IGN SECTION 1.4 OVERVIEW OF TYPES OF EXPERIMENTAL DESIGNS 17

a ne ni, — —<——<—

olegv The three subscripts designate a particular block, weight category,
vides and treatment level, in that order. The three treatment levels c, are randomly
jance. assigned to the nine cells with the restriction that each treatment level must
mized occur in any row and any column only once. In order to achieve this
jable balance, a Latin sguare design must have the same number of rows, col-
power umns, and treatment levels. Conseguently, only 9 animals can be used in
use of the design shown in Table |.4-4 instead of the 15 animals used in the two
mental designs described previously.
pbtain- The linear model for this design is

Xi 5 uto t bj Vet čije

An individual score is egual to the grand mean ,, plus a block effect 4,,
plus a column effect $,, plus a treatment eflect ;,, plus an error effect
£ijx. ME the block and column effects, x, and ,, in a Latin sguare design

obtain are appreciably greater than zero, the design may be more powerful than
of the either a completely randomized or a randomized block design. This is
a Latin % apparent if the error effect is examined by means of the procedure used
sguare. for the two designs described previously. The error effect for a Latin sguare
on the design is egual to
k in the a 6 n a
because bije 5 Kia o tu- bj-u-R
mption,
el INCOMPLETE BLOCK DESIGN
itter to . NE . š
heaviest An incomplete block design 1s particularly applicable to research
teristics situations in which the number of subjects available for each block is
less than the number of treatment levels. If, for example, only 2 albino
rats from each litter are available, and the experimenter wants to use three
treatment levels, an incomplete block design is reguired. This design is
shown in Table 1.4-5. n
TABLE 1.4-5 Incomplete Block Design
means Treatment Levels
Ki. Block means
Block (litter)
X;- Block (litter)
X.. Block (litter)

Treatment means — X., X., X., Grand mean < X..

The linear model for this design is
XjesutB; tm; t čij.

It should be noted that each block contains the same number of
subjects, each treatment level occurs the same number of times, and