The idea that “correlation does not imply causation” is arguably one of the most important ideas to understand in an applied statistics course. This idea applies to any statistical study, not just explicitly “correlational” studies, including ANOVAs and t-tests.
One example that illustrates this issue is the following finding: There is a positive correlation between the number of murders and the number of churches in a given city. Although it is possible that the presence of churches drives people into a religious frenzy and increased the number of murders, the most plausible explanation for this is the following confound: population size. That is, the higher the population size, the higher the number of murders and the higher the number of churches.
Another example (using a “t-test-like” design): There is a higher incidence of suicidal behavior among people who see psychotherapists than among those who don’t. Rather than conclude that seeing a therapist makes you more likely to want to kill yourself, it seems more plausible that people who are depressed or otherwise mentally ill (“the confound”) are more likely to both see a therapist and engage in suicidal behavior.
Recall that one way of improving our ability to make a causal inference (by ruling out confounds) is to randomly assign experimental units to the treatment conditions, rather than merely measuring/recording the “conditions” or “groups.”
For the following paper, address the following prompts:
1) (a) Give another example of a study (hypothetical or real) in which there is no random assignment and a “spurious correlation” like the above examples (in either a correlation/regression or t-test/ANOVA study), and (b) name and explain why the confound better accounts for the association/difference.
2) (a) Give an example of a real study/topic/relationship in which there has been no random assignment (because of ethical or practical reasons), yet there is general consensus that there is a causal relationship, and (b) explain why we are generally confident in there being a causal relationship.
Finally, 3) (a) Give an example of a study (hypothetical or real) in which there is random assignment, yet a causal inference would still be misleading, and (b) say why inferring causation would be misleading in this case.
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