stests: R package to perform multivariate statistical tests
Abstract
The equality between two mean vectors from multivariate normal populations can be assessed by Hotelling's T2 test, which is a multivariate extension of Student's t-test. However, when the assumption of equality between the two covariance matrices is not met, the performance of the test may be affected, leading to incorrect conclusions. This research presents 11 alternative tests implemented by the stests package in R to evaluate the statistical power. A Monte Carlo simulation study was conducted, examining factors such as sample size, distance between mean vectors, and a scalar factor between covariance matrices. The study found that the rejection rate of the null hypothesis (H0) increases with a larger discrepancy between the two mean vectors and with an increase in sample size. Conversely, as the scalar factor between the covariance matrices becomes larger, the rejection rate decreases. The results demonstrate that all the tests developed in the stests package, addressing the multivariate Behrens-Fisher problem, are viable options for comparing two mean vectors.
Keywords
Behrens-Fisher problem, Multivariate statistic, statistical test
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