Transcript Section 7.4 ~ The Search for Causality

Section 7.4 ~
The Search for Causality
Introduction to Probability and Statistics
Ms. Young
Sec. 7.4
Objective
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After this section you will understand the
difficulty of establishing causality from
correlation, and investigate guidelines that
can be used to help establish confidence in
causality.
Sec. 7.4
Establishing Causality
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Recall that just because there is a correlation, that doesn’t
necessarily mean that one variable causes the other (correlation
does not imply causality)
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The possible explanations for correlations include:
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Coincidence
Both variables may be influenced by an underlying cause
One variable actually does effect the other, but it’s just one of multiple
causes
On the other hand, correlation may imply causality
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In order to establish causality you must gather evidence using the
following guidelines:
1.
Look for situations in which the effect is correlated with the suspected
cause even while other factors vary
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2.
Ex. ~ Smoking and lung cancer; look for situations in which lung cancer still
occurred even if people smoked different brands of cigarettes or lived in
different states
Among groups that differ only in the presence or absence of the
suspected cause, check that the effect is similarly present or absent
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Ex. ~ Smoking and lung cancer; Look for the correlation among different
groups such as men, women, different races and different cultures
Sec. 7.4
Establishing Causality Cont’d…
3.
Look for evidence that larger amounts of the suspected cause produce
larger amounts of the effect
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A relationship continues as more data is collected
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4.
If the effect might be produced by other potential causes, make sure
that the effect still remains after accounting for the other potential
causes
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5.
Ex. ~ Smoking and lung cancer; since lung cancer can be caused by other
factors such as asbestos, radon gases, and lung disease make sure that the
subject didn’t get lung cancer as a result of one of these other factors
If possible, test the suspected cause with an experiment. If the
experiment cannot be performed with humans for ethical reasons,
consider doing the experiment with animals, cell cultures, or computer
models
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The best way to establish causality is by conducting an experiment if
appropriate
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6.
Ex. ~ Smoking and lung cancer; as the population of smokers increases, the cancer
rate increases
Ex. ~ Smoking and lung cancer; since it would be unethical to gather a sample of
people and ask them to smoke to see if they get lung cancer, conduct an
experiment using cell cultures or animals
Try to determine the physical mechanism by which the suspected cause
produces the effect
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Find the reason that there is a cause and effect relationship
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Ex. ~ Smoking and lung cancer; it is found that certain ingredients in cigarettes
cause cancer-causing mutations
Sec. 7.4
Hidden Causality
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Sometimes correlations (or the lack of a correlation)
can be hidden by underlying causes or confounding
variables
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Recall that confounding variables are variables that are not
intended to be a part of the study, but end up affecting the
results
Ex. ~ Cardiac bypass surgery; in past studies it was found that
people who had the surgery seemed to be doing no better on
average than patients that did have the surgery
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The confounding variables that were hiding the correlation were
that patients who had the surgery were typically in worse shape
to begin with and also the surgical techniques among different
hospitals produced different success rates
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After re-examining this relationship, it was found that cardiac
bypass surgery is a cause of prolonged life in patients with blocked
coronary arteries
Sec. 7.4
Confidence in Causality
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Some situations may never be possible to prove beyond all doubt
that there is a cause and effect relationship which means that we
must decide to act with some uncertainty about causation in
certain cases
Our legal system uses the following techniques for expressing a
legal level of confidence and these techniques can also be used to
help determine a level of confidence in causality
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Possible cause (low level of confidence) ~ Correlation is discovered, but
we cannot yet determine whether the correlation implies causality
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Probable cause (medium level of confidence) ~ We have good reason to
suspect that the correlation involves cause, perhaps because some of the
guidelines for establishing causality are satisfied
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In the legal system, possible cause (such as thinking that a particular suspect
possibly caused a particular crime) is often the reason for starting an investigation
In the legal system, probable cause is the general standard for getting a judge to
grant a warrant for a search or wiretap
Cause beyond reasonable doubt (high level of confidence) ~ We have
found a physical model that is so successful in explaining how one thing causes
another that it seams unreasonable to doubt the causality
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In the legal system, cause beyond reasonable doubt is the usual standard for
convictions
Note that beyond reasonable doubt is not the same as beyond all doubt