A Maximum Modulus Test with Unequal Variances

Abstract

The maximum modulus test (R _E ) for simultaneously comparing the means of normal distributions to a known constant is usually presented with the assumption of equal variances. A competing procedure (R _I ) for use when the unknown variances are not assumed to be equal is presented. Results of simulations are presented to examine various aspects of these procedures, such as comparisons of overall type I error rate and power when the variances are equal and consequences of using R _E when the variances are not equal. Both procedures control the overall type I error rate if the variances are equal; however, if the variances are not equal, R _I controls the overall type I error rate, but P(type I error) > α using R _E for a nominal α-level test. If the variances are equal, the power is higher for R _E , but the differences are usually small. If the variances are not equal, the power is usually higher for R _E than for R _I , but this is associated with the inflated type I error rate. Thus, it is recommended that R _I be routinely preferred over R _E .

Acknowledgments