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A review of the Behrens–Fisher problem and some of its analogs : Does the same size fit all?
Paul, Sudhir Wang, You-Gan Ullah, Insha
Paul, Sudhir
Wang, You-Gan
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
Date
2019
Type
Journal article
Journal
Revstat Statistical Journal
Book
Volume
17
Issue
4
Page Range
563-597
Article Number
ACU Department
Institute for Learning Sciences and Teacher Education (ILSTE)
Faculty of Education and Arts
Faculty of Education and Arts
Relation URI
DOI
Event URL
Open Access Status
Published as ‘gold’ (paid) open access
License
CC BY 4.0
File Access
Open