A review of the Behrens–Fisher problem and some of its analogs : Does the same size fit all?
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|
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  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|
|Journal||Revstat Statistical Journal|
|Journal citation||17 (4), p. 563–597|
|Publisher||Instituto Nacional de Estatistica|
|Web address (URL)||https://www.ine.pt/revstat/pdf/REVSTAT_v17-n4-7.pdf|
|Open access||Published as ‘gold’ (paid) open access|
|Funder||Natural Sciences and Engineering Research Council of Canada (NSERC)|
|Australian Research Council (ARC)|
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|Publication process dates|
|Deposited||19 Jul 2023|
|ARC Funded Research||This output has been funded, wholly or partially, under the Australian Research Council Act 2001|
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