Section 7.4 ~ The Search for Causality Introduction to Probability and Statistics Ms. Young

Objective Sec. 7.4 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.

Establishing Causality Recall that just because there is a correlation, that doesn’t necessarily mean that one variable causes the other (correlation does not imply causality)  The possible explanations for correlations include: 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  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  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 2. Among groups that differ only in the presence or absence of the suspected cause, check that the effect is similarly present or absent  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  A relationship continues as more data is collected Ex. ~ Smoking and lung cancer; as the population of smokers increases, the cancer rate increases 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  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 5. 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  The best way to establish causality is by conducting an experiment if appropriate 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 6. Try to determine the physical mechanism by which the suspected cause produces the effect  Find the reason that there is a cause and effect relationship Ex. ~ Smoking and lung cancer; it is found that certain ingredients in cigarettes cause cancer-causing mutations Sec. 7.4

Hidden Causality Sometimes correlations (or the lack of a correlation) can be hidden by underlying causes or confounding variables  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 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  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 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  Possible cause (low level of confidence) ~ Correlation is discovered, but we cannot yet determine whether the correlation implies causality 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  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 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 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 Sec. 7.4