4.3 Experiments and Inference About Cause
There are two types of statistical studies, and the distinction between them is one of the most
important ideas in statistics:
1. Observational Studies
 A study is an observational study if individuals are observed and variables of interest are
measured, but you do not attempt to ____________ the responses. Sample surveys
(sections 4.1 and 4.2) are one kind of observational study.
 The goal of an observational study is usually to draw conclusions about the
corresponding population or about differences between two or more populations.
 It is impossible to draw ______________ conclusions because you cannot rule out the
possibility that the observed effect is due to some variable (a ____________ variable)
other than the factor being studied.
2. Experiments
 A study is an experiment if something is deliberately done to individuals in order to
observe their responses.
 The goal of an experiment is to determine the effect of the manipulated factors on the
___________ variable.
 A well-designed experiment can result in data that provide evidence for a _________
____________ relationship.
Experimental Design
There are three basic principles of experimental design:
1. Control
Control refers to the overall effort to minimize _____________ in the way experimental units
are obtained and treated. The purpose of control is to try to eliminate the confounding effects
of ________ variables. The simplest form of control is to compare two or more __________.
Example: Treating Ulcers
“Gastric freezing” is a clever treatment for ulcers in the upper intestine. The patient swallows
a deflated balloon with tubes attached, and then a refrigerated liquid is pumped through the
balloon for an hour. The idea is that cooling the stomach will reduce its production of acid
and so relieve ulcers. An experiment showed that gastric freezing did reduce acid production
and relieve ulcer pain. The treatment was safe and easy and was widely used for several
years. The design of the experiment was:
Gastric freezing → Observe pain relief
1
4.3 Experiments and Inference About Cause
Unfortunately this experiment was poorly designed. The patients’ response may have been
due to the placebo effect. The misleading results were because the effects of the explanatory
variable were confounded with the placebo effect.
A later experiment divided ulcer patients into two groups. One group was treated by gastric
freezing as before. The other group received a placebo treatment in which the liquid in the
balloon was at body temperature rather than freezing. The results: 34% of the 82 patients in
the treatment group improved, but so did 38% of the 78 patients in the placebo group. This
and other properly designed experiments showed that gastric freezing was no better than a
placebo, and its use was abandoned.
2. Randomization: the rule used to assign the experimental units to the treatment
Randomization is arguably the most important principle of experimental design. The
principle is to assign treatments to units at random, so there are only two possible causes for
a difference in the responses to the treatments: chance or the ____________. The random
assignment of treatments allows you to assert that treatment groups are essentially ________
and so the probability that chance alone will give such a difference in the responses is
______, which means you can infer that the cause of the difference was the treatment.
3. Replication: use enough subjects to reduce chance variation
Even with control, there will still be natural ______________ among experimental units.
Replication is where each treatment is replicated on many units to ________ chance variation
in the results. Although it can also mean conducting a similar experiment in a different
location by different investigators, it’s not the kind of replication meant here. The purpose of
replication is to reduce the role of ________ variation and increase the sensitivity of the
experiment to differences between treatments.
2
4.3 Experiments and Inference About Cause
The table below summarizes the types of conclusions that can be made with different study
designs:
Study Description
Observational study based on
a probability sample
Observational study based on
a non-probability sample
Experiments with groups
formed by random
assignment of experimental
units to treatment(s)
 Subjects are
volunteers or
experimental units are
not randomly selected
from population
 Experimental
units/subjects are
randomly selected
from population
Experiments with groups not
formed by random
assignment to treatment(s)
3
Reasonable to Generalize
Conclusions to Population?
Reasonable to Draw Causeand-Effect Conclusion?
Yes
No
No
No
No
Yes
Yes
Yes
No
No
4.3 Experiments and Inference About Cause