Behrens-fisher problem under the assumption of homogeneous coefficients of variation

Abstract

The powers of the likelihood ratio (LR) test and an “asymptotically (in some sense) optimum” invariant test are examined and compared by simulation techniques with those of several other relevant tests for the problem of testing the equality of two univariate normal population means under the assumption of heterogeneous variances but homogeneous coefficients of variation. It is seen that the LR test is highly satisfactory for all values of the coefficient of variation and the “asymptotically optimum” invariant test, which is computationally much simpler than the LR test, is a reasonably good competitor for cases where the value of the coefficient of variation is greater than or equal to 3. Also, a

Keywords:

• test for the equality of means
• likelihood ratio test
• invariant test
• power of tests
• robustness