The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Inference about Variance Components in the One-Way Model
Abstract
The estimation of variance components in the one-way model is considered from a subjective Bayesian point of view. The situation in which the classical unbiased estimate of the between variance component is negative is explored in some detail. Exact and approximate posterior distributions are obtained in both the balanced and unbalanced case. Common sense aspects of the problem are emphasized, and some contrasts with other approaches. For example, Bayesianly speaking, a large negative unbiased estimate of the between variance component indicates an uninformative experiment in which the effective likelihood for that variance component is extremely flat, instead of strong evidence that the variance component is nearly zero.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The parameter σ2α in model (1) does not have any simple family of conjugate prior distributions because its marginal likelihood depends in a complex way on the data from all J groups.
“The parameter σ 2 α in model (1) does not have any simple family of conjugate prior distributions because its marginal likelihood depends in a complex way on the data from all J groups (Hill, 1965, Tiao andTan, 1965).”
From Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) (2006) · cites this paper as Hill, 1965
Citations
Cites
An Approximate Distribution of Estimates of Variance Components
Satterthwaite, F. E. (1946) · Biometrics Bulletin · doi:10.2307/3002019 · Cited by 4,373
Flagged first, then by citations
Research works printed but not linked: 29
- Anscombe F. J., 1963, Journal of the Royal Statistical Society, Series B, 25, 81, 10.1111/j.2517-6161.1963.tb00485.x · DOI
- Box G. E. P., 1964, Journal of the Royal Statistical Society, Series B, 26, 211, 10.1111/j.2517-6161.1964.tb00553.x · DOI
- 10.2307/3001494 · DOI
- Bulmer M. G., 1957, Biometrika, 44, 159, 10.1093/biomet/44.1-2.159 · DOI
- Crump S. L., 1946, Biometrics Bulletin, 2, 7, 10.2307/3002006 · DOI
- 10.2307/3001600 · DOI
- Daniels H. E., 1939, Journal of the Royal Statistical Society, Supplement, 6, 186, 10.2307/2983690 · DOI
- 10.1037/h0044139 · DOI · Paper page
- 10.2307/3001534 · DOI
- Fisher R. A., 1958, Statistical Method for Research Workers.,
- 10.1111/j.1469-1809.1935.tb02120.x · DOI
- Fisher R. A., 1960, The Design of Experiments.,
- Green J. R., 1954, Annals of Mathematical Statistics, 25, 671, 10.1214/aoms/1177728654 · DOI
- Healy M. J. R., 1963, Journal of the Royal Statistical Society, Series B, 25, 128, 10.1111/j.2517-6161.1963.tb00491.x · DOI
- 10.1214/aoms/1177706077 · DOI
- 10.1080/01621459.1963.10500833 · DOI
- Jeffreys H., 1961, Theory of Probability.,
- Nelder J. A., 1954, Biometrika, 41, 544, 10.1093/biomet/41.3-4.544 · DOI
- Raiffe H., 1961, Applied Statistical Decision Theory
- Savage L. J., 1954, The Foundations of Statistics
- Savage L. J., 1962, The Foundations of Statistical Inference, A Discussion, 10.2307/2281641 · DOI
- Savage L. J., 1961, “The Subjective Basis of Statistical Practice,”
- Scheffé H., 1961, The Analysis of Variance
- 10.1214/aoms/1177728180 · DOI
- 10.1214/aoms/1177704731 · DOI
- 10.1214/aoms/1177731946 · DOI
- Tiao G. C., 1964, “Bayesian Analysis of Random-Effect Models.,”
- 10.2307/2278459 · DOI
- 10.1017/S0021859600019663 · DOI
Cited by
Sorted by citations
The Handbook of Research Synthesis and Meta-Analysis
(2019) · doi:10.7758/9781610448864 · Cited by 4,553
Gelman, A. (2006) · Bayesian Analysis · doi:10.1214/06-ba117a · Cited by 4,050
The Effect of Improper Priors on Gibbs Sampling in Hierarchical Linear Mixed Models
Hobert, J. P., & Casella, G. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10476714 · Cited by 435
Analysis of Data from Non-Orthogonal Multistratum Designs in Industrial Experiments
Gilmour, S. G., & Goos, P. (2009) · Journal of the Royal Statistical Society Series C: Applied Statistics · doi:10.1111/j.1467-9876.2009.00662.x · Cited by 31
Tan, M. H. Y., & Jeff Wu, C. F. (2013) · Technometrics · doi:10.1080/00401706.2013.778790 · Cited by 12
Metadata
- Authors
- Hill, B. M.
- Affiliations
- Harvard University (US)
- Corresponding author
- Hill, Bruce M.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1965-09
- Volume
- 60
- Issue
- 311
- Pages
- 806-825
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W1990638774
- Cited by
- 155
- References
- 1
- Citations by year
- 2023: 1 · 2022: 3 · 2021: 2 · 2020: 4 · 2019: 4 · 2018: 2 · 2017: 1 · 2016: 4 · 2015: 4 · 2014: 2 · 2013: 3 · 2012: 3
- FWCI
- 6.02
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Keywords
- variance components, between-group variance, posterior distribution, unbalanced designs, balanced designs
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
