Chain Reversion for Detecting Associations in Interacting Variables-St. Nicolas House Analysis

(1) Background: We present a new statistical approach labeled as "St. Nicolas House Analysis" (SNHA) for detecting and visualizing extensive interactions among variables. (2) Method: We rank absolute bivariate correlation coefficients in descending order according to magnitude and create hierarchic "association chains" defined by sequences where reversing start and end point does not alter the ordering of elements. Association chains are used to characterize dependence structures of interacting variables by a graph. (3) Results: SNHA depicts association chains in highly, but also in weakly correlated data, and is robust towards spurious accidental associations. Overlapping association chains can be visualized as network graphs. Between independent variables significantly fewer associations are detected compared to standard correlation or linear model-based approaches. (4) Conclusion: We propose reversible association chains as a principle to detect dependencies among variables. The proposed method can be conceptualized as a non-parametric statistical method. It is especially suited for secondary data analysis as only aggregate information such as correlations matrices are required. The analysis provides an initial approach for clarifying potential associations that may be subject to subsequent hypothesis testing.