INTRODUCTION TO BASIC CONCEPTS IN EXPERIMENTAL DESIGN

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.. One way of increasing the power of an experimental methodology
mentioned in Section 1.3 is to choose an experimental design that provides
for a more precise estimate of treatment effects and a smaller error variance.
A randomized block design is more powerful than a completely randomized
design if the block effects in the former design account for an appreciable
portion of the total variance. It should be noted that the increased power
of the randomized block design was made possible through the use of
matched subjects. In many research situations, the increased experimental
effort reguired to match subjects may not justify the greater power obtain-
able with a randomized block design.

LATIN SOUARE DESIGN

A Latin sguare design utilizes the blocking principle to obtain
homogeneity with respect to two nuisance variables. The levels of the
two nuisance variables are assigned to the rows and columns of a Latin
sguare. Treatment levels are identified within each cell of the Latin sguare.
In the randomized block design example, subjects were eguated on the
basis of genetic characteristics. It is reasonable to assume that rats in the
same litter are also relatively homogeneous in weight. However, because
the dependent variable in the radiation example is food consumption,
the experimenter might wish to control the extraneous variable of weight.
This can be accomplished by assigning the lightest rat in each litter to
category b,, the rat intermediate in weight to category b,, and the heaviest
rat to category by. Blocking with respect to both genetic characteristics
a, and weight b, is shown in Table 1.4-4.

TABLE 1.4-4 Latin Sguare Design

Weight Categories of Rats

b, b; b,

Lightest Intermediate Heaviest Block means

Block (litter) a,

Block (litter) a,

Block (litter) a;

Weight means — X.. X.,. X..

Grand mean < X...

Treatment level means: c, < (X,,, £ Xazmi t X,zaY3 < K.
ca <(Xnia t Xi t X,32/3 < X..,
cz < (Xu t Mas 4 X,saW3 < X..s