## Completely randomised design

In this section we examine statistical designs that are often used with experiments. The design is described, together with the kind of information it can provide.

Treatments are assigned to test units on a random basis and an analysis is then performed to determine whether the treatments caused a significant difference in the test units. The design can only really measure one type of variance - that occurring between treatments, known as the 'treatment effect'.

### EXAMPLE

A motorist DIY chain is selling antifreeze in all of its outlets, but it doesn't know the most effective price to charge (see Table 9.1). It tests three different prices per can - £3.89, £4.85, and £5.89 - and records the sales from each. It randomly assigns these prices to nine experimental stores, three using each price.

 Week Price £3.89 Price £4.85 Price £5.89 1 19 9 15 2 16 13 20 3 22 20 9 4 24 18 12 Total 81 60 56

The analysis would examine the average amount of the product sold at each price. It could disclose whether the difference in sales at the lower price was a significant one or whether it was caused by chance.

It fails, however, to take into consideration the influence of such extraneous factors as weather, size of store or competitors' prices. This design assumes that the extraneous variables have had an equal impact on all the test units, which is also a shortcoming of the basic design. Such an assumption might be acceptable in a laboratory experiment where the researcher controls most of the conditions, but it is an unjustified assumption to make for experiments conducted in a real-world environment. This design is not widely used for field experiments.

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