On repeated measures designs: Hierarchical structures and time trends

Abstract

The basic anatomy of an experimental design is used as an expository introduction to the examination of several repeated measures experiments described in recent pages of this and other journals. This examination reveals problematic issues concerning some common design and analysis features of such experimental designs. In particular, the hierarchical structures and/or presence of time trends is highlighted. These issues are discussed in an attempt to assist researchers to recognize such problems, to avoid the associated difficulties in the future, and to exploit the advantages of sound design with appropriate, efficient and informative analysis. While alternate reanalyses of the data of these experiments might reveal the conclusions to be unaffected by such issues, researchers should still be cautious. In retrospect, such occurrences should be seen as fortuitous, not as justification for inefficient or less informative analyses. More importantly, such reanalyses could reveal more enlightening information, and I argue that if a design permits such information to be discovered, then it behoves researchers to perform such analyses and to make such discoveries.

Keywords:

• Analysis of variance
• coefficient of friction
• experimental design
• factorial design
• mean values
• modelling

Acknowledgement

I acknowledge the willing cooperation of Francois-Xavier Li in supplying SPSS files and answering many of my questions, and of Nathan Johnson in supplying mean value data with commentary. The assistance of reviewers in improving the manuscript is also acknowledged.