Counterbalancing and other uses of repeated-measures Latin-square designs: Analyses and interpretations

Many investigators use repeated-measures Latin-square designs to counterbalance treatments across a procedural variable such as temporal or spatial position or to reduce the number of treatment combinations given to each research participant. Effects of the counterbalancing should be analyzed statistically unless the investigator can argue persuasively that the analysis would be uninformative. Less often, investigators use these designs to create treatments; in this kind of use, effects of the Latin square (the treatment-combinations) are always analyzed statistically. The designs can also be used in intervention research. In all uses, the between-groups component of the variance associated with the Latin square is usually interpreted as a main effect of Subgroup, or of Treatment-combination, but it is also interpretable as the interaction between the two variables in the Latin square (Treatment variable x Procedural variable or Treatment variable A x Treatment variable B). Neither interpretation is inherently preferable; therefore, investigators should consider both and select and report the one that turns out to have a more convincing rationale, which will be external to the design per se. (C) 1997 Academic Press