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INTRODUCTION TO BASIC CONCEPTS IN EXPERIMENTAL DESIGN

If treatment effects are designated by r;;, the error effect can be written

bim — Xijm — tij — fm — be
It,is interesting to note the similarity between this error effect and the
error effect for a randomized block design, which is the building block
for this factorial design. The error effect for the randomized block design

was given earlier as

eye Xj;-Bj-t-R.

OUESTIONS TO CONSIDER IN SELECTING
AN APPROPRIATE DESIGN

Statisticians have provided an experimenter with a vast array of
experimental designs. On what basis should an experimenter decide which
design to use? Selection of the best experimental design for a particular
research problem reguires (l) a knowledge of the research area and (2)
a knowledge of different experimental designs. To arrive at the best experi-
mental design, an experimenter must consider the following guestions:

|. What kinds of data are reguired to test the statistical hypotheses?

(a) How many treatment levels should be used?

(b) Should the treatment levels used in the experiment be selected on an
a priori basis or by random sampling from a population of treatment
levels?

(c) Should a factorial experiment be used so that interaction efiects may

o be evaluated?

(d) Are all treatments and treatment levels of egual interesi to the

- experimenter? Experimental designs may be used that sacrifice

power in evaluating some treatments in order to gain power in
evaluating other treatments.

2. Is the proposed sample of subjects large enough to provide adeguate
precision in testing the statistical hypotheses?
(a) Do the available subjects represent a random sample from the popula-
tion of interest to the experimenter?
(b) Can the subjects be stratified into homogeneous blocks?
(c) Does the nature of the experiment permit each subject to be observed
under more than one treatment level"?
(d) Will the treatment(s) produce physical or psychological injury to the
subjects? The use of potentially injurious treatments precludes the

employment of human subjects.

3. Is the power of the proposed experimental design adeguate to test the
statistical hypotheses?
(a) What is the size of treatment effects that the experimenter considers

to be of practical interest?
(b) What are the conseguences of committing type | and type II errors?

4. Does the proposed experimental design provide maximum efficiency in
testing the statistical hypotheses?
(a) Would efficiency be improved more by using a design employing
blocks of homogeneous subjects or by using random assignment ofa
large number of subjects to the treatment levels?