OVERVIEW OF TYPES OF EXPERIMENTAL DESIGNS 19

DESIGN SECTION 1.4
že
2 pair of If we let r;; stand for all treatment effects, the error effect can be written
mer of š š m
ii plete Emtij) — Xiim — ui — Be
e pair of In this form the similarity between the error effect for this design and
do other the error effect for a completely randomized design is apparent. This latter

error effect was given earlier as

čij — Xjj — B; -b.

The similarity between the models for a completely randomized design and

ivate the a completely randomized factorial design is not surprising in view of
sa the fact that the former design is the building block for the latter design.
nt. This is h . KN
The error effect for a randomized block factorial design Is

level from
The most bim — Xijm — di — B,- ft, - bi; a.
ndomized
> by using TABLE 1.4-6 Completely Randomized Factorial Design
| also the i
sume that Radiation Levels
la, < 65?,
000 micro- Temperature Levels A treatment means
ently used
6 the three
level, and
designate a
order.
e 1.4-6 it is
x treatment
gn example B treatment means — X.,. Kea: X... Grand mean — X...
e randomly
> completely .
ctively,

TABLE 1.4-7 Randomized Block Factorial Design

Temperature Levels a, a, a, a,

Radiation Levels b, b, b, b,' ob, b, Block mean

ji interaction
ce, and litter
iation dosage
1 temperature
that radiation
ture than ata
t is called an

Block (liter) p,
Block (litter) p,
Block (litter) pz

Xi Žu. Xu Xu Xn.  Xas: Grand mean < X...

A, treatment mean < (X,,, £ Xji2 bt Xias t Ami t ee td X,z3/9 z X-
s 4 X,za/9 < X,..

Column means

A, treatment mean <(X,,, t Xzya bt Xaas bt Kam t
B, treatment mean < (X,,, t Xiiz bt Xust Xy £ Mana bt Xaia/6 z X.,.
B, treatment mean < (X,3, £ Xi22 bt Xias t Xau £ Xaaz bt Xa23/6 < X.,.
B, treatment mean < (X,3, t Xis2 t X jaz £ Xani t Xma t Xa33/6 — X..

design, using