# 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.

### Redskins Rule

**November 1, 1992November 2, 1952November 2, 1980**

### 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.