Improved Likelihood Inference on Testing the Difference of Non Centrality Parameters of Two Independent Non central t Distributions with Identical Degrees of Freedom

Abstract

Kim and Hayter (2008) showed that testing the difference of the non centralities of two non central t distributions, which have identical degrees of freedom, is the equivalent to testing the difference of two signal-to-noise ratios for two independent samples from different normal distributions. Moreover, from a biomedical research point of view, the above test is also equivalent to testing the existence of the effect size when the sample sizes of the control group and treatment group are the same. In this article, two third-order likelihood-based methods are proposed to approximate the p-value for this significance test problem. A real life example is used to illustrate that results from the proposed methods and the existing methods can be quite different. Simulation results show that the proposed methods give remarkable accuracy even when sample size reaches the smallest possible value.

Keywords:

• Canonical parameter
• Exponential family model
• Lugannani and Rice formula
• p-value function
• Signed log-likelihood ratio statistic

Mathematics Subject Classification:

• 62F03