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    Area of Science:

    • Statistics
    • Psychometrics
    • Data Science

    Background:

    • Correlating variables with different measurement scales (nominal, ordinal, interval) presents a significant challenge in statistical analysis.
    • Existing methods often lack a unified approach, leading to potential inconsistencies and limitations.

    Purpose of the Study:

    • To develop a general correlation coefficient applicable to variables of diverse scale types.
    • To ensure the proposed coefficient is invariant under permitted transformations of the variables.
    • To address the problem of individual comparisons between variables on different scales.

    Main Methods:

    • Derivation of a general correlation coefficient based on symmetrization theory.
    • Development of an E-correlation family, invariant over permitted transformations.
    • Application of the E-correlation family to a set including interval, ordinal, and nominal scales.

    Main Results:

    • A novel E-correlation family is proposed as a general correlation coefficient.
    • The coefficient demonstrates invariance across different scale types and permitted transformations.
    • A solution for the individual comparison problem across different scale types is presented.

    Conclusions:

    • The E-correlation family provides a robust and unified method for correlation analysis involving mixed-scale data.
    • This approach enhances the reliability and applicability of correlation in complex datasets.
    • The proposed solution facilitates more accurate comparisons between variables of varying measurement levels.