Testing for heterogeneity among phenotypic correlations: a comparison of methods using Monte Carlo simulations

Area of Science:

• Evolutionary biology
• Quantitative genetics
• Statistical genetics

Background:

• Phenotypic correlations can indicate genetic covariance changes.
• Detecting these correlations is crucial for understanding trait evolution.

Purpose of the Study:

• To propose and evaluate new statistical tests for heterogeneous correlations.
• To compare the performance of new and existing methods.

Main Methods:

• Comparison of approximate tests using Hotelling's z*-transformation.
• Development and assessment of a distribution-free randomization test for Spearman's rank correlations.
• Evaluation of an alternative randomization test for product-moment correlations.

Main Results:

• The approximate test with Hotelling's z*-transformation offers the highest power for detecting heterogeneous correlations under bivariate normality.
• A new randomization test for Spearman's rank correlations is recommended for non-normal or unknown distributions.
• An alternative randomization test for product-moment correlations provides a balance between power and robustness to non-normality.

Conclusions:

• The choice of statistical test significantly impacts study conclusions.
• Recommendations are provided for selecting appropriate tests based on data distribution assumptions.