scholarly journals Robustness of asymptotic and bootstrap tests for multivariate homogeneity of covariance matrices

2008 ◽  
Vol 32 (1) ◽  
pp. 157-166 ◽  
Author(s):  
Roberta Bessa Veloso Silva ◽  
Daniel Furtado Ferreira ◽  
Denismar Alves Nogueira
Keyword(s):  
Type I Error ◽  
Confidence Regions ◽  
Error Rates ◽  
Covariance Matrices ◽  
Type I ◽  
Bootstrap Test ◽  
Type I Error Rates ◽  
Normal Populations ◽  
Bartlett’S Test ◽  
Bootstrap Tests

The present work emphasizes the importance of testing hypothesis on homogeneity of covariance matrices from multivariate k populations. The violation of the assumption of the homogeneity of covariance matrices affects the performance of the tests and the coverage probability of the confidence regions. This work intends to apply two tests of homogeneity of covariance and to evaluate type I error rates and power using Monte Carlo simulation in normal populations and robustness in non normal populations. Multivariate Bartlett's test (MBT) and its bootstrap version (MBTB) were used. Different configurations are tested combining sample sizes, number of variates, correlation and number of populations. Results show that the bootstrap test was considered superior to the asymptotic test and robust, since it controls the type error I rate.

Performance of Monte Carlo Permutation and Approximate Tests for Multivariate Means Comparisons With Small Sample Sizes When Parametric Assumptions are Violated

Methodology ◽  
2009 ◽  
Vol 5 (2) ◽  
pp. 60-70 ◽  
Author(s):  
W. Holmes Finch ◽  
Teresa Davenport
Keyword(s):  
Monte Carlo ◽  
Type I Error ◽  
Permutation Tests ◽  
Error Rates ◽  
Covariance Matrices ◽  
Small Sample ◽  
Type I ◽  
Permutation Testing ◽  
Sample Sizes ◽  
Type I Error Rates

Permutation testing has been suggested as an alternative to the standard F approximate tests used in multivariate analysis of variance (MANOVA). These approximate tests, such as Wilks’ Lambda and Pillai’s Trace, have been shown to perform poorly when assumptions of normally distributed dependent variables and homogeneity of group covariance matrices were violated. Because Monte Carlo permutation tests do not rely on distributional assumptions, they may be expected to work better than their approximate cousins when the data do not conform to the assumptions described above. The current simulation study compared the performance of four standard MANOVA test statistics with their Monte Carlo permutation-based counterparts under a variety of conditions with small samples, including conditions when the assumptions were met and when they were not. Results suggest that for sample sizes of 50 subjects, power is very low for all the statistics. In addition, Type I error rates for both the approximate F and Monte Carlo tests were inflated under the condition of nonnormal data and unequal covariance matrices. In general, the performance of the Monte Carlo permutation tests was slightly better in terms of Type I error rates and power when both assumptions of normality and homogeneous covariance matrices were not met. It should be noted that these simulations were based upon the case with three groups only, and as such results presented in this study can only be generalized to similar situations.

Type I Error Rates for Yao’s and James Tests of Equality of Mean Vectors Under VarianceCovariance Heteroscedasticity

1988 ◽  
Vol 13 (3) ◽  
pp. 281-290 ◽  
Author(s):  
James Algina ◽  
Kezhen L. Tang
Keyword(s):  
Sample Size ◽  
Type I Error ◽  
Error Rates ◽  
Covariance Matrices ◽  
Type I ◽  
Type I Error Rates ◽  
Mean Vectors ◽  
Equality Of Mean Vectors

For Yao’s and James’ tests, Type I error rates were estimated for various combinations of the number of variables (p), samplesize ratio (n1: n2), sample-size-to-variables ratio, and degree of heteroscedasticity. These tests are alternatives to Hotelling’s T2 and are intended for use when the variance-covariance matrices are not equal in a study using two independent samples. The performance of Yao’s test was superior to that of James’. Yao’s test had appropriate Type I error rates when p ≥ 10, (n1 + n2)/p ≥ 10, and 1:2 ≤ n1:n2 ≤ 2:1. When (n1 + n2)/p = 20, Yao’s test was robust when n1: n2 was 5:1, 3:1, and 4:1 and p was 2, 6, and 10, respectively.

scholarly journals Control of Type I Error Rates in Bayesian Sequential Designs

2019 ◽  
Vol 14 (2) ◽  
pp. 399-425 ◽  
Author(s):  
Haolun Shi ◽  
Guosheng Yin
Keyword(s):  
Type I Error ◽  
Error Rates ◽  
Type I ◽  
Sequential Designs ◽  
Type I Error Rates

scholarly journals Sisvar: a Guide for its Bootstrap procedures in multiple comparisons

2014 ◽  
Vol 38 (2) ◽  
pp. 109-112 ◽  
Author(s):  
Daniel Furtado Ferreira
Keyword(s):  
Scientific Community ◽  
Type I Error ◽  
Multiple Comparisons ◽  
Error Rates ◽  
Type I ◽  
Type I Error Rates ◽  
Statistical Analysis System ◽  
Scientific Results ◽  
Analysis System ◽  
Multiple Comparison Procedures

Sisvar is a statistical analysis system with a large usage by the scientific community to produce statistical analyses and to produce scientific results and conclusions. The large use of the statistical procedures of Sisvar by the scientific community is due to it being accurate, precise, simple and robust. With many options of analysis, Sisvar has a not so largely used analysis that is the multiple comparison procedures using bootstrap approaches. This paper aims to review this subject and to show some advantages of using Sisvar to perform such analysis to compare treatments means. Tests like Dunnett, Tukey, Student-Newman-Keuls and Scott-Knott are performed alternatively by bootstrap methods and show greater power and better controls of experimentwise type I error rates under non-normal, asymmetric, platykurtic or leptokurtic distributions.

Sign in / Sign up

Export Citation Format

Share Document