In health related studies, non-inferiority tests are used to demonstrate that a new treatment is not worse than a currently existing treatment by more than a pre-specified margin. In this thesis, we discuss three approaches; a Z-score approach, a generalized p-value approach and a Bayesian approach, to test the non-inferiority hypotheses in two-arm trials for ratio of log-normal means. The log-normal distribution is widely used to describe the positive random variables with positive skewness which is appealing for data arising from studies with small sample sizes. We demonstrate the approaches using data arising from an experimental aging study on cognitive penetrability of posture control. We also examine the suitability of three methods under various sample sizes via simulations. The results from the simulation studies indicate that the generalized p-value and the Bayesian approaches reach an agreement approximately and the degree of the agreement increases when the sample sizes increase. However, the Z-score approach can produce unsatisfactory results even under large sample sizes.