Editing Misuse of statistics (section)

===False causality===
{{Main|Correlation does not imply causation}}

When a statistical test shows a correlation between A and B, there are usually six possibilities:

# A causes B.
# B causes A.
# A and B both partly cause each other.
# A and B are both caused by a third factor, C.
# B is caused by C which is correlated to A.
# The observed correlation was due purely to chance.

The sixth possibility can be quantified by statistical tests that can calculate the probability that the correlation observed would be as large as it is just by chance if, in fact, there is no relationship between the variables. However, even if that possibility has a small probability, there are still the five others.

If the number of people buying ice cream at the beach is statistically related to the number of people who drown at the beach, then nobody would claim ice cream causes drowning because it's obvious that it isn't so. (In this case, both drowning and ice cream buying are clearly related by a third factor: the number of people at the beach).

This fallacy can be used, for example, to prove that exposure to a chemical causes cancer. Replace "number of people buying ice cream" with "number of people exposed to chemical X", and "number of people who drown" with "number of people who get cancer", and many people will believe you. In such a situation, there may be a statistical correlation even if there is no real effect. For example, if there is a perception that a chemical site is "dangerous" (even if it really isn't) property values in the area will decrease, which will entice more low-income families to move to that area. If low-income families are more likely to get cancer than high-income families (due to a poorer diet, for example, or less access to medical care) then rates of cancer will go up, even though the chemical itself is not dangerous. It is believed<ref name=Farley2003>{{cite web|last=Farley|first=John W.|title=Power Lines and Cancer: Nothing to Fear |publisher=Quackwatch| editor-link=Stephen Barrett |editor-last=Barrett |editor-first=Stephen |url = http://www.quackwatch.org/01QuackeryRelatedTopics/emf.html |year=2003}}</ref> that this is exactly what happened with some of the early studies showing a link between EMF ([[electromagnetic field]]s) from power lines and [[Electromagnetic radiation and health#Leukemia and cancer|cancer]].<ref name=powerlines>{{cite news|last1=Vince |first1=Gaia |title=Large study links power lines to childhood cancer |url=http://www.newscientist.com/article/dn7460-large-study-links-power-lines-to-childhood-cancer.html |journal=New Scientist |date=2005-06-03 |url-status=unfit |archive-url=https://web.archive.org/web/20140816043956/http://www.newscientist.com/article/dn7460-large-study-links-power-lines-to-childhood-cancer.html |archive-date=August 16, 2014 }} Cites: {{cite journal|last1=Draper|first1=G.|title=Childhood cancer in relation to distance from high voltage power lines in England and Wales: a case-control study|journal=BMJ|volume=330|issue=7503|year=2005|pages=1290|pmc=558197|doi=10.1136/bmj.330.7503.1290|pmid=15933351}}</ref>

In well-designed studies, the effect of false causality can be eliminated by assigning some people into a "treatment group" and some people into a "control group" at random, and giving the treatment group the treatment and not giving the control group the treatment. In the above example, a researcher might expose one group of people to chemical X and leave a second group unexposed. If the first group had higher cancer rates, the researcher knows that there is no third factor that affected whether a person was exposed because he controlled who was exposed or not, and he assigned people to the exposed and non-exposed groups at random. However, in many applications, actually doing an experiment in this way is either prohibitively expensive, infeasible, unethical, illegal, or downright impossible. For example, it is highly unlikely that an [[Institutional Review Board|IRB]] would accept an experiment that involved intentionally exposing people to a dangerous substance in order to test its toxicity. The obvious ethical implications of such types of experiments limit researchers' ability to empirically test causation.