The Exact Distribution of Bartlett’s Test Statistic for Homogeneity of Variances with Unequal Sample Sizes

Chao, Min-Te; Glaser, Ronald E.

doi:10.1080/01621459.1978.10481594

Cited by 58Statistical Distribution Estimation and ApplicationsProbability and Statistical ResearchAdvanced Statistical Methods and Models

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The Exact Distribution of Bartlett’s Test Statistic for Homogeneity of Variances with Unequal Sample Sizes

Chao, Min-Te, Glaser, Ronald E.·1978·Journal of the American Statistical Association

DOI 10.1080/01621459.1978.10481594

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Abstract

An expression is derived for the null density of the Bartlett test statistic for testing equality of variances of n normal populations, when random samples not necessarily of the same size are taken. The expression permits computation of exact Bartlett critical values. As a generalization, an expression is derived for the density of the normalized ratio of an arbitrarily weighted geometric mean to the unweighted arithmetic mean, based on a sample of n independently distributed gamma random variables having common scale parameter but different shape parameters.

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The Kaiser-Meyer-Olkin values for behavioral intention, tourism motivation, and perceived value were 0.905, 0.869, and 0.919, respectively, and Bartlett's tests were significant (p < 0.001).
“The results showed that the KMO values of behavioral intention, tourism motivation, and perceived value were 0.905, 0.869, and 0.919, respectively, while the approximate square card of behavioral intention, tourism motivation, and perceived value were 3057.033 (df = 66, p < 0.001), 3782.221 (df = 136, p < 0.001), and 1581.617(df = 15, p < 0.001), respectively.”
From Health and Wellness Tourists’ Motivation and Behavior Intention: The Role of Perceived Value (2023) · cites this paper as [69]

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Optimising excipient properties to prevent aggregation in biopharmaceutical formulationsPreprint
King, T., Humphrey, J., Laughton, C. A., Thomas, N. R., & Hirst, J. D. (2023) · ChemRxiv · doi:10.26434/chemrxiv-2023-rgvlz

Authors: Chao, M.-T., & Glaser, R. E.
Affiliations: AT&T (United States) (US)
University of California, Davis (US)
Venue: Journal of the American Statistical Association
Publisher: Informa UK Limited
Published: 1978-06
Volume: 73
Issue: 362
Pages: 422-426
ISSN: 0162-1459 (ISSN-L)
1537-274X
DOI: 10.1080/01621459.1978.10481594
OpenAlex: W2084614649
Cited by: 58
References: 17
Citations by year: 2025: 2 · 2024: 2 · 2023: 5 · 2022: 1 · 2021: 3 · 2019: 1 · 2017: 1 · 2016: 2 · 2014: 2 · 2013: 1
FWCI: 2.76
Type: journal article
Language: en
Open access: closed
Locations: Journal of the American Statistical Association (publishedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
Keywords: Bartlett test, homoscedasticity, unequal sample sizes, exact distribution, critical values, healthy population, weighted geometric mean, gamma random variables, ratio of means

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The Exact Distribution of Bartlett’s Test Statistic for Homogeneity of Variances with Unequal Sample Sizes

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