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Putting the Mantel test back together again.

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Summary
This summary is machine-generated.

The Mantel test, widely used in ecology, faced critiques for inconsistent results and error rates. This study proposes using a simple difference measure to resolve these issues, improving agreement with Pearson correlations and correcting error rates.

Keywords:
Euclidean distanceMantel testPearson correlationType I and Type II errordistance-based MANOVAdualitypartial Mantel testpower

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Area of Science:

  • Ecology and Evolution
  • Statistical Methods

Background:

  • The Mantel test is a widely used ecological and evolutionary statistic.
  • Recent decades have seen significant critiques of the Mantel test due to inconsistent results and problematic Type I/II error rates.
  • Three-matrix extensions and underlying null hypotheses have also faced challenges, limiting test applications.

Purpose of the Study:

  • To examine criticisms of the Mantel test, specifically the disagreement between Pearson correlations (r) and Mantel correlations (rm), and issues with error rates.
  • To propose and validate an alternative proximity measure that resolves these identified problems.
  • To demonstrate the efficacy of the simple difference (Diff) measure in addressing limitations in Mantel tests, partial Mantel tests, and distance-based MANOVA.

Main Methods:

  • Simulations and comparative analyses were employed.
  • Contrasted Mantel test results using Euclidean distance, squared Euclidean distance, and the simple difference (Diff) with traditional bivariate Pearson correlations.
  • Evaluated Type I and Type II error rates and agreement between correlation measures.

Main Results:

  • The simple difference (Diff) measure resolves the poor agreement between bivariate Pearson and Mantel correlations.
  • Using the simple difference ensures appropriate Type I and Type II error rates, aligning r with rm when appropriate.
  • The simple difference provides a solution for issues in partial Mantel tests and distance-based MANOVA.

Conclusions:

  • The proposed simple difference measure effectively addresses the long-standing criticisms of the Mantel test.
  • This approach resolves issues with correlation agreement and statistical error rates.
  • The findings aim to restore confidence and broaden the applicability of the Mantel test in ecological and evolutionary research.