August 27, 2008

Types of Causality, III

author_brad By Bradley Wright

It’s the end of summer, the beaches are hot, friends are home, and you’re using up what little vacation time you have left. What better thing to do than think about causality? I know that I am!

Today I’m writing about two more concepts associated with causality. The overriding point of this series is to help you think through the multi-faceted nature of causality. Everyday we use causal language—this happened because of that—but we’re not always clear in our thinking about what is, and is not, a cause. So, on to more types of causation:

Interaction effects. An interaction effect occurs when the effect of one variable on another varies by levels of a third variable. Let’s say that we’re looking at how levels of variable “A” affects variable “B”, but we find out the effect of “A” varies by how much of “C” we have. If so, that’s an interaction effect.

Interaction effects are perhaps best described by example.

Would drinking a beer or two or three make you feel light-headed? Well, it depends on various factors, including what you’ve eaten. If you have just had a full meal, the food in your stomach slows down the absorption of alcohol which in turn means it has less effect on you. However, if you’re drinking on an empty clip_image002stomach, then the alcohol will have a much greater effect. This is an interaction effect. The effect of alcohol (A) on how you feel (B) depends on what you’ve eaten (C). We could think of other “C” variables as well, variables that alter the effect of alcohol on you. It also varies by your body weight, how much you’re used to drinking, your gender, and your metabolism.

Here’s another example of an interaction effect. I like watching late-night talk shows, and I find the monologues to be really funny. Recently, however, I’ve tried watching them during the day on the shows’ websites, and I didn’t enjoy them at all. The same joke, told late at night, will have me in stitches but in the middle of the day bores me. To really enjoy them I think that I have to be tired and not planning to do anything else. So, the effect of late-night jokes (A) on my laughing (B) varies by the time of day (C).

Causation & correlation. A statistical truism is that correlation does not necessarily imply causation. This reflects the fact that two variables can be spuriously correlated.

Just for laughs and giggles, though, let me point out that the opposite is true as well. Causation does not necessarily imply correlation. That is, some variable “A” can be a cause of “B” without actually being correlated with it. I know what you’re thinking—this must be some kind of sociological magic, but, really, it’s true. Here’s how it works.

The cause, “A”, might increase “B” through some mechanisms, say “C.” It might also decrease these “B” through other mechanisms, say “D”. As such, “A” has a causal impact on “B” even though there is no association between levels of “A” and “B” in a population of people.

Suppose that you ate a dark-chocolate candy bar. One of those 65% cocoa ones—you know what I’m talking about. Now, the other 35% is probably sugar and butter, which have a lot of calories which should increase you’re weight. But, the caffeine in the bar might give you enough energy so that you bounce clip_image002[5]around the house for awhile, thus burning off the calories. As such, eating dark chocolate has a causal linkage to weight gain but is not correlated with gaining weight. 

I actually used this principle in some research I conducted. For some time, criminologists have had theories about why poor people commit more crime. They have more strain put on them, fewer opportunities for conventional work, etc…. However, self-reported studies found little correlation between social class and crime. Why? Turns out that there are mechanisms though which being poor lowers crime rates, or, put more intuitively, being wealthy promotes crime. The wealthy are more likely to think that they can get away with crime, so they are less deterred by possible punishments. They also foster an ethos of risk-taking, which associates with more crime.

So, social class both increases and decreases criminal behavior, and we have causation without correlation. Cool, huh? 

Okay, back to your regular summertime activities.

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Comments

Love the opening and closing. You have a gift for making a subject which I would not normally care about very interesting.

Fascinating!

Thank you Ben and Jutta. It could just be that I pick topics people don't care about... ;-)

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