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Synthesis of Variance
Abstract
The distribution of a linear combination of two statistics distributed as is Chi-square is studied. The degree of approximation involved in assuming a Chi-square distribution is illustrated for several representative cases. It is concluded that the approximation is sufficiently accurate to use in many practical applications. Illustrations are given of its use in extending the Chi-square, the Student “t” and the Fisher “z” tests to a wider range of problems.
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Citations
Cited by
Statistical Aspects of the Analysis of Data From Retrospective Studies of Disease
(1959) · JNCI: Journal of the National Cancer Institute · doi:10.1093/jnci/22.4.719 · Cited by 14,689
Small sample inference for fixed effects from restricted maximum likelihood
Kenward, M. G., & Roger, J. H. (1997) · Biometrics · doi:10.2307/2533558 · Cited by 4,552
An Approximate Distribution of Estimates of Variance Components
Satterthwaite, F. E. (1946) · Biometrics Bulletin · doi:10.2307/3002019 · Cited by 4,373
Self-citationBootstrap-Based Improvements for Inference With Clustered Errors
Cameron, A. C., Gelbach, J. B., & Miller, D. L. (2008) · Review of Economics and Statistics · doi:10.1162/rest.90.3.414 · Cited by 4,417
Evaluating significance in linear mixed-effects models in R
Luke, S. G. (2017) · Behavior Research Methods · doi:10.3758/s13428-016-0809-y · Cited by 1,704
Metadata
- Authors
- Satterthwaite, F. E.
- Venue
- Psychometrika
- Publisher
- Cambridge University Press (CUP)
- Published
- 1941-10
- Volume
- 6
- Issue
- 5
- Pages
- 309-316
- ISSN
- 0033-3123 (ISSN-L)
- 1860-0980
- OpenAlex
- W2086244482
- Cited by
- 809
- References
- 0
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Synthesis of Variance. https://app.cochat.ai/papers/10.1007/bf02288586
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- Satterthwaite, F. E. (1941). Synthesis of Variance. Psychometrika. https://doi.org/10.1007/bf02288586
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
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.
