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Multi-level block permutation.

Anderson M Winkler1, Matthew A Webster1, Diego Vidaurre2

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Summary
This summary is machine-generated.

Permutation tests offer exact control of false positives but can be limited by data dependence. This study introduces a hierarchical permutation method to preserve data structure, enabling valid inference in complex datasets like those from the Human Connectome Project.

Keywords:
General linear modelMultiple regressionPermutation inferenceRepeated measurements

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Area of Science:

  • Statistics
  • Computational Biology
  • Data Science

Background:

  • Permutation tests are valuable for controlling false positives and using non-standard statistics.
  • Global exchangeability is often violated in real-world data, such as paired or repeated measures, and family-based studies.
  • Standard permutation methods can invalidate the null distribution when dependence structures are present.

Purpose of the Study:

  • To develop a permutation inference method that accommodates complex data dependence structures.
  • To extend block-based exchangeability to a hierarchical, multi-level definition.
  • To ensure the validity of permutation tests in the presence of known data dependencies.

Main Methods:

  • Introduced a hierarchical definition of exchangeability for nested data blocks.
  • Utilized a subset of permutations that preserve the original joint distribution and dependence structure.
  • The method is compatible with heteroscedasticity and variance groups, and can combine permutations with sign-flipping.

Main Results:

  • Demonstrated that the hierarchical permutation approach avoids false positives in datasets with dependence.
  • Applied the method to real-world data from the Human Connectome Project (HCP).
  • Provided a software implementation for the proposed permutation strategy.

Conclusions:

  • The hierarchical permutation method effectively handles complex dependence structures in statistical testing.
  • This approach extends the applicability of permutation inference to a wider range of scientific datasets.
  • The method offers a robust solution for maintaining statistical validity in the presence of data dependencies.