Sunday, October 10, 2010

Inferences of Cause and Correlation

Last time we spoke about the strongest kind of inference; one of example. The reason it is potentially the strongest is because by definition, an example exists. Sometimes we ask people to use reason alone to create an inference (that is, to connect evidence to a claim). Given the choice, evidence is more compelling if it can be viewed as something that exists to directly support the claim instead of something that can be reasoned to support the claim.

This time, we’ll talk about two more inferences; inference of Cause and inference of Correlation. Causal inference describes the instance when one thing causes another. That is one thing (like a rainstorm) causes another (like a flood) to happen. Note that many things can cause a flood, one of them being a rainstorm. Many, many times things that CAN cause others to happen are NOT the cause in a given instance. Let’s say that your sales manager says that “sales are terrible right now because of the economy.” You can look through your company information and see sales are indeed down, and you can look in the paper and see that the economy is in trouble. Both those things are happening.

However, is there any proof (valid causal inference) that the economic problems CAUSED the low sales? In our example, not yet.

In order to show that the economy is responsible for our sales dip, we would have to ask:

-Are there other things that could cause low sales?
-Have any of them happened?
-If so, how do we know it is not one of those?

If the only thing that can cause low sales is the economy AND we now that the economy is floundering, then we can accept the inference because there is nothing else that can cause the phenomenon of low sales. Intuitively, though, we know there are more things, for instance:

-Product quality issues
-Competition and Disruptive technologies
-Poor customer service
-Poor sales staff performance

Knowing that there are alternative causes doesn’t tell us that the economy isn’t the cause, but it does tell us that it COULD be something else. One would need to look at the alternative causes and analyze their contribution (if any) to the issue of low sales before one could really accept the causal inference of poor economy to low sales.
For this reason, cause is difficult to analyze thoroughly in a fast paced business environment and thorough analysis is sometimes not done in favor of dealing with the suspected cause. This is sometimes referred to as “jumping to solutions” and often can worsen the symptoms.

In our case, let’s say that the economy did affect our customers, but also a competitor had released a competing product with a few features that the customers liked and we were having a customer service problem as well. Reacting as if the problem was purely one of economics (and therefore would go away when the economy picks up) could have very serious consequences to our business. This is the fallacy of false cause.

In testing casual inferences, it is critical to determine that one thing indeed influences another, and isn’t merely being attributed. For instance, the “economy vs. sales levels” question that I raised above is too complex to be so simply explained away. Sales level rise and fall based on many things, and there most certainly are many factors that can cause price fluctuations. In fact, a strong argument can be made that sales levels frequently drop after a period when there has been too much speculation and the market needs to “normalize” in order to get healthy. So if you plan on attributing lowered sales levels to a single cause, then you need to be able to at least give some reasoning as to why the drop shouldn’t be attributed to any other reason and bring lots of evidence.

One must evaluate whether there are multiple causes and not just one. For instance, while it is true that the economy can cause sales levels to drop, so can poor customer support. If customer service was unsatisfactory to the point that customers started looking for other suppliers, it may not be the economy that caused your sales levels to go.

One must also remember that one cause can have multiple effects, for instance turning off the water main in order to stop a pipe from leaking and spilling water on the floor. It will work because there is certainly a causal relationship between the presence of water in the leaky pipe and water on the floor, but there are other effects that shutting the water main have that are perhaps unwanted.

One must evaluate whether there are common causes underlying the supposed cause and effect relationship. For example, I recently read that American babies with low birth weight tend not to grow up to go to college. Reading this, I immediately thought that a common cause underlying both conditions (low birth weight and failure to go to college) is poverty. In checking, I found that the author had misinterpreted some statistics and “bent them” to try to show why it is important for mother’s to try to achieve higher birth weights!

One must evaluate whether one is confusing temporality with causality. In other words, just because something happens BEFORE something else, doesn’t mean it is the CAUSE of it. Just because I correct someone’s work and later I start having trouble with them on the job doesn’t mean that the two events are causally
related. It could be that, once I correct them, my attitude changes about them
and they pick up my attitude. Or that the reason I am correcting them is that they are overwhelmed by the work and they would rather work somewhere else and eventually this starts to manifest as “trouble” to me.

There are many fallacies associated with causal inference. Here are two:

- The Post Hoc fallacy – (if something occurs BEFORE an event, then it means it CAUSED the event.) This fallacious thinking is used all the time. When you hear
it, question it. Just because the shack burned down after Johnny was seen near
it doesn’t mean that Johnny is guilty of burning it down. Nor does it mean he is innocent.

- Appeal from Ignorance – (Well, if the economy DIDN’T cause sales levels to drop, then what did?) This appeal is meant to put the listener in a position of either offering an alternate explanation or accepting the one offered. Remember there is a third choice – that something else caused the event and you don’t know what it is. You needn’t ever buckle to the appeal from ignorance.

Correlation differs from cause in that does NOT try to explain a relationship between two things like cause does (one thing CAUSES another). It merely
describes that two things tend to occur with each other. Correlation is called “Inference of Sign” for this reason – it says that one thing is a SIGN of another, without explaining the relationship.

My favorite example of this is the relationship of college degrees to competence. If a person has a college degree in a given subject, we accept it as a sign that they have expertise in the subject. Is it certain that they do? No. Are there other things that can account for expertise? Yes? However, when all things are considered, a college degree is a SIGN of expertise in that subject. We aren’t trying to explain the relationship. That is trying to say that college degrees CAUSE people to be competent. We are just expressing that one thing (competence) tends to accompany another (a degree) and that we can count on that relationship holding within certain limits.

How do we test correlative inference? The classic tests for Inference from Sign are:

- Does the sign usually appear with the thing signified (ex: college degree and expertise)?
- Does the sign frequently appear without the thing signified (ex: college degree and incompetence)?
- Are there countersigns (absence of college degree and expertise)?
- Could the correlation be a coincidence?
- Is it really a causal relationship?


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