Experimental Design in Statistics
The term experimental design refers to a plan for
assigning experimental units to
conditions. A good experimental design serves three purposes.
- Causation. It allows the experimenter to
make causal inferences about the relationship between
independent variables and a
- Control. It allows the experimenter to
rule out alternative explanations due to the
confounding effects of extraneous variables (i.e.,
variables other than the independent variables).
- Variability. It reduces variability
within treatment conditions, which makes it easier to detect
differences in treatment outcomes.
An Experimental Design Example
Consider the following hypothetical experiment. Acme Medicine
is conducting an experiment to test a
new vaccine, developed to immunize people against the common cold.
To test the vaccine, Acme has 1000 volunteers - 500 men
and 500 women. The participants range in age from 21 to 70.
In this lesson, we describe three experimental designs - a
completely randomized design, a randomized block design, and a
matched pairs design. And we show how each design might be
applied by Acme Medicine to understand the effect of the
vaccine, while ruling out confounding effects of other factors.
Completely Randomized Design
The completely randomized design is probably the
simplest experimental design, in terms of data analysis and
convenience. With this design, participants are randomly assigned
A completely randomized design layout for the Acme Experiment is
shown in the table to the right. In this design, the experimenter
randomly assigned participants to one of two treatment conditions.
They received a
or they received the vaccine. The same number of participants (500) were
assigned to each treatment condition (although this is not required).
The dependent variable is the number of colds reported in each
treatment condition. If the vaccine is effective, participants in
the "vaccine" condition should report significantly fewer colds
than participants in the "placebo" condition.
A completely randomized design relies on
to control for the effects of extraneous variables. The experimenter
assumes that, on averge, extraneous factors will affect treatment
conditions equally; so any significant differences between conditions
can fairly be attributed to the independent variable.
Randomized Block Design
With a randomized block design, the experimenter
divides participants into subgroups called blocks,
such that the variability within blocks is less than the
variability between blocks. Then, participants within each block are
randomly assigned to treatment conditions. Because this design
reduces variability and potential confounding, it produces a better
estimate of treatment effects.
The table to the right shows a randomized block design for the
Acme experiment. Participants are assigned to blocks, based on
gender. Then, within each block, participants are randomly assigned
to treatments. For this design, 250 men get the placebo, 250 men
get the vaccine, 250 women get the placebo, and 250 women
get the vaccine.
It is known that men and women are physiologically different
and react differently to medication. This design ensures that
each treatment condition has an equal proportion of men and women.
As a result, differences between treatment conditions cannot
be attributed to gender. This randomized block design removes
gender as a potential source of variability and as a
potential confounding variable.
In this Acme example, the randomized block design is an improvement
over the completely randomized design. Both designs use randomization
to implicitly guard against confounding. But only the randomized
block design explicitly controls for gender.
Note 1: In some blocking designs, individual participants may receive
multiple treatments. This is called using the participant
as his own control. Using the participant as his own control
is desirable in some experiments (e.g., research on learning or
fatigue). But it can also be a problem (e.g., medical studies where
the medicine used in one treatment might interact with the medicine
used in another treatment).
Note 2: Blocks perform a similar function in experimental design as
perform in sampling. Both divide observations into
subgroups. However, they are not the same. Blocking is
associated with experimental design, and stratification is
associated with survey sampling.
Matched Pairs Design
A matched pairs design is a special case of the
randomized block design. It is used when the experiment has
only two treatment conditions; and participants can be grouped
into pairs, based on some blocking variable. Then, within each
pair, participants are randomly assigned to different treatments.
The table to the right shows a matched pairs design for the
Acme experiment. The 1000 participants are grouped into 500
matched pairs. Each pair is matched on gender and age.
For example, Pair 1 might be two women, both age 21. Pair
2 might be two women, both age 22, and so on.
For the Acme example, the matched pairs design is an improvement
over the completely randomized design and the randomized
block design. Like the other designs, the matched pairs design
uses randomization to control for confounding. However, unlike
the others, this design explicitly controls for two potential
lurking variables - age and gender.
Test Your Understanding of This Lesson
Which of the following statements are true?
I. A completely randomized design offers no control for
II. A randomized block design controls for the placebo effect.
III. In a matched pairs design, participants within each pair receive
the same treatment.
(A) I only
(B) II only
(C) III only
(D) All of the above.
(E) None of the above.
The correct answer is (E). In a
completely randomized design,
experimental units are randomly assigned to treatment conditions.
provides some control for
By itself, a
randomized block design
does not control for the
To control for the placebo effect, the experimenter must include a
placebo in one of the treatment levels. In a
matched pairs design,
experimental units within each pair are assigned to different