Open AccessON SOME SOLUTIONS OF THE MULTIVARIATE BEHRENS FISHER PROBLEM
Author(s) -
SU Gulumbe,
B. Shehu,
S Dahiru
Publication year - 2021
Publication title -
journal of mathematical sciences and computational mathematics
Language(s) - English
Resource type - Journals
eISSN - 2688-8300
pISSN - 2644-3368
DOI - 10.15864/jmscm.2211
Subject(s) - type i and type ii errors , sample size determination , statistics , mathematics , multivariate statistics , covariance , multivariate normal distribution , robustness (evolution) , table (database) , multivariate analysis of variance , computer science , biochemistry , chemistry , data mining , gene
Multivariate Behrens-Fisher Problem is a problem that deals with testing the equality of two means from multivariate normal distribution when the covariance matrices are unequal and unknown. However, there is no single procedure served as a better performing solution to this problem, Adebayo (2018). In this study effort is made in selecting five different existing procedures and examined their power and rate to which they control type I error using a different setting and conditions observed from previous studies. To overcome this problem a code was designed via R Statistical Software, to simulate random normal data and independently run 1000 times using MASS package in other to estimate the power and rate at which each procedure control type I error. The simulation result depicts that, in a setting when variance covariance matrices S 1 > S 2 associated with a sample sizes (n 1 > n 2 ) in Table 4.1, 4.2, 4.5, and 4.6, shows that, Adebayos’ procedure performed better but at a sample sizes (n 1 = n 2 and n 1 < n 2 ) Hotelling T 2 is recommended in terms of power. For type I error rate where robustness and nominal level matters we found that under some settings none of the procedure maintained nominal level as revealed in Table 4.11 and 4.15. The results presented in Table 4.9 to 4.16 shows that when nominal level matters Krishnamoorthy came first, followed by Adebayos’, Yaos’, Johansons’ then Hotelling T 2 were recommended in the sequentially under the settings used in this study.