To answer these questions you should go for mean comparison tests. For example, the F test is not able to answer the question of whether every one of the three varieties gave significantly higher yield than that of the check variety or whether there is significant difference among the three varieties. The information in analysis of variance table does not identify the specific pairs or groups of varieties that differed. If there are missing observations in the experiment then the analysis becomes complicated.Despite of its great potential for controlling experimental error this design is not being used widely in agricultural experiments. Due to these restrictions the Latin square design is practically being used in experiments only where the number of treatments is not less than four and not greater than eight.
In agricultural experiments where the land requirement is rigid then the actual layout in the field is laborious and approach to the central plots becomes difficult.On the other hand if the number of treatment is small, the degree of freedom associated with experimental error becomes too small for the error to be reliably estimated.The experiment becomes impractical if the number of treatment is very large because of large number of replications required. The requirement of Latin square design that all treatment appears only once in each row and column block also becomes a major restriction.Latin square design has following restrictions: As in nutrition trials on dairy cattle, only a few cows may be available for financial reasons. Laboratory trials with replication over time, such that the difference among experimental units conducted at the same time and among those conducted over time constitute the two known sources of variability.Greenhouse trials in which the experimental pots are arranged in straight line perpendicular to the glass or screen walls, such that the difference among rows of pots and the distance from the glass wall are expected to be the two major sources of variability among the experimental pots.Insecticide field trials where the insect migration has a predictable direction that is perpendicular to the dominant fertility gradient of the experimental field.Field trials where fertility gradient exists in two directions perpendicular to each other, or has a unidirectional fertility gradient but also has residual effects from previous trials.Latin square design can be used in following conditions:
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