Correlation does not imply causation

Cum hoc ergo propter hoccausationcorrelationcorrelation implies causationCircular cause and consequencecorrelation and causationcorrelation does not prove causationinferring causation from correlationThird-cause fallacyWrong direction
In statistics, the phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two variables solely on the basis of an observed association or correlation between them.wikipedia
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Correlation and dependence

correlationcorrelatedcorrelations
In statistics, the phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two variables solely on the basis of an observed association or correlation between them.
However, in general, the presence of a correlation is not sufficient to infer the presence of a causal relationship (i.e., correlation does not imply causation).

Post hoc ergo propter hoc

post hoc, ergo propter hocpost hocpost hoc fallacy
This differs from the fallacy known as post hoc ergo propter hoc ("after this, therefore because of this"), in which an event following another is seen as a necessary consequence of the former event.
A logical fallacy of the questionable cause variety, it is subtly different from the fallacy cum hoc ergo propter hoc ("with this, therefore because of this"), in which two events occur simultaneously or the chronological ordering is insignificant or unknown.

Causality

causalcause and effectcausation
In statistics, the phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two variables solely on the basis of an observed association or correlation between them. The third-cause fallacy (also known as ignoring a common cause or questionable cause ) is a logical fallacy where a spurious relationship is confused for causation.
A mere observation of a correlation is not nearly adequate to establish causality.

Questionable cause

false causeFallacy of false causeNon causa pro causa
The complementary idea that "correlation implies causation" is an example of a questionable-cause logical fallacy, in which two events occurring together are taken to have established a cause-and-effect relationship.

Convergent cross mapping

Methods have been proposed that use correlation as the basis for hypothesis tests for causality, including the Granger causality test and convergent cross mapping.
Convergent cross mapping (CCM) is a statistical test for a cause-and-effect relationship between two time series variables that, like the Granger causality test, seeks to resolve the problem that correlation does not imply causation.

Spurious relationship

spurious correlationspuriousmisleading results
The third-cause fallacy (also known as ignoring a common cause or questionable cause ) is a logical fallacy where a spurious relationship is confused for causation.
In statistics, a spurious relationship or spurious correlation is a mathematical relationship in which two or more events or variables are associated but not causally related, due to either coincidence or the presence of a certain third, unseen factor (referred to as a "common response variable", "confounding factor", or "lurking variable").

Epidemiology

epidemiologistepidemiologicalepidemiologists
In a widely studied example of the statistical fallacy, numerous epidemiological studies showed that women taking combined hormone replacement therapy (HRT) also had a lower-than-average incidence of coronary heart disease (CHD), leading doctors to propose that HRT was protective against CHD.
"Correlation does not imply causation" is a common theme for much of the epidemiological literature.

Statistics

statisticalstatistical analysisstatistician
In statistics, the phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two variables solely on the basis of an observed association or correlation between them.
(See Correlation does not imply causation.)

Coefficient of determination

R-squaredR'' 2 R 2
A caution that applies to R 2, as to other statistical descriptions of correlation and association is that "correlation does not imply causation."

Coincidence

coincidencescoincidentalCoincidentally
To establish cause and effect (i.e., causality) is notoriously difficult, as is expressed by the commonly heard statement that "correlation does not imply causation."

Statistical hypothesis testing

hypothesis testingstatistical teststatistical tests
Methods have been proposed that use correlation as the basis for hypothesis tests for causality, including the Granger causality test and convergent cross mapping.
Many of the philosophical criticisms of hypothesis testing are discussed by statisticians in other contexts, particularly correlation does not imply causation and the design of experiments.

Health effects of tobacco

health effectsHealth effects of tobacco smokingsmoking
For example, the tobacco industry has historically relied on a dismissal of correlational evidence to reject a link between tobacco and lung cancer, as did biologist and statistician Ronald Fisher.
These studies were widely criticized as showing correlation, not causality.

Near-sightedness

myopiamyopicnearsightedness
Numerous studies have found correlations between myopia, on the one hand, and intelligence and academic achievement, on the other; it is not clear whether there is a causal relationship.

Ronald Fisher

R.A. FisherR. A. FisherFisher
For example, the tobacco industry has historically relied on a dismissal of correlational evidence to reject a link between tobacco and lung cancer, as did biologist and statistician Ronald Fisher.
Fisher publicly spoke out against the 1950 study showing that smoking tobacco causes lung cancer, arguing that correlation does not imply causation.

Variable and attribute (research)

variablesvariablevariables data
In statistics, the phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two variables solely on the basis of an observed association or correlation between them.

Logical consequence

entailmententailsfollows from
This differs from the fallacy known as post hoc ergo propter hoc ("after this, therefore because of this"), in which an event following another is seen as a necessary consequence of the former event.

Hormone replacement therapy

menopausal hormone therapyhormone therapyestrogen replacement therapy
In a widely studied example of the statistical fallacy, numerous epidemiological studies showed that women taking combined hormone replacement therapy (HRT) also had a lower-than-average incidence of coronary heart disease (CHD), leading doctors to propose that HRT was protective against CHD.

Coronary artery disease

coronary heart diseaseischemic heart diseaseischaemic heart disease
In a widely studied example of the statistical fallacy, numerous epidemiological studies showed that women taking combined hormone replacement therapy (HRT) also had a lower-than-average incidence of coronary heart disease (CHD), leading doctors to propose that HRT was protective against CHD.

Randomized controlled trial

randomized controlled trialsrandomized clinical trialrandomized control trial
But later randomized controlled trials showed that use of HRT led to a small but statistically significant increase in the risk of CHD.

Statistical significance

statistically significantsignificantsignificance level
But later randomized controlled trials showed that use of HRT led to a small but statistically significant increase in the risk of CHD.

Social class

classsocial classesclasses
Reanalysis of the data from the epidemiological studies showed that women undertaking HRT were more likely to be from higher socioeconomic groups (ABC1), with better-than-average diet and exercise regimens.

NRS social grade

ABC1social gradesocial grades
Reanalysis of the data from the epidemiological studies showed that women undertaking HRT were more likely to be from higher socioeconomic groups (ABC1), with better-than-average diet and exercise regimens.

Granger causality

degree of causalityGrangergranger causality analysis
Methods have been proposed that use correlation as the basis for hypothesis tests for causality, including the Granger causality test and convergent cross mapping.