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When we observe two events A and B, how do we find out if they are causally related? One possibility is that A is the cause of B. But there are many other alternatives to consider. Here we discuss some of the main ones. Please refer to the diagram below.

Case #1 - A and B are not causally related

• The fact that A is followed by B does not make A the cause of B. Even when there seems to be a correlation between A and B, it is possible that they are not causally connected. Perhaps the correlation is accidental.
• It is important to consider a control situation where A is absent, and see if B would still occur.
• See also the Simposon's paradox.

Case #2 - A is the cause of B

• For a particular event A to be the cause of B, it is necessary that A happens earlier than B.
• If a type of event A is positively correlated with B, this is one relevant piece of evidence that A is the cause of B. But we need to rule out the other possibilities which are discussed here.
• If we can change B by changing A, this also supports the hypothesis that A is the cause of B. See Mill's method of concomitant variation.

Case #3 - B is the cause of A

• Sometimes correlation goes both ways. The fact that A causes B can explain the correlation, but maybe the reality is that B is the cause of A. For example, people who are depressed tend to have low self-esteem. Perhaps the former is the cause of the latter, but it is also possible that low self-esteem causes depression by making a person socially withdrawn and lacking in motivation. We need further observations to determine which possibility it is.

Case #4 - A and B form a causal loop

• In many cases two causal factors can reinforce each other by forming a causal loop. In the example above, it is more plausible to think that depression affects self-esteem, and a lower self-esteem can cause further depression.
• Of course, causal loops happen only between types of events. If a particular event A is the cause of a particular event B, then A must happen earlier than B and so B cannot be the cause of A.

Case #5 - A is a minor cause of B

• An effect can have more than one cause, and some may be more important than others.

Case #6 - A and B have a common cause

• Young children with larger noses tend to be more intelligent, but it is not because the nose size somehow accelerates cognitive development. Rather young children with larger noses are children who are older, and older children are more intelligent than younger ones because their brains have developed further. So A and B are correlated not because A is the cause of B, but because there is an underlying common cause.

Case #7 - B is a side effect of A

• These are cases where the effect might be wrongly attributed to A when in fact it is due to some side effect of A.
• It has been shown that medicine can have a placebo effect. The subjective belief that one is being treated can bring about relief from an illness even if the medical treatement being given is not really effective against the illness. For example, a patient might report that his pain has decreased as a result to taking a pill, even though the pill is a sugar pill with no effect on pain.