Comparing the variances of several treatments with that of a control treatment: Theory and applications

A common and important problem in medicine, economics and environmental studies is the comparison of the variances of several treatments with that of a control treatment. Among the existing methods, Spurrier's optimal test based on multivariate F distribution has exact type I error rates. However, it requires equal sample sizes among the treatment groups. To extend the application scope, in this paper, we propose a new efficient test for comparing several variances with a control using the marginal inferential model (MIM). Simulation studies show that the MIM test guarantees the exact type I error rate whether the sample size is equal or unequal. Moreover, the power of the MIM test is competitive with that of Spurrier's optimal test. Finally, two real examples are used to demonstrate the application of the proposed method.