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Abstract Researchers theorize that many real-world networks exhibit community structure where within-community edges are more likely than between-community edges. While numerous methods exist to cluster nodes into different communities, less work has addressed this question: given some network, does it exhibitstatistically meaningfulcommunity structure? We answer this question in a principled manner by framing it as a statistical hypothesis test in terms of a general and model-agnostic community structure parameter. Leveraging this parameter, we propose a simple and interpretable test statistic used to formulate two separate hypothesis testing frameworks. The first is an asymptotic test against a baseline value of the parameter while the second tests against a baseline model using bootstrap-based thresholds. We prove theoretical properties of these tests and demonstrate how the proposed method yields rich insights into real-world datasets.
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On Bayes factors for hypothesis tests
Abstract We develop alternative families of Bayes factors for use in hypothesis tests as alternatives to the popular default Bayes factors. The alternative Bayes factors are derived for the statistical analyses most commonly used in psychological research – one-sample and two-samplet tests, regression, and ANOVA analyses. They possess the same desirable theoretical and practical properties as the default Bayes factors and satisfy additional theoretical desiderata while mitigating against two features of the default priors that we consider implausible. They can be conveniently computed via an R package that we provide. Furthermore, hypothesis tests based on Bayes factors and those based on significance tests are juxtaposed. This discussion leads to the insight that default Bayes factors as well as the alternative Bayes factors are equivalent to test-statistic-based Bayes factors as proposed by Johnson.Journal of the Royal Statistical Society Series B: Statistical Methodology,67, 689–701. (2005). We highlight test-statistic-based Bayes factors as a general approach to Bayes-factor computation that is applicable to many hypothesis-testing problems for which an effect-size measure has been proposed and for which test power can be computed.
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- Award ID(s):
- 2145308
- PAR ID:
- 10556700
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Psychonomic Bulletin & Review
- Volume:
- 32
- Issue:
- 3
- ISSN:
- 1069-9384
- Format(s):
- Medium: X Size: p. 1070-1094
- Size(s):
- p. 1070-1094
- Sponsoring Org:
- National Science Foundation
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