A review of the Behrens–Fisher problem and some of its analogs : Does the same size fit all?
Journal article
Paul, Sudhir, Wang, You-Gan and Ullah, Insha. (2019). A review of the Behrens–Fisher problem and some of its analogs : Does the same size fit all? Revstat Statistical Journal. 17(4), p. 563–597.
Authors | Paul, Sudhir, Wang, You-Gan and Ullah, Insha |
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Abstract | The traditional Behrens–Fisher (B-F) problem is to test the equality of the means μ1 and μ2 of two normal populations using two independent samples, when the quotient of the population variances is unknown. Welch [43] developed a frequentist approximate solution using a fractional number of degrees of freedom t-distribution. We make a a comprehensive review of the existing procedures, propose new procedures, evaluate these for size and power, and make recommendation for the B-F and its analogous problems for non-normal populations. On the other hand, we investigate and answer a question: does the same size fit all all, i.e. is the t-test with Welch’s degree of freedom correction robust enough for the B-F problem analogs, and what sample size is appropriate to use a normal approximation to the Welch statistic. |
Keywords | Behrens–Fisher problem; beta-binomial model; negative binomial model; Weibull model |
Year | 2019 |
Journal | Revstat Statistical Journal |
Journal citation | 17 (4), p. 563–597 |
Publisher | Instituto Nacional de Estatistica |
ISSN | 1645-6726 |
Web address (URL) | https://www.ine.pt/revstat/pdf/REVSTAT_v17-n4-7.pdf |
https://www.ine.pt/revstat/tables.html | |
Open access | Published as ‘gold’ (paid) open access |
Page range | 563–597 |
Funder | Natural Sciences and Engineering Research Council of Canada (NSERC) |
Australian Research Council (ARC) | |
Publisher's version | License File Access Level Open |
Output status | Published |
Publication dates | |
Online | Oct 2019 |
Publication process dates | |
Accepted | Sep 2017 |
Deposited | 19 Jul 2023 |
ARC Funded Research | This output has been funded, wholly or partially, under the Australian Research Council Act 2001 |
Grant ID | DP130100766 |
DP160104292 |
https://acuresearchbank.acu.edu.au/item/8z558/a-review-of-the-behrens-fisher-problem-and-some-of-its-analogs-does-the-same-size-fit-all
Download files
Publisher's version
OA_Paul_2019_A_review_of_the_Behrens_Fisher.pdf | |
License: CC BY 4.0 | |
File access level: Open |
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