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    Area of Science:

    • Statistics
    • Biostatistics
    • Psychometrics

    Background:

    • Standard univariate and multivariate methods for analyzing repeated measures designs are sensitive to violations of the multisample sphericity assumption, particularly with unequal group sizes.
    • Recent advancements have introduced alternative statistical tests that do not rely on the sphericity assumption.

    Purpose of the Study:

    • To introduce a novel approximate degrees of freedom (df) approach designed to enhance the precision of the Brown-Forsythe (BF) procedure.
    • To address limitations of existing methods by ensuring positive df values and providing solutions invariant under linear data transformations.

    Main Methods:

    • Development of a new approximate degrees of freedom (df) method for analyzing repeated measures data.
    • Comparison of the new method's Type I error rate control against the modified empirical generalized least squares and Brown-Forsythe (BF) methods using Monte Carlo simulations.

    Main Results:

    • The proposed approximate df method demonstrated superior performance compared to the modified empirical generalized least squares and Brown-Forsythe (BF) methods.
    • The new approach consistently maintained better control over Type I error rates across various conditions.

    Conclusions:

    • The novel approximate degrees of freedom (df) procedure offers a more robust and precise alternative for analyzing continuous data in repeated measures designs with unequal group sizes.
    • This method overcomes key limitations of traditional tests, providing reliable statistical inference.