Causation When C causes E, C helps to make E happen. Learning about - - PowerPoint PPT Presentation

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Reasoning about Causation

Justin C. Fisher SMU Dept. of Philosophy

Causation

When C causes E, C helps to make E happen.

Learning about causes allows us… … to predict what effects will occur … to bring about desirable outcomes … to prevent undesirable outcomes Science often seeks evidence of what causes what. Pseudo-science often makes bad causal claims.

Which causal claims should we believe?

The Cause of E versus A Cause of E

Most events had many causes working together. Q: What caused the fire? A: That the match was struck, that the match-tip contained certain chemicals, that the room contained

• xygen, etc…

Particular Events vs Types of Events

We can often say which particular billiard ball caused another to move. We can’t yet say which particular cigarettes caused someone’s cancer. But we do have strong evidence that one type of event (smoking) causes another type

• f event (cancer).

9/26/2016 2 Decapitation causes death

(virtually 100% of the time)

Deterministic Causation versus Probabilistic Causation

Smoking causes death

(it increases the probability

• f dying sooner)

Post Hoc, Ergo Propter Hoc

(After this, therefore because of this.)

Causation and Counterfactuals

“C caused E” is roughly equivalent to

“if C had differed in certain ways, then E

would have differed too.”

Counterfactuals may be hard to assess for particular events. Our best guide usually is to look at other similar events where the alleged cause differed, and to observe whether the alleged effect differed too.

Correlation

“Trait A is correlated with Trait B in a particular sample” = the percentage of sample members with B is higher among those that have A than among those that lack A. = learning that a sample member has A statistically increases the probability that it has B (and vice versa). In the strongest possible (aka perfect) correlation, everything that is an A is a B, and vice versa. In a very weak correlation, A’s are only a tiny bit more likely to be B’s than non-A’s are. In a negative correlation, A’s are less likely to be B’s than non-A’s are (i.e., not-A is positively correlated with B).

(Correlation can also be defined for measurable traits, like height and mass, not just binary traits that you either have or lack.)

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Causation = Correlation

We’ll consider: Cases of Causation without Correlation Cases of Correlation without Causation

Causation without Correlation

(Correlation is always defined with respect to a sample. Depending on what’s in the sample, correlations can be weird.)

Let’s imagine: Eating olive oil causes longer life. Eating garlic causes shorter life. In our sample, the olive oil eaters also are the garlic eaters. In our sample, eating olive

• il causes, but need not be

correlated with, longer life.

Causation without Correlation

(Correlation is always defined with respect to a sample. Depending on what’s in the sample, correlations can be weird.)

Let‘s imagine: Eating olive oil causes longer life. Eating garlic causes shorter life. In our sample, the olive oil eaters also are the garlic eaters. In our sample, eating olive

• il causes, but need not be

correlated with, longer life. Moral #1: If you want causal relations to show up as correlations in a sample, it’s best to use a sample that is diverse, without other potential inhibitors being correlated with the potential causes we’re considering.

Causation without Correlation

(Correlation is always defined with respect to a sample. Depending on what’s in the sample, correlations can be weird.)

Let‘s imagine: Eating olive oil causes longer life. Eating garlic causes shorter life. In our sample, the olive oil eaters also are the garlic eaters. In our sample, eating olive

• il causes, but need not be

correlated with, longer life. Moral #2: If you can’t get (or make) a diverse sample without other correlations built into it, then you’ll need to “control for” other factors. E.g., if we attend just to garlic eaters, and if this sub-sample is large enough, then a correlation between olive oil and longevity should appear within it (and similarly within the non-garlic-eaters).

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Correlation without Causation (1)

Some observed correlations are pure coincidences.

One way to address this concern is to enlarge the sample to include many instances where C is present, many where C is absent, many where E is present and many where E is absent. The larger the (random) sample, the less risk a strong correlation would be produced by mere coincidence.

Correlation without Causation (2)

Some correlations are between two effects of a common cause.

E.g., a visible storm might cause pilot to turn on sign, then also cause turbulence.

Observational studies can attempt to “control for” potential common causes (as described earlier). In random controlled trials, randomly triggering either effect of a common cause will not increase the likelihood of the other effect.

Correlation without Causation (3) How to distinguish Cause from Effect

Pay close attention to timing: causes precede effects. Use random controlled trials. The effect should occur more often in cases where we randomly trigger the cause than in cases where we don’t. In contrast, the cause should not vary in response to our randomly triggering the effect.