The phrase " **correlation does not imply causation**" refers to the inability to legitimately deduce a cause-and-effect relationship between two events or variables "Variable (research)") solely on the basis of an observed association or correlation between them.[\[1\]](https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation?utm_source=chatgpt.com#cite_note-Tufte_2006_5-1)[\[2\]](https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation?utm_source=chatgpt.com#cite_note-Aldrich1995-2) The 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. This fallacy is also known by the Latin phrase _**cum hoc ergo propter hoc**_ ('with this, therefore because of this'). 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, and from conflation, the errant merging of two events, ideas, databases, etc., into one. As with any logical fallacy, identifying that the reasoning behind an argument is flawed does not necessarily imply that the resulting conclusion is false. Statistical methods have been proposed that use correlation as the basis for hypothesis tests for causality, including the Granger causality test and convergent cross mapping. The Bradford Hill criteria, also known as Hill's criteria for causation, are a group of nine principles that can be useful in establishing epidemiologic evidence of a causal relationship. ## Usage and meaning of terms \ [edit\] ### "Imply" \ [edit\] In casual use, the word "implies" loosely means _suggests_, rather than _requires_. However, in logic, the technical use of the word "implies" means "is a _sufficient condition_ for."[\[3\]](https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation?utm_source=chatgpt.com#cite_note-sufficient-3) That is the meaning intended by statisticians when they say causation is not certain. Indeed, _p implies q_ has the technical meaning of the material conditional: _if p then q_ symbolized as _p → q_. That is, "if circumstance _p_ is true, then _q_ follows." In that sense, it is always correct to say "Correlation does not _imply_ causation." ### "Cause" \ [edit\] The word " cause" (or "causation") has multiple meanings in English. In philosophical terminology, "cause" can refer to necessary, sufficient, or contributing causes. In examining correlation, "cause" is most often used to mean "one contributing cause" (but not necessarily the only contributing cause).  Dinosaur illiteracy and extinction may be correlated, but that would not mean the variables had a causal relationship. ## Causal analysis \ [edit\] This section is an excerpt from Causal analysis.\ [edit\] Causal analysis is the field of experimental design and statistics pertaining to establishing cause and effect.[\[4\]](https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation?utm_source=chatgpt.com#cite_note-4) Typically it involves establishing four elements: correlation, sequence in time (that is, causes must occur before their proposed effect), a plausible physical or information-theoretical mechanism for an observed effect to follow from a possible cause, and eliminating the possibility of common and alternative ("special") causes "Common cause and special cause (statistics)"). Such analysis usually involves one or more controlled or natural experiments.[\[5\]](https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation?utm_source=chatgpt.com#cite_note-5) ## Examples of illogically inferring causation from correlation \ [edit\] ### Third factor C (the common-causal variable) causes both A and B \ [edit causes both A and B")\] Main article: Spurious relationship The **third-cause fallacy** (also known as _ignoring a common cause_[\[8\]](https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation?utm_source=chatgpt.com#cite_note-labossiere-8) or _questionable cause_[\[8\]](https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation?utm_source=chatgpt.com#cite_note-labossiere-8)) is a logical fallacy in which a spurious relationship is confused for causation. It asserts that X causes Y when in reality, both X and Y are caused by Z. It is a variation on the _post hoc ergo propter hoc_ fallacy and a member of the questionable cause group of fallacies. All of those examples deal with a lurking variable, which is simply a hidden third variable that affects both of the variables observed to be correlated. That third variable is also known as a confounding variable, with the slight difference that confounding variables need not be hidden and may thus be corrected for in an analysis. Note that the Wikipedia link to lurking variable redirects to confounding. A difficulty often also arises where the third factor, though fundamentally different from A and B, is so closely related to A and/or B as to be confused with them or very difficult to scientifically disentangle from them (see Example 4). Example 1Sleeping with one's shoes on is strongly correlated with waking up with a headache.Therefore, sleeping with one's shoes on causes headache. The above example commits the correlation-implies-causation fallacy, as it prematurely concludes that sleeping with one's shoes on causes headache. A more plausible explanation is that both are caused by a third factor, in this case going to bed drunk, which thereby gives rise to a correlation. So the conclusion is false. Example 2Young children who sleep with the light on are much more likely to develop myopia in later life.Therefore, sleeping with the light on causes myopia. This is a scientific example that resulted from a study at the University of Pennsylvania Medical Center. Published in the May 13, 1999, issue of _Nature "Nature (journal)")_,[\[9\]](https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation?utm_source=chatgpt.com#cite_note-QuinnMyopiaNature-9) the study received much coverage at the time in the popular press.[\[10\]](https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation?utm_source=chatgpt.com#cite_note-10) However, a later study at Ohio State University did not find that infants sleeping with the light on caused the development of myopia. It did find a strong link between parental myopia and the development of child myopia, also noting that myopic parents were more likely to leave a light on in their children's bedroom.[\[11\]](https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation?utm_source=chatgpt.com#cite_note-11)[\[12\]](https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation?utm_source=chatgpt.com#cite_note-ZadnikJones2000-12)[\[13\]](https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation?utm_source=chatgpt.com#cite_note-GwiazdaOng2000-13)[\[14\]](https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation?utm_source=chatgpt.com#cite_note-StoneMaguire2000-14) In this case, the cause of both conditions is parental myopia, and the above-stated conclusion is false. Example 3As ice cream sales increase, the rate of drowning deaths increases sharply.Therefore, ice cream consumption causes drowning. This example fails to recognize the importance of time of year and temperature to ice cream sales. Ice cream is sold during the hot summer months at a much greater rate than during colder times, and it is during these hot summer months that people are more likely to engage in activities involving water, such as swimming. The increased drowning deaths are simply caused by more exposure to water-based activities, not ice cream. The stated conclusion is false.