Correlation does not equal causation
From RationalWiki
Correlation does not equal causation is a quip that expresses the logical fallacy involved in the dichotomy between events that merely have a tendency to occur together, versus sequences of events that are actually causal. The form of fallacy that it addresses is known as post hoc, ergo propter hoc.
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[edit] Explanations and examples
[edit] Simple example
Two events can consistently correlate with each other but not have any causal relationship. An example is the relationship between reading ability and shoe size across the whole population of the United States. If someone performed such a survey they would find that the larger shoe sizes correlate with better reading ability, but this does not mean large feet cause good reading skills. Instead it is caused by the fact that young children have small feet and have not yet (or only recently) been taught to read.
[edit] In science
In science, correlational studies are often used to test for the existence of interesting patterns, but they are never used to claim a cause. In order to make a causal claim you must run an experiment or series of experiments and further studies using the scientific method. This is in order to validate that one event is indeed directly influencing the other and is the reason behind the detected correlation. Many woo and pseudoscience pushers conflate correlation with causation in order to make a claim of validity. For example, if someone gets a common cold, and takes vitamin C, their cold will go away in 5-7 days. The claim is then made that the vitamin C caused the cold to go away. However, the cold would have gone away anyway, whether or not the vitamin C was taken, and so the validity claim is false. The placebo effect is another correlation with "treatment" that quacks use to create false validity.
Correlations seem to tap into a deep part of human psychology. As pattern recognition machines, we are hyper-responsive to any potential signal in our environment. People will often take two completely unrelated events and decide that they must cause each other because they seem to correlate. Someone may decide that when they wear a given shirt they have good luck, this is often combined with a powerful confirmation bias to create magical thinking.
[edit] In parody
In the Church of the Flying Spaghetti Monster, a key "belief" is that global warming is caused by a lack of pirates sailing the oceans. This is shown by a graph correllating increasing surface temperatures of the earth with a decline in the number of pirates. While it is certainly true that priacy has decreased and temperatures have gone up, there is nothing directly connecting the two trends.
