Blocks Latin Square

The randomized Blocks Latin square design is superior to the Latin square in many ways. The randomized block design is available for a very wide range of treatments (2 to 24) and there is no limitation on the number of replications. The analysis of variance is also very flexible. If there is an attack of some disease or pest in one or two of the blocks, the data for these blocks can be easily omitted without any complication in the analysis, while the results from a Latin square experiment require a much more complicated analysis under similar circumstance, in the field also the randomized block trial is easier to manage. It can be equally accommodated in a rectangular or square field or a field of any other shape. While in a Latin square trial, it is necessary that the shape of the feels terms or fertility variations in two directions at right angles (or heat amounts to diagonal trending fertility). The Latin square design is likely to be more efficient.

The Latin square arrangement is desirable only in the special cases, where the land exhibits market trends in fertility. The design, as it requires many replications as there are treatments, is suitable for 5 to 10 treatments. In comparison of small number of treatments, the number of replications is found to be inadequate while for a larger number of treatments, the number has to be unduly increased. For the small number of treatments, however, more than one Latin square may be laid out to secure an adequate replication.

Latin cubes

The basic idea of a Latin square can be extended to patterns in three dimensions or more. But practical applications of Latin cubes and related designs are very few.

Factorial experiment

In an Endeavour to improve the logical foundations of a scientific experimentation, the factorial design has proved one of the most fruitful developments. The Factorial experiments allow the experimenters to evaluate the combined effect of two or more experimental variables when used simultaneously. The information obtained from factorial experiments is more complete then they obtained from a series of single factor experiments, in the series that factorial experiments allow the evaluation of interaction effects. The interaction effect is an effect attributed to the combination of variables above and beyond these which can be predicted from the variable considered singly. For e.g., the factors affecting the growth and yield of a crop-manufacturing, seed rate, dates at which various operations are performed, methods of cultivation, and so on and the effect of any one may be dependent upon the conditions in respect of others. The Conclusions from an experiment to determine the optimal amount of phosphoric fertilizer to apply to a crop, would become useless if later work showed that the amount of a some other fertilizer, the depth of plough or the variety used in the experiment had been far from the best, unless there were strong reasons for believing that a change in optima; conditions in respect of these factors would not appreciably affect the requirement of phosphate. The three main reasons for involving the levels of various factors in one experiment are:

(i) To obtain the information, on the average effect of all the factored economically. From a single experiment of average size.

(ii) To broaden the basis of interference on one factor by testing it, number varied conditions of others: and

(iii) To assess the manner in which the effects of factors interact one another. These are not independent entirely but the emphasis varies with the subject of experimentation.