Permutation tests for hypothesis testing with animal social network data: Problems and potential solutions.

Area of Science:

• Ecology
• Network Analysis
• Statistical Methods

Background:

• Permutation tests are crucial for analyzing animal social network data to test null hypotheses.
• Common permutation methods (pre-network and node) have limitations, often leading to high type I and type II error rates due to unaddressed biases or complex social structures.

Purpose of the Study:

• To address the limitations of existing permutation tests in animal social network analysis.
• To introduce and evaluate a novel 'double permutation' approach to reduce error rates in hypothesis testing.

Main Methods:

• Developed a 'double permutation' technique combining pre-network permutations (to control nuisance effects) with node permutations (to test non-random structures).
• Conducted extensive simulations to assess error rates under various confounding conditions.
• Compared the performance of the double permutation method against traditional single permutation approaches and simple covariate adjustments.

Main Results:

• The double permutation approach demonstrated significantly lower type I error rates compared to single permutation methods across simulated scenarios.
• In conditions where pre-network permutation tests showed over 30% type I error, the double permutation method maintained error rates around 5%.
• Simulations indicated that the double permutation method is more robust against confounding effects in social network data.

Conclusions:

• The 'double permutation' procedure offers a more reliable solution for testing null hypotheses with animal social network data, mitigating issues of elevated type I and type II errors.
• Alternative robust inference methods, including mixed-effects models and restricted permutations, are also discussed.
• The study emphasizes the importance of explicitly considering and propagating uncertainty in network analyses.