ABSTRACT
There are both good and bad Latin square designs from the point of view of the estimation of carryover effects. The good designs fall into a class named “digram-balanced” squares by W. Wagenaar, which have the property that each treatment is preceded and followed equally often by each other treatment. Extra-period cross-over designs have been known for some time, and construction of these designs simply involves repeating the treatments given to each subject in the last period for one extra period. The Latin squares designs are referred to as digram-balanced, and are the most efficient Latin squares designs available for separating treatment from carryover effects. Experimenters may also be interested in whether there are differences among periods, or even whether there are differences among sequences. In the presence of significant carryover effects, there is, in general, no way to test whether periods are significant.
