Cited by 1,624Psychometric Methodologies and TestingStatistical Methods and Bayesian InferenceStatistical Methods and Applications

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The Analysis of Covariance Structures: Goodness-of-Fit Indices

HOELTER, JON W.·1983·Sociological Methods & Research

DOI 10.1177/0049124183011003003

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Abstract

A major problem encountered in covariance structure analyses involves decisions concerning whether or not a given theoretical model adequately represents the data used for its assessment. Given that X 2 goodness-of-fit tests are joint functions of the difference between theoretical and empirical covariance structures and sample size, gauging the impact of sample size on such tests is essential. In this paper, we propose a simple index (critical N) and tentative acceptance criterion, which, by focusing on sample size, provide an improved method for assessing goodness-of-fit. Both small- and large-sample examples are presented, illustrating the utility of the proposed method for assessing theoretical models.

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Significance tests and goodness of fit in the analysis of covariance structures.
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Authors: HOELTER, J. W.
Affiliations: University of Cincinnati (US)
Corresponding author: HOELTER, JON W.
Venue: Sociological Methods & Research
Publisher: SAGE Publications
Published: 1983-02
Volume: 11
Issue: 3
Pages: 325-344
ISSN: 0049-1241 (ISSN-L)
1552-8294
DOI: 10.1177/0049124183011003003
OpenAlex: W2023172395
Cited by: 1,624
References: 20
Citations by year: 2026: 48 · 2025: 82 · 2024: 74 · 2023: 82 · 2022: 83 · 2021: 73 · 2020: 62 · 2019: 72 · 2018: 58 · 2017: 51 · 2016: 75 · 2015: 72 · 2014: 65 · 2013: 65 · 2012: 61
FWCI: 19.05
Type: journal article
Language: en
Open access: closed
Licence: journals.sagepub.com/page/policies/text-and-data-mining-license (tdm)
Locations: Sociological Methods & Research (publishedVersion)
RePEc: Research Papers in Economics (submittedVersion)
Topics: Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Keywords: structural equation modeling, goodness-of-fit tests, sample size, model fit assessment, chi-square test, small sample inference, acceptance criteria

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The Analysis of Covariance Structures: Goodness-of-Fit Indices

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