Latin Squares Design:
This design suggests that test will form a square because there will be as many test units as treatments. This design is used to control important extraneous influence. It is assumed that each treatment occurs once with each store on a block. There are several stores in a block. There must be as many blocks as there are treatments. It may be three four and so on. Three blocks three treatment four blocks four treatments and so on. This is the reason why it is called a square design.
Thus the price treatment will reveal the impact of price at different times stores: consequently one can conclude the price effect on sales. There are some special feature of this design (i) each treatment is applied once in each store of a block(ii) each store is tested once in each time and (iii) the order of testing runs both ways i .e 1 to 2 and 2 to 1 during an equal number of times. Thus the extraneous factors impacts affecting them are minimized. The varying store characteristics and sequence in which the treatments appear are concealed.
The design measures the error resulting from two non interacting variable i, ,e the different in test stores and the difference in time on the results as the effect of the treatment on the results. The statistical interpretation is a complex one because a treatment is observed in case of several stores at several points of time. The variances of vertical effects the variances of horizontal effects and the variances of treatment have to be calculated. These can be analyzed by adopting several methods.
The sum of the vertical column may be used to determine the vertical dimension or the column effect similarly the sum of horizontal column may be assess the horizontal dimension or row effect. The treatments total effect can be determined by analyzing the impact of the treatment on the sale. A degree of freedom may be applied to correct the row column and treatment effects.