Latin square Designs

In experiments where the animal/person/experimental unit remains on the treatment from the start of the experiment until the end we can call this a continuous trial. Completely Randomised Design (One-Way ANOVA), Two-Way ANOVA (Randomised Complete Block Designs) and Factorial Models are all examples of continuous trials. In a Latin square, however, each animal will receive each treatment during the course of the experiment.

In a continuous trial, particularly with animals, it is common to place animals on a standard diet/treatment, prior to their random allocation to the experimental treatments. For example, one might have a standardisation period (S.P.) prior to the experiment; this might be the preceeding lactation if one was carrying out a whole (complete) lactation study with dairy cattle, or it might be the weight gain in the month preceeding the start of the trial in a feeding trial. We take account of, or exploit, the high repeatability of lactation milk yield from one lactation to another, or the relatively high corrrelation between successive weights on a growth trial; all these with the objective of reducing the experimental error, by covariance adjustment for the measures taken during the standardisation period. Since, in the Latin square design, two or more treatments are contrasted on the same experimental unit (e.g. animal, cow) the between-experimental unit (between cow) variation does not enter into the experimental error. Thus, the covariance feature is not needed, and the standardisation period (S.P.) plays a minor role, if any. However, in view of the value of standardising experimental conditions it would seem eminently desirable to routinely employ a short standardisation period, although such data will not (and cannot) be used in the analysis. The basic cross-over design and analysis presented here assumes that there are no carry-over effects, or equivalently, that they are removed by any 'wash-out' period between the treatment periods, or that the length of time on the treatments is sufficient to remove such residual effects. For a more advanced consideration of cross-over designs (which include this simple two-factor crossover as well as Latin squares) where carry-over effects may be present see Ratkowsky et al; Cross-over experiments, Design, Analysis and Application.

R.I. Cue ©
Department of Animal Science,McGill University
last updated : 2010 May 1