TY - JOUR

T1 - A Review of the Behrens–Fisher Problem and Some of its Analogs

T2 - Does the Same Size Fit All?

AU - Paul, Sudhir

AU - Wang, You-Gan

AU - Ullah, Insha

N1 - Publisher Copyright:
© 2019, National Statistical Institute. All rights reserved.

PY - 2019/10

Y1 - 2019/10

N2 - 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.

AB - 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.

KW - Fisher problem

KW - The Behrens

KW - The Weibull model

KW - The beta-binomial model

KW - The negative binomial model

UR - http://www.scopus.com/inward/record.url?scp=85073442954&partnerID=8YFLogxK

U2 - 10.57805/revstat.v17i4.281

DO - 10.57805/revstat.v17i4.281

M3 - Article

SN - 1645-6726

VL - 17

SP - 563

EP - 597

JO - Revstat Statistical Journal

JF - Revstat Statistical Journal

IS - 4

ER -