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172 EXPERIMENTAL DESIGNS

all three residential areas, and the general effect of a 5-cent reduction on those
in the suburbs alone will also be known by seeing the effects in the first cell. If
the highest average daily number of increased passengers is 75 for a 7-cent
decrease for the crowded urban area route, followed by an increase of 30 for the
retirees’ areas for the 10-cent decrease, and an increase of 5 passengers for a 5-
cent reduction for the suburbs, the bus company manager can work out a cost-
benefit analysis and decide on the course of action to be taken. Thus, the
randomized block design is a more powerful technique, providing more infor-
mation for decision making. However, the cost of this experimental design will
be higher.

LATIN SQUARE DESIGN

Whereas the randomized block design helps the experimenter to minimize the
effects of one nuisance variable (variation among the rows) in evaluating the
treatment effects, the Latin square design is very useful when two nuisance
blocking factors (i.e., variations across both the rows and the columns) are to
be controlled. Each treatment appears an equal number of times in any one
ordinal position in each row. For instance, in studying the effects of bus fare
reduction on passengers, two nuisance factors could be (1) the day of the week:
(a) midweek (Tuesday through Thursday), (b) weekend, (c) Monday and Fri-
day, and (2) the (three) residential localities of the passengers. A three by three
Latin square design can be created in this case, to which will be randomly
assigned the three treatments (5, 7, and 10 cent fare reduction), such that each
treatment occurs only once in each row and column intersection. The Latin
square design would look as in Figure 7.10. After the experiment is carried out
and the net increase in passengers under each treatment calculated, the average
treatment effects can be gauged. The price reduction that offers the best advan-
tage can also be assessed.
A problem with the Latin square design is that it presupposes the absence of
interaction between the treatments and blocking factors, which may not always
be the case. We also need as many cells as there are treatments. Furthermore, it
is an uneconomical design compared to some others.

Figure 7.10
Illustration of the Latin square design.

Day of the Week
Residential Area Midweek Weekend Monday/Friday

Suburbs X 1 X 2 X 3
Urban X 2 X 3 X 1
Retirement X 3 X 1 X 2