A note on the exact computation of the Student Snedecor and sample correlation coefficient distribution functions
Abstract
Summary. By using the exact expression of the correlation coefficient distribution function under the alternative hypothesis in the case of a random sample from a normal population, the distribution functions of the Student - and Snedecor -distributions are provided in closed form. The distribution functions obtained are implemented as routines in the symbolic programming language Mathematica.
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The test for correlations between two normally distributed variables uses the exact sample correlation coefficient distribution or, optionally, a large-sample approximation based on Fisher's r-to-z transformation.
“The latter test uses the exact sample correlation coefficient distribution (Barabesi & Greco, 2002) or, optionally, a large-sample approximation based on Fisher's r-to-z transformation.”
From G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences (2007) · cites this paper as Barabesi & Greco, 2002
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Holonomic properties and recurrence formula for the distribution of sample correlation coefficient
Mura, H., Hashiguchi, H., Nakagawa, S., & Ono, Y. (2019) · SUT Journal of Mathematics · doi:10.55937/sut/1571147806
- Authors
- Barabesi, L., & Greco, L.
- Affiliations
- University of Siena (IT)
- Corresponding author
- Barabesi, Lucio
- ORCID
- Barabesi, Lucio
- Venue
- Journal of the Royal Statistical Society: Series D (The Statistician)
- Publisher
- Wiley
- Published
- 2002-03
- Volume
- 51
- Issue
- 1
- Pages
- 105-110
- ISSN
- 0039-0526 (ISSN-L)
- 1467-9884
- OpenAlex
- W2069855582
- Cited by
- 7
- References
- 10
- Citations by year
- 2021: 2 · 2019: 1
- FWCI
- 0.38
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the Royal Statistical Society Series D (The Statistician) (publishedVersion)
- Use Siena air (University of Siena) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Modeling and Simulation › Mathematical and Computational Methods
- Keywords
- t-distribution, closed-form expressions, alternative hypothesis, healthy population, Mathematica implementation
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