power criterion often recommends smaller, less costly, experimental designs.

Keywords

Statistical minimum power specification Power distribution ANOVA

This is a preview of subscription content, log in to check access.

Cohen J (1988) Statistical power analysis for the behavior science. Lawrence Erlbaum Associates, New YorkGoogle Scholar

2.

Dean A, Voss D, Draguljić D et al (1999) Design and analysis of experiments, vol 1. Springer, New YorkCrossRefGoogle Scholar

3.

Fairweather PG (1991) Statistical power and design requirements for environmental monitoring. Mar Freshw Res 42(5):555–567CrossRefGoogle Scholar

4.

Gerrodette T (1987) A power analysis for detecting trends. Ecology 68(5):1364–1372CrossRefGoogle Scholar

5.

Kullback S, Rosenblatt HM (1957) On the analysis of multiple regression in \(k\) categories. Biometrika 44(1/2):67–83MathSciNetCrossRefGoogle Scholar

6.

Wendelberger JR, Moore LM, Hamada MS (2009) Making tradeoffs in designing scientific experiments: a case study with multi-level factors. Qual Eng 21(2):143–155CrossRefGoogle Scholar

7.

Wu CF, Hamada MS (2011) Experiments: planning, analysis, and optimization, vol 552. Wiley, New YorkzbMATHGoogle Scholar