Testing Equality of Several Normal Means to a Specified Standard

Abstract

The problem of testing equality of several normal means to a specifed value when the population variances are unknown is considered. Two test procedures, one obtained by using Fisher's method of combining independent tests and the other based on the maximum of independent t statistics are proposed. In addition, the likelihood ratio test statistic and its asymptotic null distribution are derived. Power comparisons of these three test procedures are made using simulation. Assuming that the unknown variances are equal, these tests are again compared with an appropriately modified analysis of variance procedure. Based on the simulation study, the likehood ratio test and Fisher's method are recommended for use in general. When the variances are equal, the modified analysis of variance test is superior.

• Likelihood Ratio Tests
• Maximum Likelihood
• Moment Estimation
• Tests for Normality

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Notes on contributors

K. Krishnamoorthy

Dr. Krishnamoorthy is an Assistant Professor in the Department of Statistics.

Arvind K. Shah

Dr. Shah is Professor of Statistics in the Department of Mathematics and Statistics.