CHAPTER 4
Designing Studies
4.2
Experiments
The Practice of Statistics, 5th Edition
Starnes, Tabor, Yates, Moore
Bedford Freeman Worth Publishers
Experiments
Learning Objectives
After this section, you should be able to:
 DISTINGUISH between an observational study and an experiment.
 EXPLAIN the concept of confounding.
 IDENTIFY the experimental units, explanatory and response variables,
and treatments in an experiment.
 EXPLAIN the purpose of comparison, random assignment, control, and
replication in an experiment.
 DESCRIBE a completely randomized design for an experiment.
 DESCRIBE the placebo effect and the purpose of blinding in an
experiment.
 INTERPRET the meaning of statistically significant in the context of an
experiment.
 EXPLAIN the purpose of blocking in an experiment. DESCRIBE a
randomized block design or a matched pairs design for an experiment.
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Observational Study vs. Experiment
An observational study observes individuals and measures
variables of interest but does not attempt to influence the
responses.
An experiment deliberately imposes some treatment on
individuals to measure their responses.
When our goal is to understand cause and effect, experiments are the
only source of fully convincing data.
The distinction between observational study and experiment is one of
the most important in statistics.
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• See example on p.235
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Observational Study vs. Experiment
Observational studies of the effect of an explanatory variable on a
response variable often fail because of confounding between the
explanatory variable and one or more other variables.
Well-designed experiments take steps to prevent confounding.
Confounding occurs when two variables are associated in
such a way that their effects on a response variable cannot be
distinguished from each other.
To explain confounding you should explain how the variable you chose is
associated with the explanatory variable and also how it affects the response
variable.
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• AP Exam Tip on p.236
– “Diet is a confounding variable because people with bad diets are more
likely to have a heart attack”
• Need to explain why diet is also associated with the choice to take
hormones.
• Would need to say something about why a better diet might be
more common in the group of women who choose to take
hormones.
• AP common error on p.236
– For the hormone example you would need to explain not only that
wealthier people tend to go to the doctor more often and to be healthier
overall, but also that wealthier people are more likely to get hormone
replacement. Thus, it could actually be the overall healthiness of
wealthy women that caused the reduction in heart attacks, not any
hormones they may have taken.
• CYU on p.237
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The Language of Experiments
An experiment is a statistical study in which we actually do something
(a treatment) to people, animals, or objects (the experimental units) to
observe the response. Here is the basic vocabulary of experiments.
A specific condition applied to the individuals in an experiment is
called a treatment. If an experiment has several explanatory
variables, a treatment is a combination of specific values of these
variables.
The experimental units are the smallest collection of individuals
to which treatments are applied. When the units are human
beings, they often are called subjects.
Often times the explanatory variables in an experiment are called factors.
If an experiment has several factors, the combinations of each level of each
factor form the treatments.
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• See example on p.239
• http://www.ted.com/talks/michael_norton_how_to_buy_happiness#t107021
– Describes a multifactor experiment to determine if money can buy
hapiness.
– There are 2 factors, amount of money & how it is spent.
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How to Experiment Badly
Many laboratory experiments use a design like the one in the online
SAT course example on p.240:
Experimental Units
Treatment
Measure
Response
In the lab environment, simple designs often work well.
Field experiments and experiments with animals or people deal
with more variable conditions.
Outside the lab, badly designed experiments often yield worthless
results because of confounding.
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How to Experiment Well
The remedy for confounding is to perform a comparative experiment in
which some units receive one treatment and similar units receive
another. Most well designed experiments compare two or more
treatments.
Comparison alone isn’t enough, if the treatments are given to groups
that differ greatly, bias will result. The solution to the problem of bias is
random assignment.
In an experiment, random assignment means that experimental
units are assigned to treatments using a chance process.
See example on p.241
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Principles of Experimental Design
Principles of Experimental Design
The basic principles for designing experiments are as follows:
1. Comparison. Use a design that compares two or more treatments.
2. Random assignment. Use chance to assign experimental units to
treatments. Doing so helps create roughly equivalent groups of
experimental units by balancing the effects of other variables among
the treatment groups.
3. Control. Keep other variables that might affect the response the
same for all groups.
4. Replication. Use enough experimental units in each group so that
any differences in the effects of the treatments can be distinguished
from chance differences between the groups.
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• See example on p.243
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Completely Randomized Design
In a completely randomized design, the treatments are assigned
to all the experimental units completely by chance.
Some experiments may include a control group that receives an
inactive treatment or an existing baseline treatment.
Group 1
Experimental
Units
Compare
Results
Random
Assignment
Group 2
The Practice of Statistics, 5th Edition
Treatment
1
Treatment
2
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• See example on p.245
• Read exam tip on p.246
• CYU on p.247
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Experiments: What Can Go Wrong?
The logic of a randomized comparative experiment depends on our
ability to treat all the subjects the same in every way except for the
actual treatments being compared.
Good experiments, therefore, require careful attention to details to
ensure that all subjects really are treated identically.
The response to a dummy treatment is called the placebo effect.
In a double-blind experiment, neither the subjects nor those who
interact with them and measure the response variable know which
treatment a subject received.
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• See example on p.247
• http://www.cbsnews.com/videos/treating-depression-is-there-aplacebo-effect/
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Inference for Experiments
In an experiment, researchers usually hope to see a difference in the
responses so large that it is unlikely to happen just because of chance
variation.
We can use the laws of probability, which describe chance behavior, to
learn whether the treatment effects are larger than we would expect to
see if only chance were operating.
If they are, we call them statistically significant.
An observed effect so large that it would rarely occur by chance is
called statistically significant.
A statistically significant association in data from a well-designed
experiment does imply causation.
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Blocking
When a population consists of groups of individuals that are “similar
within but different between,” a stratified random sample gives a better
estimate than a simple random sample. This same logic applies in
experiments.
A block is a group of experimental units that are known before the
experiment to be similar in some way that is expected to affect the
response to the treatments.
In a randomized block design, the random assignment of
experimental units to treatments is carried out separately within each
block.
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Matched Pairs Design
A common type of randomized block design for comparing two treatments
is a matched pairs design. The idea is to create blocks by matching
pairs of similar experimental units.
A matched pairs design is a randomized blocked experiment in which
each block consists of a matching pair of similar experimental units.
Chance is used to determine which unit in each pair gets each
treatment.
Sometimes, a “pair” in a matched-pairs design consists of a single unit
that receives both treatments. Since the order of the treatments can
influence the response, chance is used to determine with treatment is
applied first for each unit.
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Experiments
Section Summary
In this section, we learned how to…
 DISTINGUISH between an observational study and an experiment.
 EXPLAIN the concept of confounding.
 IDENTIFY the experimental units, explanatory and response variables,
and treatments in an experiment.
 EXPLAIN the purpose of comparison, random assignment, control, and
replication in an experiment.
 DESCRIBE a completely randomized design for an experiment.
 DESCRIBE the placebo effect and the purpose of blinding in an
experiment.
 INTERPRET the meaning of statistically significant in the context of an
experiment.
 EXPLAIN the purpose of blocking in an experiment. DESCRIBE a
randomized block design or a matched pairs design for an experiment.
The Practice of Statistics, 5th Edition
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