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A Nonstochastic Interpretation of Reported Significance Levels
Abstract
Tests of significance are often made in situations where the standard assumptions underlying the probability calculations do not hold. As a result, the reported significance levels become difficult to interpret. This article sketches an alternative interpretation of a reported significance level, valid in considerable generality. This level locates the given data set within the spectrum of other data sets derived from the given one by an appropriate class of transformations. If the null hypothesis being tested holds, the derived data sets should be equivalent to the original one. Thus, a small reported significance level indicates an unusual data set. This development parallels that of randomization tests, but there is a crucial technical difference: our approach involves permuting observed residuals; the classical randomization approach involves permuting unobservable, or perhaps nonexistent, stochastic disturbance terms.
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Cites
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FITTING MULTIVARIATE MODELS TO COMMUNITY DATA: A COMMENT ON DISTANCE-BASED REDUNDANCY ANALYSIS
McArdle, B. H., & Anderson, M. J. (2001) · Ecology · doi:10.1890/0012-9658(2001)082[0290:fmmtcd]2.0.co;2 · Cited by 4,001
Permutation inference for the general linear model
Winkler, A. M., Ridgway, G. R., Webster, M. A., Smith, S. M., & Nichols, T. E. (2014) · NeuroImage · doi:10.1016/j.neuroimage.2014.01.060 · Cited by 3,563
Legendre, P., & Anderson, M. J. (1999) · Ecological Monographs · doi:10.1890/0012-9615(1999)069[0001:dbratm]2.0.co;2 · Cited by 2,695
Bivariate line‐fitting methods for allometry
Warton, D. I., Wright, I. J., Falster, D. S., & Westoby, M. (2006) · Biological Reviews · doi:10.1017/s1464793106007007 · Cited by 2,319
Metadata
- Authors
- Freedman, D., & Lane, D.
- Venue
- Journal of Business & Economic Statistics
- Publisher
- Informa UK Limited
- Published
- 1983-10
- Volume
- 1
- Issue
- 4
- Pages
- 292-298
- ISSN
- 0735-0015 (ISSN-L)
- 1537-2707
- OpenAlex
- W2052357007
- Cited by
- 483
- References
- 20
- FWCI
- 0.97
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
