On Selecting Tests for Equality of Two Normal Mean Vectors

Area of Science:

• Statistics
• Multivariate Analysis
• Hypothesis Testing

Background:

• The standard procedure for comparing two normal mean vectors involves a preliminary test for covariance matrix equality before applying the Hotelling T-squared test.
• When covariance matrices are unequal, approximate solutions for the multivariate Behrens-Fisher problem are necessary.

Purpose of the Study:

• To evaluate the performance of the conventional approach using the Hotelling T-squared test.
• To assess the properties of an approximate invariant test for the multivariate Behrens-Fisher problem.

Main Methods:

• Comparative analysis of statistical tests.
• Simulation studies to evaluate Type I error rates and test performance under varying conditions.
• Focus on the Hotelling T-squared test and an approximate invariant test (Krishnamoorthy & Yu, 2004).

Main Results:

• Simulation results show that the conventional approach frequently leads to inflated Type I error rates.
• The approximate invariant test demonstrates robust control of Type I error rates with arbitrary covariance matrices.
• The approximate test's performance is comparable to the Hotelling T-squared test when covariance matrices are equal.

Conclusions:

• The conventional method for testing normal mean vector equality is unreliable when covariance matrices differ.
• The approximate invariant test offers a more robust and accurate alternative for the multivariate Behrens-Fisher problem.
• This approximate test provides a reliable solution across different covariance matrix scenarios.