Estimation of heterogeneous error variances

Estimation of heterogeneous error variances

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ABSTRACT WE consider a set of _pq_ observations _x__ij_ in a two-way classification, which we may suppose represented by the model where α_i_ and β_j_ are constants and the ε_ij_ are independent normal random errors with zero means and variances σ_j_2; α_i_, β_j_ and σ_j_2 are unknown, and it is desired to estimate σ_j_2. The problem arises, for example, in investigating the accuracy of a food-tasting panel; α_i_ depends on the food-specimen tasted, β_j_ is the bias and σ_j_2 the residual error variance of the _j_th panel member. Access through your institution Buy or subscribe This is a preview of subscription content, access via your institution ACCESS OPTIONS Access through your institution Subscribe to this journal Receive 51 print issues and online access $199.00 per year only $3.90 per issue Learn more Buy this article * Purchase on SpringerLink * Instant access to full article PDF Buy now Prices may be subject to local taxes which are calculated during checkout ADDITIONAL ACCESS OPTIONS: * Log in * Learn about institutional subscriptions * Read our FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS SIMPLE NESTED BAYESIAN HYPOTHESIS TESTING FOR META-ANALYSIS, COX, POISSON AND LOGISTIC REGRESSION MODELS Article Open access 23 March 2023 PRINCIPAL COMPONENT ANALYSIS Article 22 December 2022 THE QUEST FOR THE RELIABILITY OF MACHINE LEARNING MODELS IN BINARY CLASSIFICATION ON TABULAR DATA Article Open access 27 October 2023 REFERENCES * Kendall, M. G., _J. Roy. Statist. Soc._, B (in the press). Download references AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Statistical Laboratory, University of Cambridge, A. S. C. EHRENBERG Authors * A. S. C. EHRENBERG View author publications You can also search for this author inPubMed Google Scholar RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE EHRENBERG, A. Estimation of Heterogeneous Error Variances. _Nature_ 166, 608 (1950). https://doi.org/10.1038/166608a0 Download citation * Issue Date: 07 October 1950 * DOI: https://doi.org/10.1038/166608a0 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this content: Get shareable link Sorry, a shareable link is not currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative

ABSTRACT WE consider a set of _pq_ observations _x__ij_ in a two-way classification, which we may suppose represented by the model where α_i_ and β_j_ are constants and the ε_ij_ are


independent normal random errors with zero means and variances σ_j_2; α_i_, β_j_ and σ_j_2 are unknown, and it is desired to estimate σ_j_2. The problem arises, for example, in investigating


the accuracy of a food-tasting panel; α_i_ depends on the food-specimen tasted, β_j_ is the bias and σ_j_2 the residual error variance of the _j_th panel member. Access through your


institution Buy or subscribe This is a preview of subscription content, access via your institution ACCESS OPTIONS Access through your institution Subscribe to this journal Receive 51 print


issues and online access $199.00 per year only $3.90 per issue Learn more Buy this article * Purchase on SpringerLink * Instant access to full article PDF Buy now Prices may be subject to


local taxes which are calculated during checkout ADDITIONAL ACCESS OPTIONS: * Log in * Learn about institutional subscriptions * Read our FAQs * Contact customer support SIMILAR CONTENT


BEING VIEWED BY OTHERS SIMPLE NESTED BAYESIAN HYPOTHESIS TESTING FOR META-ANALYSIS, COX, POISSON AND LOGISTIC REGRESSION MODELS Article Open access 23 March 2023 PRINCIPAL COMPONENT ANALYSIS


Article 22 December 2022 THE QUEST FOR THE RELIABILITY OF MACHINE LEARNING MODELS IN BINARY CLASSIFICATION ON TABULAR DATA Article Open access 27 October 2023 REFERENCES * Kendall, M. G.,


_J. Roy. Statist. Soc._, B (in the press). Download references AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Statistical Laboratory, University of Cambridge, A. S. C. EHRENBERG Authors * A.


S. C. EHRENBERG View author publications You can also search for this author inPubMed Google Scholar RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE


EHRENBERG, A. Estimation of Heterogeneous Error Variances. _Nature_ 166, 608 (1950). https://doi.org/10.1038/166608a0 Download citation * Issue Date: 07 October 1950 * DOI:


https://doi.org/10.1038/166608a0 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this content: Get shareable link Sorry, a shareable link is not currently


available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative