## Latin square design

This design enables the researcher to isolate the impact of two major extraneous sources as well as measuring the impact of the treatment. It is a complex design and can cost time and money. The additional efficiency it provides must be weighed against the extra costs and the greater expertise needed by the user. It assumes there is no interaction between the factors being measured.

Again expanding on the antifreeze example, this shows how the Latin square design can be used to control for the impact of store size and the type of store selling the antifreeze (Table 9.3).

 Size of outlet (weekly sales) Type of store <£5000 £5000-£10,000 > £10,000 Supermarket Price 2 Price 3 Price 1 Convenience store Price 1 Price 2 Price 3 Drugstore Price 3 Price 1 Price 2

In using the Latin square design the number of extraneous variables to be controlled must equal the number of treatments. Thus, in our example, three levels of store size are needed and three different types of store will be involved. The rows and columns of the resulting matrix contain the extraneous variables. The treatment (different prices) is assigned so that each price level occurs only once in each row and column.

Latin square designs are particularly useful in experiments where it is important to establish controls for the effect of store size, the type of store or the time period. The main limitations of the design are:

• It requires equal numbers of rows, columns and treatment levels. This can pose problems when four or five treatments are involved.

• Regardless of the number of treatments, it can still only control two extraneous variables.

• It assumes that the extraneous variables do not interact with one another or even with the treatment: a questionable assumption in many marketing experiments.

 Experiment period 20/6-3/7 4/7-17/7 18/7-31/7 Treatment Sales Treatment Sales Treatment Sales First replication Store 1 Store 2 Store 3 A 765 B 488 C 410 B 330 C 307 A 258 C 813 A 579 B 301 Second replication Store 1 Store 2 Store 3 A 724 C 411 B 308 B 366 A 478 C 271 C 633 B 366 A 588 Third replication Store 1 Store 2 Store 3 A 562 B 381 C 322 B 308 C 478 A 412 C 166 A 233 B 65

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