This research introduces a statistical framework for determining the optimal number of LLM-generated survey responses to create reliable confidence intervals for human population parameters.

• Too many synthetic responses create misleadingly narrow confidence intervals
• Too few responses result in excessively wide intervals
• The optimal approach balances statistical efficiency with accurate uncertainty quantification
• Provides mathematically rigorous methods to address distribution shifts between synthetic and real populations

For medical researchers, this framework enables more reliable use of LLM-simulated responses in clinical surveys and trials, potentially reducing costs while maintaining statistical validity when human data is scarce or expensive to collect.

Uncertainty Quantification for LLM-Based Survey Simulations