Correlation Does Not Imply Causation

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Wiki article

Correlation does not imply causation

https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation

Correlation does not imply causation is a phrase used inscienceandstatisticsto emphasize that acorrelationbetween two variables does not

necessarily imply that onecausesthe other.[1][2]

Manystatistical testscalculate correlation betweenvariables. A few go further and calculate the

likelihood of a true causal relationship; examples are theGranger causalitytest andconvergent cross mapping.

The counter assumption, that correlation proves causation, is considered aquestionable causelogical fallacyin that two events

occurring togetherare taken to have a cause-and-effect relationship. This fallacy is also known as cum hoc ergo propter hoc, Latin for "with this,

therefore because of this", and "false cause". A similar fallacy, that an event that follows another wasnecessarily a consequenceof the first event,

is sometimes described aspost hoc ergo propter hoc(Latinfor "after this, therefore because of this").

In a widely studied example, numerousepidemiological studiesshowed that women who were taking combinedhormone replacement

therapy(HRT) also had a lower-than-average incidence ofcoronary heart disease(CHD), leading doctors to propose that HRT was protective

against CHD. Butrandomized controlled trialsshowed that HRT caused a small but statistically significant increase in risk of CHD. Re-analysis of

the data from the epidemiological studies showed that women undertaking HRT were more likely to be from highersocio-economic groups(ABC1),

with better-than-average diet and exercise regimens. The use of HRT and decreased incidence of coronary heart disease were coincident effects

of a common cause (i.e. the benefits associated with a higher socioeconomic status), rather than cause and effect, as had been supposed.

[3]

As with any logical fallacy, identifying that the reasoning behind an argument is flawed does not imply that the resulting conclusion is false. In the

instance above, if the trials had found that hormone replacement therapy caused a decrease in coronary heart disease, but not to the degree

suggested by the epidemiological studies, the assumption of causality would have been correct, although the logic behind the assumption would

still have been flawed.
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Contents

[hide]

1 Usage

2 General pattern

3 Examples of illogically inferring causation from correlation

o 3.1 B causes A (reverse causation)

o 3.2 A and B cause C which causes D (string of causation)

o 3.3 A causes B and B causes A (bidirectional causation)

o 3.4 Third factor C (the commo n-causal variable) causes both A and B

4 Relation to the ecological fallacy

5 Determining causation

o 5.1 In academia

o 5.2 Causality construed from counterfactual states

o 5.3 Causality predicted by an extrapolation of trends

6 Use of correlation as scientific evidence

7 See also

8 References

9 External links

Usage[edit]

Inlogic, the technical use of the word "implies" means "to be asufficientcircumstance." This is the meaning intended by statisticians when they

say causation is not certain. Indeed,p implies q has the technical meaning oflogical implication:if p then q symbolized asp q. That is "if

circumstancep is true, then q necessarily follows." In this sense, it is always correct to say "Correlation does not implycausation."
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However, in casual use, the word "imply" loosely means suggests rather than requires. The idea that correlation and causation are connected is

certainly true; where there is causation, there is likely to be correlation. Indeed, correlation is used when inferring causation; the important point is

that such inferences are made after correlations are confirmed to be real and all causational relationship are systematically explored using large

enough data sets.

Edward Tufte, in a criticism of the brevity of "correlation does not imply causation," deprecates the use of "is" to relate correlation and causation

(as in "Correlation is not causation"), citing its inaccuracy as incomplete.[1]

While it is not the case that correlation is causation, simply stating their

nonequivalence omits information about their relationship. Tufte suggests that the shortest true statement that can be made about causality and

correlation is one of the following:[4]

"Empirically observed covariation is a necessary but not sufficient condition for causality."

"Correlation is not causation but it sure is a hint."

General pattern[edit]

For any two correlated events A and B, the following relationships are possible:

A causes B;

B causes A;

A and B are consequences of a common cause, but do not cause each other;

There is no connection between A and B; the correlation is coincidental.

Less clear-cut correlations are also possible. For example, causality is not necessarily one-way; in apredator-prey relationship, predator numbers

affect prey, but prey numbers, i.e. food supply, also affect predators.

The cum hoc ergo propter hoclogical fallacy can be expressed as follows:

1. A occurs in correlation with B.

2. Therefore,A causes B.
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In this type of logical fallacy, one makes a premature conclusion aboutcausalityafter observing only acorrelationbetween two or more factors.

Generally, if one factor (A) is observed to only be correlated with another factor (B), it is sometimes taken for granted thatA is causing B, even

when no evidence supports it. This is a logical fallacy because there are at least five possibilities:

1. A may be the cause ofB.

2. B may be the cause ofA.

3. some unknown third factorCmay actually be the cause of bothA and B.

4. there may be a combination of the above three relationships. For example, B may be the cause ofA at the same time asA is the cause

ofB (contradicting that the only relationship betweenA and B is thatA causes B). This describes aself-reinforcingsystem.

5. the "relationship" is acoincidenceor so complex or indirect that it is more effectively called a coincidence (i.e. two events occurring at the

same time that have no direct relationship to each other besides the fact that they are occurring at the same time). A largersample

sizehelps to reduce the chance of a coincidence, unless there is asystematic errorin the experiment.

In other words, there can be no conclusion 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 requires further investigation, even when the

relationship betweenA and B isstatistically significant, a largeeffect sizeis observed, or a large part of thevariance is explained.

Examples of illogically inferring causation from correlation[edit]

This section includes alist of references, related reading orexternal links, but the sources of this section remain unclear because

it lacksinline citations. Pleaseimprovethis article by introducing more precise citations. (July 2012)

B causes A (reverse causation)[edit]

Example 1

The more firemen fighting a fire, the bigger the fire is observed to be.

Therefore firemen cause an increase in the size of a fire.
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In this example, the correlation between the number of firemen at a scene and the size of the fire does not imply that the fi remen cause

the fire. Firemen are sent according to the severity of the fire and if there is a large fire, a greater number of firemen are sent; therefore, it

is rather that fire causes firemen to arrive at the scene. So the above conclusion is false.

Example 2

The faster windmills are observed to rotate, the more wind is observed to be.

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 doesnt need windmills to exist, while windm ills

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.A and B cause C which causes D (string of causation)[edit]

Lack of religion is associated with increased rates of depression.

Therefore, lack of religion directly causes increased rates of depression.

In this example, the correlation between lack of religion and depression does not imply that lack of religion causes

depression. Depression is caused in part by how people are treated. Some cultures might be suspicious of people who

have a lack of religion, so people who have a lack of religion are more likely to be discriminated against and to fall into

depression. So the above conclusion is false.A causes B and B causes A (bidirectional causation)[edit]

Increased pressure is associated with increased temperature.

Therefore pressure causes temperature.

Theideal gas law, , describes the direct relationship between pressure and temperature (along

with other factors) to show that there is a direct correlation between the two properties. For a fixed volume and

mass of gas, an increase in temperature will cause an increase in pressure; likewise, increased pressure will
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cause an increase in temperature. This demonstrates bidirectional causation. The conclusion that pressure

causes temperature is true but is not logically guaranteed by the premise.

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

Main article:Spurious relationship

All these examples deal with alurking variable, which is simply a hidden third variable that affects both causes

of the correlation; for example, the fact that it is summer in Example 3. 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

Sleepingwith one'sshoeson is strongly correlated with waking up with aheadache.

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 beddrunk, 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 developmyopiain later life.

Therefore, sleeping with the light on causes myopia.

This is a scientific example that resulted from a study at theUniversity of

PennsylvaniaMedical Center. Published in the May 13, 1999 issue ofNature,[5]

the study

received much coverage at the time in the popular press.[6]

However, a later study atOhio

State Universitydid not find thatinfantssleeping 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
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bedroom.[7][8][9][10]

In this case, the cause of both conditions is parental myopia, and the above-

stated conclusion is false.

Example 3

Asice creamsales increase, the rate ofdrowningdeaths increases sharply.

Therefore, ice cream consumption causes drowning.

The aforementioned example fails to recognize the importance of time and

temperature in relationship to ice cream sales. Ice cream is sold during the

hotsummermonths 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 asswimming. 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 rvalue (strength of

correlation) of +.59.[11]

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 which 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
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Since the 1950s, both the atmosphericCO2level andobesitylevels have increased sharply.

Hence, atmospheric CO2 causes obesity.

Richer populations tend to eat more food and consume more

energy

Example 6

HDL("good")cholesterolis negatively correlated with incidence of heart attack.

Therefore, taking medication to raise HDL will decrease the chance of having a heart attack.

Further research[12]

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.

Relation to the ecological fallacy[edit]

There is a relation between this subject-matter and

theecological fallacy, described in a 1950 paper by William

S. Robinson.[13]

Robinson shows that ecological

correlations, where the statistical object is a group of

persons (i.e. an ethnic group), does not show the same

behaviour as individual correlations, where the objects of

inquiry are individuals: "The relation between ecological

and individual correlations which is discussed in this paper

provides a definite answer as to whether ecological

correlations can validly be used as substitutes for individual
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correlations. They cannot." (...) "(a)n ecological correlation

is almost certainly not equal to its corresponding individual

correlation."

Determining causation[edit]

In academia[edit]

Main articles:CausalityandCausality (physics)

The point of view that correlation implies causation may be

regarded as a theory ofcausalitywhich is somewhat

inherent to the field ofstatistics. Withinacademiaas a

whole, the nature of causality is systematically investigated

from severalacademic disciplines,

includingphilosophyandphysics.

In academia, there is a significant number of theories on

causality; The Oxford Handbook of Causation (Beebee et

al. 2009) encompasses 770 pages. Among the more

influential theories withinphilosophyareAristotle'sFour

causesandAl-Ghazali'soccasionalism.[14]

David

Humeargued that causality is based on experience, and

experience similarly based on the assumption that the

future models the past, which in turn can only be based on

experience leading tocircular logic. In conclusion, he

asserted thatcausality is not based on actual reasoning:

only correlation can actually be perceived.[15]

Immanuel

Kant, according to Beebee et al., held that "a causal
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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 in

would then lack strict universality, or necessity".[16]

Outside the field of philosophy, theories of causation can

be identified inclassical mechanics,statistical

mechanics,quantum

mechanics,spacetimetheories,biology,social sciences,

andlaw.[17]

In order for a correlation to be established as

causal withinphysics, it is normally understood that the

cause and the effect must be connected through a

localmechanism(cf. for instance the concept ofimpact) or

anonlocalmechanism (cf. the concept offield), in

accordance with knownlaws of nature.

From the point of view ofthermodynamics, universal

properties of causes as compared to effects have been

identified through theSecond law of thermodynamics,

confirming the ancient, medieval andDescartian[18]

view

that "the cause is greater than the effect" for the particular

case ofthermodynamic free energy. This, in turn, would

appear to be challenged by popular interpretations of the

concepts ofnonlinear systemandButterfly effect, in which

small causes are regarded to be able to cause large effects

due to, respectively, unpredictability and an unlikely

triggering of large amounts ofpotential energy.
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Causality construed from counterfactualstates[edit]

See also:Verificationism

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. This is referred

to as the Fundamental Problem of Causal Inference it is

impossible to directly observe causal effects.[19]

A major goal of scientificexperimentsand statistical

methods is to approximate as best as possible the

counterfactual state of the world.[20]

For example, one could

run anexperiment on identical twinswho 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, this would be strong evidence that studying
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(or going to the amusement park) had a causal effect on

test scores. In this case, correlation between studying and

test scores would almost certainly imply causation.

Well-designedexperimental studiesreplace equality of

individuals as in the previous example by equality of

groups. This is achieved by randomization of the subjects

to two or more groups. Although not a perfect system, the

likeliness of being equal in all aspects rises with the

number of subjects placed randomly in the

treatment/placebogroups. From the significance of the

difference of the effect of the treatment vs. the placebo,

one can conclude the likeliness of the treatment having a

causal effect on the disease. This likeliness can be

quantified in statistical terms by theP-value[dubiousdiscuss]

.

Causality predicted by an extrapolation oftrends[edit]

See also:Inertia

When experimental studies are impossible and only pre-

existing data are available, as is usually the case for

example ineconomics,regression analysiscan be used.

Factors other than the potential causative variable of

interest are controlled for by including them as regressors

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
https://en.wikipedia.org/wiki/Experimenthttps://en.wikipedia.org/wiki/Experimenthttps://en.wikipedia.org/wiki/Experimenthttps://en.wikipedia.org/wiki/Placebohttps://en.wikipedia.org/wiki/Placebohttps://en.wikipedia.org/wiki/Placebohttps://en.wikipedia.org/wiki/P-valuehttps://en.wikipedia.org/wiki/P-valuehttps://en.wikipedia.org/wiki/Wikipedia:Disputed_statementhttps://en.wikipedia.org/wiki/Wikipedia:Disputed_statementhttps://en.wikipedia.org/wiki/Wikipedia:Disputed_statementhttps://en.wikipedia.org/wiki/Talk:Correlation_does_not_imply_causation#Dubioushttps://en.wikipedia.org/wiki/Talk:Correlation_does_not_imply_causation#Dubioushttps://en.wikipedia.org/wiki/Talk:Correlation_does_not_imply_causation#Dubioushttps://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=12https://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=12https://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=12https://en.wikipedia.org/wiki/Inertiahttps://en.wikipedia.org/wiki/Inertiahttps://en.wikipedia.org/wiki/Inertiahttps://en.wikipedia.org/wiki/Economicshttps://en.wikipedia.org/wiki/Economicshttps://en.wikipedia.org/wiki/Economicshttps://en.wikipedia.org/wiki/Regression_analysishttps://en.wikipedia.org/wiki/Regression_analysishttps://en.wikipedia.org/wiki/Regression_analysishttps://en.wikipedia.org/wiki/Regression_analysishttps://en.wikipedia.org/wiki/Economicshttps://en.wikipedia.org/wiki/Inertiahttps://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=12https://en.wikipedia.org/wiki/Talk:Correlation_does_not_imply_causation#Dubioushttps://en.wikipedia.org/wiki/Wikipedia:Disputed_statementhttps://en.wikipedia.org/wiki/P-valuehttps://en.wikipedia.org/wiki/Placebohttps://en.wikipedia.org/wiki/Experiment


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causation due the presence of bidirectional causation) can

be avoided by using explanators (regressors) that are

necessarilyexogenous, 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

variablesfor the explanators (chosen based on their known

exogeneity), etc. SeeCausality#Statistics and

Economics.Spurious correlationdue to 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 the model. In

particular, underlying time trends of both the dependent

variable and the independent (potentially causative)

variable must be controlled for by including time as another

independent variable.[citation needed]

Use of correlation as scientificevidence[edit]

Much of scientific evidence is based upon a correlation of

variables[21]

they 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
https://en.wikipedia.org/wiki/Dependent_and_independent_variables#Use_in_statisticshttps://en.wikipedia.org/wiki/Dependent_and_independent_variables#Use_in_statisticshttps://en.wikipedia.org/wiki/Dependent_and_independent_variables#Use_in_statisticshttps://en.wikipedia.org/wiki/Exogenoushttps://en.wikipedia.org/wiki/Exogenoushttps://en.wikipedia.org/wiki/Exogenoushttps://en.wikipedia.org/wiki/Instrumental_variableshttps://en.wikipedia.org/wiki/Instrumental_variableshttps://en.wikipedia.org/wiki/Instrumental_variableshttps://en.wikipedia.org/wiki/Instrumental_variableshttps://en.wikipedia.org/wiki/Causality#Statistics_and_Economicshttps://en.wikipedia.org/wiki/Causality#Statistics_and_Economicshttps://en.wikipedia.org/wiki/Causality#Statistics_and_Economicshttps://en.wikipedia.org/wiki/Causality#Statistics_and_Economicshttps://en.wikipedia.org/wiki/Spurious_relationshiphttps://en.wikipedia.org/wiki/Spurious_relationshiphttps://en.wikipedia.org/wiki/Spurious_relationshiphttps://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=13https://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=13https://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=13https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_note-Steven-21https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_note-Steven-21https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_note-Steven-21https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_note-Steven-21https://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=13https://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttps://en.wikipedia.org/wiki/Spurious_relationshiphttps://en.wikipedia.org/wiki/Causality#Statistics_and_Economicshttps://en.wikipedia.org/wiki/Causality#Statistics_and_Economicshttps://en.wikipedia.org/wiki/Instrumental_variableshttps://en.wikipedia.org/wiki/Instrumental_variableshttps://en.wikipedia.org/wiki/Exogenoushttps://en.wikipedia.org/wiki/Dependent_and_independent_variables#Use_in_statistics


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people commit the opposite fallacy dismissing correlation

entirely, as if it does not suggest causation. This would

dismiss a large swath of important scientific evidence.[21]

In conclusion, correlation is a valuable type of scientific

evidence in fields such as medicine, psychology, and

sociology. But first correlations must be confirmed as real,

and then every possible causative relationship must be

systematically explored. In the end correlation can be used

as powerful 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. But it is also 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[edit]

Affirming the consequent

Chain reaction

Confirmation bias

Confounding

Design of experiments

Domino effect

Ecological fallacy

Four causes
https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_note-Steven-21https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_note-Steven-21https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_note-Steven-21https://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=14https://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=14https://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=14https://en.wikipedia.org/wiki/Affirming_the_consequenthttps://en.wikipedia.org/wiki/Affirming_the_consequenthttps://en.wikipedia.org/wiki/Chain_reactionhttps://en.wikipedia.org/wiki/Chain_reactionhttps://en.wikipedia.org/wiki/Confirmation_biashttps://en.wikipedia.org/wiki/Confirmation_biashttps://en.wikipedia.org/wiki/Confoundinghttps://en.wikipedia.org/wiki/Confoundinghttps://en.wikipedia.org/wiki/Design_of_experimentshttps://en.wikipedia.org/wiki/Design_of_experimentshttps://en.wikipedia.org/wiki/Domino_effecthttps://en.wikipedia.org/wiki/Domino_effecthttps://en.wikipedia.org/wiki/Ecological_fallacyhttps://en.wikipedia.org/wiki/Ecological_fallacyhttps://en.wikipedia.org/wiki/Four_causeshttps://en.wikipedia.org/wiki/Four_causeshttps://en.wikipedia.org/wiki/Four_causeshttps://en.wikipedia.org/wiki/Ecological_fallacyhttps://en.wikipedia.org/wiki/Domino_effecthttps://en.wikipedia.org/wiki/Design_of_experimentshttps://en.wikipedia.org/wiki/Confoundinghttps://en.wikipedia.org/wiki/Confirmation_biashttps://en.wikipedia.org/wiki/Chain_reactionhttps://en.wikipedia.org/wiki/Affirming_the_consequenthttps://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=14https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_note-Steven-21


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Mierscheid Law

Normally distributed and uncorrelated does not imply

independent

Observational study

Occam's razor

Pirates and global warming

Synchronicity

References[edit]

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PowerPoint: Pitching Out Corrupts Within.Cheshire,

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13. ^Robinson, W.S. (1950). "Ecological Correlations and

the Behavior of Individuals".American Sociological

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14. ^Beebee et al., 2009

15. ^David Hume (Stanford Encyclopedia of Philosophy)

16. ^Beebee et al. 2009

17. ^Beebee et al. 2009

18. ^Lloyd, A.C., The principle that the cause is greater

than its effect, Pronesis 21(2), 1976

19. ^Paul W. Holland. 1986. "Statistics and Causal

Inference" Journal of the American Statistical

Association, Vol. 81, No. 396. (Dec., 1986), pp. 945

960.

20. ^Judea Pearl. 2000. Causality: Models, Reasoning, and

Inference, Cambridge University Press.

21. ^abNovella."Evidence in Medicine: Correlation and

Causation".Science and Medicine. Science-Based

Medicine.

External links[edit]

"The Art and Science of cause and effect": a slide

show and tutorial lecture by Judea Pearl

Causal inference in statistics: An overview, by Judea

Pearl (September 2009)
https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-13https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-13https://en.wikipedia.org/wiki/Digital_object_identifierhttps://en.wikipedia.org/wiki/Digital_object_identifierhttp://dx.doi.org/10.2307%2F2087176http://dx.doi.org/10.2307%2F2087176http://dx.doi.org/10.2307%2F2087176https://en.wikipedia.org/wiki/JSTORhttps://en.wikipedia.org/wiki/JSTORhttp://www.jstor.org/stable/2087176http://www.jstor.org/stable/2087176http://www.jstor.org/stable/2087176https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-14https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-14https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-15http://plato.stanford.edu/entries/hume/#CausationNhttp://plato.stanford.edu/entries/hume/#CausationNhttp://plato.stanford.edu/entries/hume/#CausationNhttps://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-16https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-16https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-17https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-17https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-18https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-18https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-19https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-19https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-20https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-20https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-Steven_21-0https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-Steven_21-0https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-Steven_21-1https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-Steven_21-1https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-Steven_21-1http://www.sciencebasedmedicine.org/index.php/evidence-in-medicine-correlation-and-causation/http://www.sciencebasedmedicine.org/index.php/evidence-in-medicine-correlation-and-causation/http://www.sciencebasedmedicine.org/index.php/evidence-in-medicine-correlation-and-causation/http://www.sciencebasedmedicine.org/index.php/evidence-in-medicine-correlation-and-causation/https://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=16https://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=16https://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=16http://singapore.cs.ucla.edu/LECTURE/lecture_sec1.htmhttp://singapore.cs.ucla.edu/LECTURE/lecture_sec1.htmhttp://ftp.cs.ucla.edu/pub/stat_ser/r350.pdfhttp://ftp.cs.ucla.edu/pub/stat_ser/r350.pdfhttp://ftp.cs.ucla.edu/pub/stat_ser/r350.pdfhttp://singapore.cs.ucla.edu/LECTURE/lecture_sec1.htmhttps://en.wikipedia.org/w/index.php?title=Correlation_does_not_imply_causation&action=edit&section=16http://www.sciencebasedmedicine.org/index.php/evidence-in-medicine-correlation-and-causation/http://www.sciencebasedmedicine.org/index.php/evidence-in-medicine-correlation-and-causation/https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-Steven_21-1https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-Steven_21-0https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-20https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-19https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-18https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-17https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-16http://plato.stanford.edu/entries/hume/#CausationNhttps://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-15https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-14http://www.jstor.org/stable/2087176https://en.wikipedia.org/wiki/JSTORhttp://dx.doi.org/10.2307%2F2087176https://en.wikipedia.org/wiki/Digital_object_identifierhttps://en.wikipedia.org/wiki/Correlation_does_not_imply_causation#cite_ref-13


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