Missing values in replicated Latin squares

Designs based on any number of replicated Latin squares are examined for their robustness against the loss of up to three observations randomly scattered throughout the design. The information matrix for the treatment effects is used to evaluate the average variances of the treatment differences for each design in terms of the number of missing values and the size of the design. The resulting average variances are used to assess the overall robustness of the designs. In general, there are 16 different situations for the case of three missing values when there are at least three Latin square replicates in the design. Algebraic expressions may be determined for all possible configurations, but here the best and worst cases are given in detail. Numerical illustrations are provided for the average variances, relative efficiencies, minimum and maximum variances and the frequency counts, showing the effects of the missing values for a range of design sizes and levels of replication.