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Abstract:
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This work aims to address the problem of multiple comparisons on treatment means in the presence of unequal error variances. A modification to an existing approximate procedure that requires iteratively evaluating the multiplicity-adjusted critical value for each individual component is suggested for improving the performance of preserving the specified familywise error as well as maintaining stability across individual error rates. In addition, a simulation-based approach for the approximation of equal-coordinate quantile of a multivariate t distribution(MVT) is proposed that possesses similar asymptotic properties as the numerical approach currently employed. Apart from its computational strength, another advantage of the simulation approach lies in the fact that it has the ability to accommodate more general situations, including MVT with fractional degrees of freedom. More importantly, it provides the basis for the practical implementation of the new approach proposed in this work. A Monto Carlo study is conducted to illustrate the superiority of the new approach relative to various other existing approaches, especially as the number of independent comparison gets larger.
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