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The phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two events or variables solely on the basis of an observed association or
correlation In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statisti ...
between them. 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 ''Post hoc ergo propter hoc'' (Latin: 'after this, therefore because of this') is an informal fallacy that states: "Since event Y ''followed'' event X, event Y must have been ''caused'' by event X." It is often shortened simply to ''post hoc fall ...
'' ("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 Conflation is the merging of two or more sets of information, texts, ideas, opinions, etc., into one, often in error. Conflation is often misunderstood. It originally meant to fuse or blend, but has since come to mean the same as equate, treati ...
, 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 Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industr ...
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 variables that, like the Granger causality test, seeks to resolve the problem that correlation does not imply causation.' Sugihara G., May R., Y ...
.


Usage and meaning of terms


"Imply"

In casual use, the word "implies" loosely means ''suggests'', rather than ''requires''. However, in
logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premis ...
, the technical use of the word "implies" means "is a '' sufficient condition'' for." 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 The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol \rightarrow is interpreted as material implication, a formula P \rightarrow Q is true unless P is true and Q i ...
: ''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"

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). If there is causation, there is correlation but also a sequence in time from cause to effect, a plausible mechanism, and sometimes common and intermediate causes. Correlation is often used to infer causation because it is a necessary condition: that is, if A causes B, then A and B must necessarily be correlated. However it is not a sufficient condition.


Causal analysis

Causal analysis is the field of
experimental design The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...
and statistics pertaining to establishing cause and effect. For any two correlated events, A and B, the are four possible relationships: * A causes B (direct causation); * B causes A (reverse causation); * A and B are both caused by C (common causation); * There is no connection between A and B; the correlation is a
coincidence A coincidence is a remarkable concurrence of events or circumstances that have no apparent causal connection with one another. The perception of remarkable coincidences may lead to supernatural, occult, or paranormal claims, or it may lead t ...
. These relationships are not mutually exclusive; they may exist in any combination. For example, it is possible that both A can cause effect B ''and'' B can cause effect A (bidirectional or cyclic causation). No conclusion can thus be made regarding the ''existence'' or the ''direction'' of a cause-and-effect relationship only from the fact that A and B are correlated. Determining whether there is an actual cause-and-effect relationship, and if so which direction the causality is, requires further investigation. If the relationship between ''A'' and ''B'' is statistically significant, the final relationship in the list above ("coincidence") may be statistically ruled out, but the correlation itself will not clarify whether A caused B, B caused A, or A and B were both caused by some other effect, C.


In philosophy and physics

The nature of causality is systematically investigated in several academic disciplines, including philosophy and
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...
. In academia, there are a significant number of theories on causality; ''The Oxford Handbook of Causation'' encompasses 770 pages. Among the more influential theories within philosophy are
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical Greece, Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatet ...
's
Four causes The four causes or four explanations are, in Aristotelian thought, four fundamental types of answer to the question "why?", in analysis of change or movement in nature: the material, the formal, the efficient, and the final. Aristotle wrote t ...
and
Al-Ghazali Al-Ghazali ( – 19 December 1111; ), full name (), and known in Persian-speaking countries as Imam Muhammad-i Ghazali (Persian: امام محمد غزالی) or in Medieval Europe by the Latinized as Algazelus or Algazel, was a Persian polym ...
's occasionalism.
David Hume David Hume (; born David Home; 7 May 1711 NS (26 April 1711 OS) – 25 August 1776) Cranston, Maurice, and Thomas Edmund Jessop. 2020 999br>David Hume" ''Encyclopædia Britannica''. Retrieved 18 May 2020. was a Scottish Enlightenment phil ...
argued that beliefs about causality are based on experience, and experience similarly based on the assumption that the future models the past, which in turn can be based only on experience, which leads to circular logic. In conclusion, he asserted that causality is not based on actual reasoning: only correlation can actually be perceived.
Immanuel Kant Immanuel Kant (, , ; 22 April 1724 – 12 February 1804) was a German philosopher and one of the central Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works in epistemology, metaphysics, ethics, and aes ...
, according to , held that "a causal principle according to which every event has a cause, or follows according to a causal law, cannot be established through induction as a purely empirical claim, since it would then lack strict universality, or necessity". Outside the field of philosophy, theories of causation can be identified in
classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...
, statistical mechanics,
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, q ...
,
spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why diffe ...
theories,
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditar ...
,
social science Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of soc ...
s, and law. To establish a correlation as causal within
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...
, it is normally understood that the cause and the effect must connect through a local mechanism (cf. for instance the concept of impact) or a nonlocal mechanism (cf. the concept of field), in accordance with known laws of nature. From the point of view of
thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...
, universal properties of causes as compared to effects have been identified through the
Second Law of Thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...
, confirming the ancient, medieval and Cartesian view that "the cause is greater than the effect" for the particular case of thermodynamic free energy. That in turn is challenged by popular interpretations of the concepts of
nonlinear system In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
s and the butterfly effect in which small events cause large effects because of, respectively, unpredictability and an unlikely triggering of large amounts of
potential energy In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potentia ...
.


Causality construed from counterfactual states

Intuitively, causation seems to require not just a correlation, but a counterfactual dependence. Suppose that a student performed poorly on a test and guesses that the cause was his not studying. To prove this, one thinks of the counterfactual – the same student writing the same test under the same circumstances but having studied the night before. If one could rewind history, and change only one small thing (making the student study for the exam), then causation could be observed (by comparing version 1 to version 2). Because one cannot rewind history and replay events after making small controlled changes, causation can only be inferred, never exactly known. That is referred to as the Fundamental Problem of Causal Inference – it is impossible to directly observe causal effects. A major goal of scientific
experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs wh ...
s and statistical methods is to approximate as best possible the counterfactual state of the world. For example, one could run an experiment on identical twins who were known to consistently get the same grades on their tests. One twin is sent to study for six hours while the other is sent to the amusement park. If their test scores suddenly diverged by a large degree, that would be strong evidence that studying (or going to the amusement park) had a causal effect on test scores. In that case, correlation between studying and test scores would almost certainly imply causation. Well-designed experimental studies replace equality of individuals as in the previous example by equality of groups. The objective is to construct two groups that are similar except for the treatment that the groups receive. That is achieved by selecting subjects from a single population and randomly assigning them to two or more groups. The likelihood of the groups behaving similarly to one another (on average) rises with the number of subjects in each group. If the groups are essentially equivalent except for the treatment they receive, and a difference in the outcome for the groups is observed, then this constitutes evidence that the treatment is responsible for the outcome, or in other words the treatment causes the observed effect. However, an observed effect could also be caused "by chance", for example as a result of random perturbations in the population. Statistical tests exist to quantify the likelihood of erroneously concluding that an observed difference exists when in fact it does not exist (for example, see
P-value In null-hypothesis significance testing, the ''p''-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small ''p''-value means ...
).


Causality predicted by an extrapolation of trends

When experimental studies are impossible, and only pre-existing data are available, as is usually the case for example in
economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analy ...
,
regression analysis In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ...
can be used. Factors other than the potential causative variable of interest are controlled for by including them as
regressors Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or dema ...
in addition to the regressor representing the variable of interest. False inferences of causation due to reverse causation (or wrong estimates of the magnitude of causation because of the presence of bidirectional causation) can be avoided by using explanators (regressors) that are necessarily exogenous, such as physical explanators like rainfall amount (as a determinant of, say, futures prices), lagged variables whose values were determined before the dependent variable's value was determined,
instrumental variables In statistics, econometrics, epidemiology and related disciplines, the method of instrumental variables (IV) is used to estimate causal relationships when controlled experiments are not feasible or when a treatment is not successfully delivered ...
for the explanators (chosen based on their known exogeneity), etc. See causality in statistics and economics. Spurious correlation from mutual influence from a third, common, causative variable, is harder to avoid: the model must be specified such that there is a theoretical reason to believe that no such underlying causative variable has been omitted from its analysis.


Examples of illogically inferring causation from correlation


B causes A (reverse causation or reverse causality)

Reverse causation or reverse causality or wrong direction is an informal fallacy of questionable cause where cause and effect are reversed. The cause is said to be the effect and vice versa. ;Example 1 :The faster that windmills are observed to rotate, the more wind is observed. :Therefore, wind is caused by the rotation of windmills. (Or, simply put: windmills, as their name indicates, are machines used to produce wind.) In this example, the correlation (simultaneity) between windmill activity and wind velocity does not imply that wind is caused by windmills. It is rather the other way around, as suggested by the fact that wind does not need windmills to exist, while windmills need wind to rotate. Wind can be observed in places where there are no windmills or non-rotating windmills—and there are good reasons to believe that wind existed before the invention of windmills. ;Example 2 :Subjects with low cholesterol correlate with an increase in mortality. :Therefore, low cholesterol increases your risk of mortality. It is the other way around since the disease, such as cancer, causes a low cholesterol because of a myriad of factors, such as weight loss, and an increase in mortality. This is also seen with ex-smokers. Ex-smokers are more likely to die of lung cancer than current smokers. When lifelong smokers are told they have lung cancer, many quit smoking. This change can make it seem as if ex-smokers are more likely to die of lung cancer than current smokers. This can also be seen in alcoholics. As alcoholics become diagnosed with cirrhosis of the liver, many quit drinking. However, they also experience an increased risk of mortality. In these instances, it is the diseases that cause an increased risk of mortality, but the increased mortality is attributed to the beneficial effects that follow the diagnosis, making healthy changes look unhealthy. ;Example 3 In other cases it may simply be unclear which is the cause and which is the effect. For example: :''Children that watch a lot of TV are the most violent. Clearly, TV makes children more violent''. This could easily be the other way round; that is, violent children like watching more TV than less violent ones. ;Example 4 A correlation between
recreational drug use Recreational drug use indicates the use of one or more psychoactive drugs to induce an altered state of consciousness either for pleasure or for some other casual purpose or pastime by modifying the perceptions and emotions of the user. When a ...
and psychiatric disorders might be either way around: perhaps the drugs cause the disorders, or perhaps people use drugs to
self medicate The self is an individual as the object of that individual’s own reflective consciousness. Since the ''self'' is a reference by a subject to the same subject, this reference is necessarily Subjective character of experience, subjective. The sen ...
for preexisting conditions. Gateway drug theory may argue that
marijuana Cannabis, also known as marijuana among other names, is a psychoactive drug from the cannabis plant. Native to Central or South Asia, the cannabis plant has been used as a drug for both recreational and entheogenic purposes and in variou ...
usage leads to usage of harder drugs, but hard drug usage may lead to marijuana usage (see also '' confusion of the inverse''). Indeed, in the
social science Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of soc ...
s where controlled experiments often cannot be used to discern the direction of causation, this fallacy can fuel long-standing scientific arguments. One such example can be found in
education economics Education economics or the economics of education is the study of economic issues relating to education, including the demand for education, the financing and provision of education, and the comparative efficiency of various educational programs ...
, between the screening/ signaling and human capital models: it could either be that having innate ability enables one to complete an education, or that completing an education builds one's ability. ;Example 5 A historical example of this is that Europeans in the
Middle Ages In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire ...
believed that
lice Louse ( : lice) is the common name for any member of the clade Phthiraptera, which contains nearly 5,000 species of wingless parasitic insects. Phthiraptera has variously been recognized as an order, infraorder, or a parvorder, as a resul ...
were beneficial to health since there would rarely be any lice on sick people. The reasoning was that the people got sick because the lice left. The real reason however is that lice are extremely sensitive to
body temperature Thermoregulation is the ability of an organism to keep its body temperature within certain boundaries, even when the surrounding temperature is very different. A thermoconforming organism, by contrast, simply adopts the surrounding temperatur ...
. A small increase of body temperature, such as in a
fever Fever, also referred to as pyrexia, is defined as having a temperature above the normal range due to an increase in the body's temperature set point. There is not a single agreed-upon upper limit for normal temperature with sources using val ...
, makes the lice look for another host. The medical
thermometer A thermometer is a device that measures temperature or a temperature gradient (the degree of hotness or coldness of an object). A thermometer has two important elements: (1) a temperature sensor (e.g. the bulb of a mercury-in-glass thermomete ...
had not yet been invented and so that increase in temperature was rarely noticed. Noticeable symptoms came later, which gave the impression that the lice had left before the person became sick. In other cases, two phenomena can each be a partial cause of the other; consider poverty and lack of education, or procrastination and poor self-esteem. One making an argument based on these two phenomena must however be careful to avoid the fallacy of circular cause and consequence. Poverty is ''a'' cause of lack of education, but it is not the ''sole'' cause, and vice versa.


Third factor C (the common-causal variable) causes both A and B

The third-cause fallacy (also known as ''ignoring a common cause''Labossiere, M.C.
''Dr. LaBossiere's Philosophy Pages''
or ''questionable cause'') 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 ''Post hoc ergo propter hoc'' (Latin: 'after this, therefore because of this') is an informal fallacy that states: "Since event Y ''followed'' event X, event Y must have been ''caused'' by event X." It is often shortened simply to ''post hoc fall ...
'' 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 causes of the correlation. 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 1 :Sleeping 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 2 :Young 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 The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universit ...
Medical Center Medical center or medical centre may refer to: Medical care * A collection of medical services on the same site, such as the services of a general practitioner, pharmacist, pathology, radiology, dentist etc. * Clinic * Hospital * Academic medic ...
. Published in the May 13, 1999, issue of ''
Nature Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans ar ...
'', the study received much coverage at the time in the popular press. However, a later study at
Ohio State University The Ohio State University, commonly called Ohio State or OSU, is a public land-grant research university in Columbus, Ohio. A member of the University System of Ohio, it has been ranked by major institutional rankings among the best pu ...
did not find that
infant An infant or baby is the very young offspring of human beings. ''Infant'' (from the Latin word ''infans'', meaning 'unable to speak' or 'speechless') is a formal or specialised synonym for the common term ''baby''. The terms may also be used t ...
s 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. In this case, the cause of both conditions is parental myopia, and the above-stated conclusion is false. ;Example 3 :As 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. ;Example 4 :A hypothetical study shows a relationship between test anxiety scores and shyness scores, with a statistical ''r'' value (strength of correlation) of +.59. :Therefore, it may be simply concluded that shyness, in some part, causally influences test anxiety. However, as encountered in many psychological studies, another variable, a "self-consciousness score", is discovered that has a sharper correlation (+.73) with shyness. This suggests a possible "third variable" problem, however, when three such closely related measures are found, it further suggests that each may have bidirectional tendencies (see " bidirectional variable", above), being a cluster of correlated values each influencing one another to some extent. Therefore, the simple conclusion above may be false. ;Example 5 :Since the 1950s, both the atmospheric CO2 level and
obesity Obesity is a medical condition, sometimes considered a disease, in which excess body fat has accumulated to such an extent that it may negatively affect health. People are classified as obese when their body mass index (BMI)—a person's ...
levels have increased sharply. :Hence, atmospheric CO2 causes obesity. Richer populations tend to eat more food and produce more CO2. ;Example 6 : HDL ("good")
cholesterol Cholesterol is any of a class of certain organic molecules called lipids. It is a sterol (or modified steroid), a type of lipid. Cholesterol is biosynthesized by all animal cells and is an essential structural component of animal cell membr ...
is negatively correlated with incidence of heart attack. :Therefore, taking medication to raise HDL decreases the chance of having a heart attack. Further research has called this conclusion into question. Instead, it may be that other underlying factors, like genes, diet and exercise, affect both HDL levels and the likelihood of having a heart attack; it is possible that medicines may affect the directly measurable factor, HDL levels, without affecting the chance of heart attack.


Bidirectional causation: A causes B, and B causes A

Causality is not necessarily one-way; in a
predator-prey relationship Predation is a biological interaction where one organism, the predator, kills and eats another organism, its prey. It is one of a family of common feeding behaviours that includes parasitism and micropredation (which usually do not kill the ...
, predator numbers affect prey numbers, but prey numbers, i.e. food supply, also affect predator numbers. Another well-known example is that cyclists have a lower Body Mass Index than people who do not cycle. This is often explained by assuming that cycling increases
physical activity Physical activity is defined as any voluntary bodily movement produced by skeletal muscles that requires energy expenditure.Global Recommendations on Physical Activity for Health, 2009. World Health Organization. Geneva, Switzerland. Accessed 13/ ...
levels and therefore decreases BMI. Because results from prospective studies on people who increase their bicycle use show a smaller effect on BMI than cross-sectional studies, there may be some reverse causality as well (i.e. people with a lower BMI are more likely to cycle).


The relationship between A and B is coincidental

The two variables are not related at all, but correlate by chance. The more things are examined, the more likely it is that two unrelated variables will appear to be related. For example: *The result of the last home game by the
Washington Commanders The Washington Commanders are a professional American football team based in the Washington metropolitan area. The Commanders compete in the National Football League (NFL) as a member club of the league's National Football Conference (NFC) ...
prior to the presidential election predicted the outcome of every presidential election from 1936 to 2000 inclusive, despite the fact that the outcomes of football games had nothing to do with the outcome of the popular election. This streak was finally broken in
2004 2004 was designated as an International Year of Rice by the United Nations, and the International Year to Commemorate the Struggle Against Slavery and its Abolition (by UNESCO). Events January * January 3 – Flash Airlines Flight 60 ...
(or
2012 File:2012 Events Collage V3.png, From left, clockwise: The passenger cruise ship Costa Concordia lies capsized after the Costa Concordia disaster; Damage to Casino Pier in Seaside Heights, New Jersey as a result of Hurricane Sandy; People gather ...
using an alternative formulation of the original rule). *The Mierscheid law, which correlates the Social Democratic Party of Germany's share of the popular vote with the size of crude steel production in Western Germany. *Alternating bald–hairy Russian leaders: A bald (or obviously balding) state leader of Russia has succeeded a non-bald ("hairy") one, and vice versa, for nearly 200 years. *The Bible code, Hebrew words predicting historical events supposedly hidden within the
Torah The Torah (; hbo, ''Tōrā'', "Instruction", "Teaching" or "Law") is the compilation of the first five books of the Hebrew Bible, namely the books of Genesis, Exodus, Leviticus, Numbers and Deuteronomy. In that sense, Torah means the s ...
: the huge number of combinations of letters makes appearances of any word in sufficiently lengthy text statistically insignificant.


Use of correlation as scientific evidence

Much of scientific evidence is based upon a correlation of variables that are observed to occur together. Scientists are careful to point out that correlation does not necessarily mean causation. The assumption that A causes B simply because A correlates with B is often not accepted as a legitimate form of argument. However, sometimes people commit the opposite fallacy of dismissing correlation entirely. That would dismiss a large swath of important scientific evidence. Since it may be difficult or ethically impossible to run controlled double-blind studies, correlational evidence from several different angles may be useful for ''prediction'' despite failing to provide evidence for ''causation''. For example, social workers might be interested in knowing how child abuse relates to academic performance. Although it would be unethical to perform an experiment in which children are randomly assigned to receive or not receive abuse, researchers can look at existing groups using a non-experimental correlational design. If in fact a negative correlation exists between abuse and academic performance, researchers could potentially use this knowledge of a statistical correlation to make predictions about children outside the study who experience abuse even though the study failed to provide causal evidence that abuse decreases academic performance. The combination of limited available methodologies with the dismissing correlation fallacy has on occasion been used to counter a scientific finding. 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 Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath who was active as a mathematician, statistician, biologist, geneticist, and academic. For his work in statistics, he has been described as "a genius who ...
, frequently in its behalf. Correlation is a valuable type of scientific evidence in fields such as medicine, psychology, and sociology. Correlations must first be confirmed as real, and every possible causative relationship must then be systematically explored. In the end, correlation alone cannot be used as evidence for a cause-and-effect relationship between a treatment and benefit, a risk factor and a disease, or a social or economic factor and various outcomes. It is one of the most abused types of evidence because it is easy and even tempting to come to premature conclusions based upon the preliminary appearance of a correlation.


See also


References

; Bundled references


Bibliography

* * {{DEFAULTSORT:Correlation Does Not Imply Causation Causal fallacies Causal inference Covariance and correlation English phrases Misuse of statistics