SECTION 1.4 OVERVIEW OF TYPES OF EXPERIMENTAL DESIGNS 13

V o o o m z o ——<—

is the completely randomized design. This design can be used to compare
any number of treatment levels. When two treatment levels are used, the
statistical test employed in the analysis is eguivalent to a test by means
of a t ratio for uncorrelated groupS. The general features of the design
can be illdstrated by the microwave radiation example cited earlier. Let
b,, ba, and by stand for treatment levels 0, 20,000, and 40,000 microwatts
of radiation, respectively. Fifteen albino rats are assigned to the threc
treatment levels by means of a table of numbers. Food consumption of
the rats assigned to each treatment level is indicated by X;; where i
designates the ith rat in treatment level j. Table 1.4-2 shows the layout
of a completely randomized design. The average food consumption of
rats in each treatment level is designated by X.;. The dot in the subscript
indicates the variable over which summation has occurred. In this ex-
ample,: treatment means are obtained by summing the scores over the
i < 1 through 5 rats. The average food consumption for all 15 rats is
designated by X.. .

TABLE 1.4-2 Completely Randomized Design

a

Treatment Levels

b, b, b,
a m o
Xu X,2 X,3
Xn X22 X.3
Xi Xza A33

41 Xa X.3
Xsi Xsa Xs3
a

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

Here conclusions concerning the effects of microwave radiation
are restricted to the three treatment levels and to the 15 rats included in
the experiment. Edgington (1966) recently emphasized that random assign-
ment of subjects to treatment levels is essential if an experimenter wishes
to draw statistical inferences concerning treatment eflects from non-
randomly selected subjects." Because of the importance of the principle
of random assignment, an experimenter should always describe his tech-
nigue for assigning subjects to treatment levels.

Associated with every experimental design is a mathematical
model that purports to include all sources of variability affecting individual
scores. To the extent that the model accurately represents these sources
of variability, the experimenter can evaluate the effects of a treatment.
The linear model for a completely randomized design is

"Few experiments in the behavioral sciences are carried out with randomly selected subjects.
When a random sample is used, the population sampled is likely to be so specific as to be of
little interest.