Advancing the Delphi method: a binomial test approach for enhanced environmental consensus analysis

Purpose This study presents a methodological enhancement to the Delphi method by integrating the binomial test to improve the reliability, transparency and consistency of expert consensus analysis. The approach aims to address existing limitations in consensus validation by introducing a statistically grounded confidence coefficient. The method is applied within the domain of environmental management, using three diverse case studies: risk assessment of Shadegan Wetland, ecotourism land evaluation along the Dez River and environmental impact assessment of a gas power plant. Design/methodology/approach A structured, multi-stage Delphi survey was conducted among a panel of environmental experts. Responses were analyzed using both descriptive statistics and the binomial test to quantify the strength of expert agreement. This hybrid approach enhances consensus interpretation and ensures statistical validation of expert input, supporting a more robust and reproducible decision-making framework. Findings The integration of the binomial test resulted in a more selective and statistically validated set of consensus criteria compared to traditional methods. The proposed model demonstrated improved interpretability and alignment with real-world environmental conditions across all three case studies, reinforcing its effectiveness in refining parameter selection and prioritization. Originality/value This research introduces a replicable and adaptable framework for statistically validating consensus in Delphi studies. By bridging qualitative expert input with quantitative validation, the proposed approach addresses a critical methodological gap in Delphi applications. The findings offer practical implications for decision-making in environmental management and extend the applicability of the Delphi method to interdisciplinary fields requiring structured consensus-building.