But how do you know A causes B?

1. The behavior (observations of A followed by B) is repeated.
2. You find a statistical correlation between A and B.
3. You can duplicate the behavior under "controlled conditions."

The process of testing and getting FDA (USA) approval for a new drug uses all three of these methods -- the process is rigorous. In some other cases, you might be able to get by with just one. But if you don't have at least one in hand, you may not get away with saying it -- at least for causes that are non-trivial.

A trivial case, such as A=dropping an egg and B=making a mess on the kitchen floor, is something you don't have to actually demonstrate to anyone. But something trivial like that seldom comes up. If it does, then you have to wrestle with the concept of grandmothering (i.e. telling your audience what they already know). Which is another subject.

Here are some situations that are easily mistaken for A -> B:

1. !B -> A (something that's not B causes A)

   This often happens in the case of government regulation. We may *think* that government regulation leads to increased public safety (with respect to some product or system), when in reality it's more like something has gone wrong with some samples of the product, or some case of the system, and the resulting public outcry has caused the government to step in. Once the government does step in, then you have to observe all over again to be sure the intervention has the desired effect. You can't assume it.

2. A -> ~B (A causes something that's similar to or related to B)

   When this happens, sometimes engineers will infer B from the ~B they know. Simple examples include using chemical level in a process tank to infer flow rate into the tank; or using a mathematical "observer" on a spacecraft to infer the location of the Sun when the spacecraft is on the dark side of its orbit and can't pick up the Sun on its sensors.

3. A -> (B + dB) <- some other cause you can't see (or measure)

The cause you can't see could be noise (which comes in in nearly all cases of measurement, whether automated or via surveys of people's feelings) or some environmental disturbance. The effect you observe is slightly different from the effect directly caused by A. If you assume B + dB actually IS B, however, you can end up taking other actions that can make things worse -- perhaps even driving you further away from B.

If you can establish that A -> B, then you may want to go a step further, to A -> B -> C. There are some things that you have to prove beyond the proof of single cause/single effect as given above:

1. A, B, and C actually have to be along the same chain of events in the first place.
2. A, B, and C have to be sequential and always in the same sequence.
3. You know the sequence.

Here are some situations that are easily mistaken for A -> B -> C:

1. A -> B and A -> C directly (B is just a side effect)
2. A is sitting by itself, and B -> C (no relationship between A and C at all, through B or otherwise)

   This one may be an example of the fallacy of assuming A -> C just because C happened after A.

3. A -> B, and C is sitting by itself (meaning that C would have happened anyway, or at least whether A caused B or not)

   Ditto.

4. A -> B -> (other events) -> C (other critical events occur in the sequence)

   Here you have to be careful: first you have to find any other critical events; then you have to make sure those links in the causal chain aren't acted upon in any of the other ways given above. The more critical events, obviously the trickier it is to prove that A -> C by whatever path you may choose. This often is seen in production lines, where causality must be shown in order to effectively improve quality in the overall process; it's also seen in complex processes like power plants, where in order to optimize the process (by any measurement you'd care to make), you have to do something less than optimal to individual steps within the process.

Reference

Ramage and Bean, Writing Arguments. Needham Heights, MA: Allyn & Bacon, 1998.