A Two Factor ANOVA-like Test for Correlated Correlations: CORANOVA.

Area of Science:

• Neuroscience
• Biostatistics
• Psychology

Background:

• Traditional methods like Fisher's Z are unsuitable for testing homogeneity of correlated correlations.
• Existing methods, such as Olkin and Finn's, have limitations with non-normal data and small samples.
• There is a need for a method to test complex interactions, like region by gender, in correlated correlations.

Purpose of the Study:

• To propose a novel nonparametric method for testing interactions and main effects in correlated correlations.
• To address the limitations of existing statistical procedures for analyzing correlated correlation structures.
• To provide a robust method applicable to smaller samples and non-normal data in neuroscience research.

Main Methods:

• A nonparametric permutation-based approach analogous to two-way ANOVA is proposed.
• Hypotheses focus on the homogeneity of correlations rather than means.
• The method avoids asymptotic distributional assumptions, enhancing applicability.

Main Results:

• Simulations confirmed the method maintains the correct statistical level across various data types and sample sizes.
• The proposed method demonstrated superior efficiency compared to Fisher's Z and Olkin-Finn tests.
• The method successfully identified a biologically meaningful sex by region interaction in brain blood flow and memory performance correlations.

Conclusions:

• The developed nonparametric method provides a robust and flexible tool for analyzing correlated correlations.
• This approach is particularly valuable in neuroscience for examining complex interactions in brain-behavior relationships.
• The method offers an improvement over existing techniques, especially for non-normal data and smaller sample sizes.