The Latin square Design is more effective than the randomized  block design. Here, there researcher isolates two major variations causing extraneous variables inedited to determent influence. The design assumes that there is no interaction between the factors being measured. 

This design requires an expert experimenter to effectively conduct the experiment. It is a complex design as compared to pervious ones because it requires more effort. cost, and time. So the additional effectiveness accrued by this design must be weight against the cost and time required to conduct it.

Expanding our previous example of sale of soap packets. Here we add store chains X, Y and Z along with the variable store size this design the number of extraneous variables to be controlled must be equal in number to the number of treatments (three in our example). Thus, there levels of store sizes are needed, and stores form three different chains will eb involved. The rows and columns of the resulting matrix contain the extraneous variables. The treatment (different prices) are assigned so that each price level occurs only once in each row and column. This is exhibited.

Latin Square Design

Chain	Above Rs. 1.000	Rs. 6.00 to 1,000	Below Rs. 600
X	Price 2	Price 3	Price 1
Y	Price 1	Price 2	Price 3
Z	Price 3	Price 1	Price 2

Latin Square Designs are particularly useful in retail studies where it is particularly important to establish control for the effect of store size, type of store (supermarket vs. general store or time period.

This design has shortcomings such as: (i) It recognizes equal number of rows, columns, and treatment levels, this can pose a problem when form r five treatments are involved, (ii) regardless of the number of treatments, it still can only control two extraneous variables, (iii) it assumes that extraneous variables do not interact with each other or even with the treatment. This is a questionable assumption in many marketing experiments. Thus, the Latin Square Design is also having its merits and demerits like any other design.

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