COUNTERBALANCING AND OTHER USES OF REPEATED-MEASURES LATIN-SQUARE DESIGNS - ANALYSES AND INTERPRETATIONS

Many investigators use repeated-measures Latin-square designs to count erbalance treatments across a procedural variable such as temporal or spatial position or to reduce the number of treatment combinations giv en to each research participant. Effects of the counterbalancing shoul d be analyzed statistically unless the investigator can argue persuasi vely that the analysis would be uninformative. Less often, investigato rs use these designs to create treatments; in this kind of use, effect s 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 Subgr oup, or of Treatment-combination, but it is also interpretable as the interaction between the two variables in the Latin square (Treatment v ariable x Procedural variable or Treatment variable A x Treatment vari able B). Neither interpretation is inherently preferable; therefore, i nvestigators should consider both and select and report the one that t urns out to have a more convincing rationale, which will be external t o the design per se. (C) 1997 Academic Press