What are some cases in which correlation does imply causation?
Philosophically, there are several cases I can think of:If the effect has an acceptable cause, then the effect is correlated with the cause.If, under a particular formalism a behavior is feasible (prior-to-effect), then the behavior is correlated under the formalism, subject to empirical enquiry.If an effect corresponds ('matches’) the data, it is said to be defeasibly correlated, that is, after the effect.If a cause is correlated with an effect.So that is it: FEASIBLE, DEFEASIBLE, ACCEPTABLE, and CAUSAL.And there is one more which is possible logical correlations.So, FEASIBLE, DEFEASIBLE, ACCEPTABLE, CAUSAL, and SOMETIMES LOGICAL.Note: Some of this is due to postgraduate studies related to my Dad Michael Coppedge who has a PhD from Yale specializing in Venezuelan Democracy.See also:Social Science LinksOr maybe for comparison…Method of Aesthetic-Metaphysical Selection
Correlation vs. causation?
Correlation does not imply causation is a phrase used in the sciences and the statistics to emphasize that correlation between two variables does not imply that one causes the other. Its negation, correlation proves causation, is a logical fallacy by which two events that occur together are claimed to have a cause-and-effect relationship. The fallacy is also known as *** hoc ergo propter hoc (Latin for "with this, therefore because of this") and false cause. By contrast, the fallacy post hoc ergo propter hoc requires that one event occurs before the other and so may be considered a type of *** hoc. In a widely-studied example, numerous epidemiological studies showed that women who were 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. But controlled trials showed that HRT caused a small and significant increase in risk of CHD. Re-analysis of the data showed that women undertaking HRT were more likely to be from socio-economic groups ABC1, with better than average diet and exercise regimes. The two were coincident effects of a common cause, rather than cause and effect as had been supposed.
Correlation and Causation Inconvenient Truth?
Ah! You have probably just added another year of life to each of the surviving Koch brothers! Correlation does not imply causation. So how do we determine causation? This is not an easy task within the science community and that is why the Koch brothers cling so tightly to often having it repeated. This will show some of the difficulties involved with determining causation from any correlation. - http://www.michaelnielsen.org/ddi/if-cor... So did Al Gore try too hard to show a causation with the correlation? Certainly! Just as the denial industry tries to eliminate anthropogenic causation with their claims that since climate has changed before, even before mankind came into existence, then how can mankind be a causation this time? As if everything will always be a natural process and mankind will have no influence on this. You can also look at the probability of any possibility that may exist. When it concerns our current changing climate The Laws of Physics, Chemistry and Thermodynamics will tell us that adding more greenhouse gases to our atmosphere will lead to a warming of our climate above and beyond the natural variations within our climate. To date, no one has been able to show that this is incorrect, in any manner.
What are some examples of "Correlation does not equal causation"?
There are several reasons why correlation doesn't imply causation. I will go into lurking variables and confounding variables, which are types of relationships which illustrate why causation cannot be implied. Confounding VariableExample: When ice cream sales increase, swimming pool deaths also seem to increase. Hence, eating ice cream leads to drownings in swimming pools.In this case, there is a factor that impacts both the cause and effect, a "confounding variable". Generally, during the summer months people buy more ice cream because it is hot outside. Independent of that, people go to the swimming pool a lot more often in the summer as another way to cool off -- which would inevitably lead to more pool drownings. However, this doesn't give you license to say that people are more likely to drown in pools after eating ice cream.Source: Designing and conducting health system research projects, volume 1, Proposal development and fieldworkLurking VariableExample: In educational reporting it is often stated that Asian students in the United States perform better on benchmark X than students of other races. Consequently, there are wild theories about why ethnicity implies educational performance (evolutional, structural differences in brain). However, these claims are made without acknowledging there are other "lurking" variables, such as education level of parents, socioeconomic status of the student, that contribute heavily to the benchmark score. An individual Hispanic or African-American student should have no trouble attaining high scores given similar background otherwise -- simply being Asian is not a determinant of score.Source: AP Statistics Causation and Lurking Variables
Does no correlation always imply no causation?
As a counter example, think of a simple linear regression model with one predictor (x) and one omitted variable (z).[math]\begin{aligned}y_i = \alpha + \beta x_i + \delta z_i + \varepsilon_i\end{aligned}[/math] We know that the bias in this case has the form:[math]\begin{aligned}E[\widehat{\beta}] = \beta + \delta \frac{Cov(x,z)}{Var(x)}\end{aligned}[/math]In the formula you can see that if [math] \beta = - \delta \frac{Cov(x,z)}{Var(x)} [/math] then the expected value of your estimator, and the correlation between y and x, is zero. The story here is that what you observe is "inversely related" in a very specific fashion with the other relevant variable that you don't observe. So the computed correlation will be null, even though you could have a causal link between x an y.
Are there any examples of causation without correlation?
I guess it can be possible. Bear with me, some amateur Chaos Theory ahead.To establish a correlation between variables, you usually start from a set of observations where the precision of the measurements is not arbitrarily small. That is, every correlation that you attempt to establish is stained with uncertainty. Now usually, slightly different initial conditions result in slightly different results. For example Throw the ball with a bit more force upward, it will go a bit higher. That is, if your measurements don’t correlate with the effect, you may assume that there is no causal link.But what if small changes in initial conditions can produce vastly different results? Now the tiny bits of uncertainty in your measurements could very well cause effects that you could not relate to the effects you witness. To cite the common illustration of Chaos Theory: The movements of the wings of a butterfly in Charleroi may cause a typhoon in the Philippines. So assume there is causation, good luck finding the correlation!It is important to note that Chaos does not necessarily imply randomness in the sense that it can arise in wholly deterministic systems. You could technically measure all the movements and position of all atoms in the universe and predict the typhoon from the butterfly’s ride. Good luck finding the correlation tho!Here is a beautiful Creative Commons butterfly picture. Cheers!I think there is a deeper philosophical meaning to this, sometimes, shit just happens. There are no reasons besides the universe up to make your life miserable (or fun, your call ;-)
Correlation doesn't imply causation, but it sure can suggest it. How often does it turn out to be the case that correlation actually is causation?
There are many situations where you would consistently expect correlation to go in the opposite direction as the actual casual relationship.For example, suppose you were an insurance company and wanted to know how the number of fire engines sent to a house fire affected the amount of damage caused. If you blindly ran a regression, you would find that the more fire engines sent to the fire the larger the damage. It would be a mistake to interpret this as evidence that fire engines cause fire damage. What is really happening is that more fire engines are sent to the more severe fires.Economists face a similar problem when trying to measure how the price of a good affects demand. There may be external factors we don't have data on that cause the seller to expect less demand in the next month and therefore lower their prices. If we don't have access to the signal the seller is seeing, then we might incorrectly interpret the data as saying lower prices cause people to buy less.