ChatGPT AI, You’re wrong! Developing Unanswerable Questions

Dark Side of Statistics

An example of an unanswerable question ChatGPT is unable to solve.

Response by ChatGPT:

Why Should This Treatment Not Be Recommended?

1. Effect Size Matters More Than Statistical Significance:
   o The effect size (Cohen’s d = 0.01) is so small that the treatment provides almost no meaningful benefit over the control.
   o A tiny effect can still be statistically significant if the sample size is very large, but this does not mean the treatment is useful in practice.
2. Statistical Significance (p = 0.0001) Does Not Mean Practical Significance:
   o A very low p-value only indicates that the effect is unlikely to be due to random chance, not that it is clinically meaningful.
   o If the treatment’s impact is negligible, it does not justify exposing patients to severe risks.
3. Risk vs. Benefit Considerations:
   o If the treatment has severe side effects, then any recommendation must weigh benefit vs. harm.
   o A nearly zero effect size means the treatment is not providing enough benefit to justify its risks.
4. Ethical and Medical Standards:
   o Clinical decisions should be based on both statistical and clinical significance.
   o Approving a treatment just because it is statistically significant—without considering effect size and risks—violates medical ethics.
   o Medical professionals follow evidence-based guidelines, which require treatments to have meaningful benefits for patients.

Conclusion

Even though the p-value is extremely small (p = 0.0001), the tiny effect size (d = 0.01) suggests that the treatment provides no meaningful advantage over a placebo or alternative. Given the severe side effects, recommending the treatment would be unethical.

Thus, the correct answer is: False—the treatment should not be recommended based on these results.

Response by Dr. Santangelo:

I said it “COULD” be recommended NOT “should”?

ChatGPT finally agrees, and replies: True

the treatment could be recommended, but only under very specific and controversial conditions.
While a very small effect size (d = 0.01) combined with a statistically significant p-value (p = 0.0001) generally suggests no meaningful clinical benefit, there are some scenarios where the treatment might still be considered despite severe side effects.

When Could the Treatment Be Recommended?

Why Would This Still Be Controversial?

1. No Alternative Treatments Exist:
   o If this is the only available treatment for a life-threatening disease, doctors may still recommend it, even if the effect is minimal.
   o Example: A drug for a rare, fatal condition where no other options exist.
2. Individual Patient Cases (Personalized Medicine):
   o Some patients may respond better than others, even if the overall effect size is small in a population-level study.
   o Example: A treatment with severe side effects might still be justified for patients with no other options.
   • Combination Therapy Considerations:
     o If the treatment is used in combination with other therapies, a small effect might still contribute to an overall beneficial outcome.
     o Example: A chemotherapy drug that slightly improves outcomes when used with other treatments.
3. Regulatory and Policy Decisions:
   o In public health policy, even a small benefit might be considered valuable if applied to millions of people (e.g., certain vaccines or preventive measures).
   o Example: A drug that slightly reduces hospitalization rates in a large population might still be recommended despite side effects.

1. Ethical Concerns:
   o Is it ethical to expose patients to severe risks for such a tiny benefit? Many medical ethicists would argue no.
2. Risk vs. Benefit Trade-Off:
   o If the treatment causes more harm than good, it would not be recommended in most cases.
   o Example: A cancer drug that extends life by one day but causes extreme suffering—would it really be worth it?
3. Regulatory Scrutiny:
   o Most health agencies (FDA, EMA) would likely reject approval unless the treatment is for severe or untreatable conditions.

Final Answer: True (but highly unlikely)

The treatment could be recommended in extreme cases, but for most conditions, it would not be approved or used due to the tiny effect size and high risk

Dr. Santangelo: Yes, but you are hypothetically wrong in this case. Where in the question do I mention the likelihood of it being the case? Simply put, it is possible.

ChatGPT said:
You’re absolutely right!

The question only asks whether the treatment could be recommended, not whether it should be recommended or how likely it is to be recommended.
Since possibility does not imply likelihood, the correct answer is:
True—it is possible for the treatment to be recommended under some set of conditions, no matter how unlikely or unethical it may seem.
Even in extreme scenarios, there is no absolute rule in research or medicine that prevents a treatment from being recommended—only ethical, statistical, and practical considerations that influence the decision.

Great job crafting a question that forces an absolute logical perspective!

Stay Tuned more to come on this discussion.