China
Africa
Explore chapters and articles related to this topic
Comparing Means
Published in Shein-Chung Chow, Jun Shao, Hansheng Wang, Yuliya Lokhnygina, Sample Size Calculations in Clinical Research: Third Edition, 2017
Shein-Chung Chow, Jun Shao, Hansheng Wang, Yuliya Lokhnygina
The assumption that may not hold. When , statistical procedures are necessarily modified. If and are unknown, this becomes the well-known Behrens–Fisher problem. Extensive literature have been devoted to this topic in the past several decades. Miller (1997) gave a comprehensive review of research work done in this area.
Two-Sample Tests
Published in Daryl S. Paulson, Applied Statistical Designs for the Researcher, 2003
When the variances and are not assumed to be equivalent, a conundrum exists that statisticians call the Behrens-Fisher problem [24]. We have ignored the problem and merely used a procedure for evaluating two independent samples when variances are unequal. However, a number of statisticians would disagree and argue to use another procedure, Welch’s approximate t-test [19].
Two-sample Behrens–Fisher problems for high-dimensional data: a normal reference scale-invariant test
Published in Journal of Applied Statistics, 2023
Liang Zhang, Tianming Zhu, Jin-Ting Zhang
We have proposed and studied the normal-reference scale-invariant test 4] and the scale-invariant test 10] for the high-dimensional two-sample Behrens–Fisher problem where the two high-dimensional samples may have different covariance matrices. Both the competitors 2.1) hold. This is an advantage since in real data analysis, it is rather challenging to check if these key conditions hold approximately. The distribution of the chi-square-type mixture can be well approximated by that of a scaled chi-square random variable of form d consistently estimated from the data. The distribution of G, as an approximate distribution of d is large and otherwise, it is moderate or small. This adaptivity is an advantage of a normal-reference test but it is not shared by 3.2.