What common inferential error discussed in class best describes the following anecdote:

In the medical world, a frequently observed phenomenon is that those who have adverse outcomes (death or permanent quality of life decrease) after being diagnosed with serious medical conditions exhibit serious vitamin D deficiencies (a statistically significant decrease when comparing those with adverse outcomes to those who recovered). Since vitamin D is most associated with exposure to sunlight and low level UV radiation, many homeopathic practicioners recommend that getting more sunlight increases the probability that sick patients are more likely to recover.

Question

What common inferential error discussed in class best describes the following anecdote:

In the medical world, a frequently observed phenomenon is that those who have adverse outcomes (death or permanent quality of life decrease) after being diagnosed with serious medical conditions exhibit serious vitamin D deficiencies (a statistically significant decrease when comparing those with adverse outcomes to those who recovered).  Since vitamin D is most associated with exposure to sunlight and low level UV radiation, many homeopathic practicioners recommend that getting more sunlight increases the probability that sick patients are more likely to recover.

BlackTom AI · Accepted Answer

The passage presents a scenario in which people who end up with adverse medical outcomes also show vitamin D deficiencies. The implied conclusion by some practitioners is that increasing sunlight (and thus vitamin D) will improve recovery. To analyze the inferential error, consider what is being assumed about the relationships between variables.

Option discussion:
- Reversing the cause-and-effect: One common inference is that vitamin D deficiency causes worse outcomes, leading to the recommendation to increase sunlight to improve recovery. In reality, the data show that having a serious illness can lead to reduced sun exposure and lower vitamin D levels, so the observed association may reflect illness causing deficiency rather than deficiency causing worse outcomes. This is an example of reverse causation: the direction of the causal arrow is opposite of what is concluded.

- Confounding (a separate but related concern): Another frequent issue in such anecdotes is confounding, where an unmeasured factor (e.g., overall health status, mobility, comorbidities) affects both vitamin D levels and outcomes. This could explain the association without implying that vitamin D directly influences recovery. However, the question asks for the common inferential error that best describes the anecdote, and reverse causation specifically captures the misdirection of the causal link from illness to vitamin D deficiency to recovery.

- Correlation does not imply causation: While this is a foundational principle relevant to many observational findings, the more precise misinterpretation here involves the mistaken direction of causality (reverse causation) rather than a general caution about correlation alone. The anecdote explicitly hints at sunlight affecting recovery, which presumes a causal path that runs from vitamin D/sunlight to outcomes, not the other way around.

- Post hoc ergo propter hoc (after this, therefore because of this): This is a broader logical fallacy about temporal sequencing. The described reasoning fits somewhat, but the core issue here is the direction of causality rather than merely temporal order. Reverse causation more accurately pinpoints the error.

In summary, the best label for the inferential error in the anecdote is reverse causation: illness leads to both adverse outcomes and lower vitamin D, but the argument treats low vitamin D as a cause of worse outcomes rather than a consequence of illness, thereby reversing the true causal direction.

FA25_QTM_110_1 Quiz #10: Bayesian Thinking and Logic

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