Correlations and Causality on the GRE – Part I

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Comic via xkcd

The makers of the GRE frequently create arguments in Reading Comprehension passages that conflate correlation with causation, and thus you must understand the distinction between the two.

In statistics, "correlation" refers to a statistical relationship between two interdependent variables (e.g. height and weight, studying and grades, etc.). A correlation alone does not prove a causal relationship, but it can suggest that a causal relationship does, in fact, exist. For instance, a correlation between height and weight cannot be interpreted to mean that either one causes the other. On the other hand, a correlation between studying and grades implies that studying causes higher grades, but the correlation alone is not sufficient to prove that such a causal relationship exists.

An empirically observable correlation between two interdependent variables is a necessary, but not sufficient, condition for causality.

On the GRE, correlations usually function as evidence presented in support of a causal conclusion:

Premise: A and B are correlated

Conclusion: A causes B

Usually, the problem with such arguments is the presumption that correlation proves causation. It does not, as there could be some third factor that could explain (i.e. provide a causal explanation for) the observed correlation, or other means of interpreting the relationship.

Here's an example of a typical causal argument involving a correlation:

Scientists have long suspected that isoflavones, a class of biologically active organic compounds, tend to improve one's cognitive performance. Now these views have acquired strong support from a recent study showing that college students who took soy isoflavone supplements for 3 months did significantly better on various reasoning tasks than students who never took such supplements.

The structure of the argument is as follows:

Premise: Soy isoflavone supplementation is correlated with improved cognitive performance.

Conclusion: Soy isoflavone supplementation causes an improvement in cognitive performance.

When analyzing such arguments, it is important to consider why the correlation observed may not be sufficient to establish the causal conclusion. The problem is usually with the way in which the study was controlled. For instance, if the students examined were not randomly assigned to each group, this would imply a selection bias in the experimental group and compromise the validity of the conclusion. Indeed, if those who are particularly driven or ambitious tend to take performance-enhancing supplements, and also tend to do better on various reasoning tasks than their less ambitious counterparts, the correlation between isoflavone supplementation and performance could be explained by a third factor (ambition) causing both the alleged “cause” and the “effect.”

To eliminate the possibility of bias, it may also be important to conduct a double-blind study in which neither the students nor the researchers know who belongs to the control group and who belongs to the experimental group until after all data have been recorded. Without a double-blind study, it is possible that the correlation observed is a function of a placebo effect, or of the experimenters’ own subjective bias towards the expected result.

Arguments that follow this pattern of reasoning are typically followed by one of the following question types:

  1. Weaken
  2. Strengthen
  3. Flaw in the Reasoning

Part II of this blog article will examine how a specific question type could test your ability to understand the difference between correlations and causations, and provide an example of how correct and incorrect answer choices might appear. Stay tuned!