Min-Mid-Max Scaling, Limits of Agreement, and Agreement Score
It addresses foundational issues in statistical agreement analysis for researchers in fields like psychology and medicine, though it appears incremental as it builds directly on Cohen's framework.
The paper solves a 60-year-old problem from Cohen's work by developing a new agreement measure that isolates chance-expected agreement, forced agreement, and disagreement, and formulates the lower limit of Cohen's kappa.
In this paper, I solve a 60-year old question posed by Cohen's seminal paper (1960) and offer an agreement measure centered around the chance-expected agreement while isolating marginally forced agreement and disagreement. To achieve this, I formulate the minimum feasible agreement given row and column marginals by devising a new algorithm that minimizes the sum of diagonals in contingency tables. Based on this result, I also formulate the lower limit of the most common agreement measure-Cohen's kappa. Finally, I study the lower limit of maximum feasible agreement and devise two statistics of distribution similarity for agreement analysis.