Modified generalized p-value and confidence interval by Fisher s fiducial approach

In this study, we develop two simple generalized confidence intervals for the difference between means of two normal populations with heteroscedastic variances which is usually referred to as the Behrens-Fisher problem. The developed confidence intervals are compared with the generalized confidence interval in the literature. We also propose modified fiducial based approach using Fisher's fiducial inference for comparing the mean of two lognormal distributions and compare them with the other tests in the literature. A Monte Carlo simulation study is conducted to evaluate performances of the proposed methods under different scenarios. The simulation results indicate that the developed confidences intervals for the Behrens-Fisher problem have shorter interval lengths and they give better coverage accuracy in some cases. The modified ducial based approach is the best to provide satisfactory results in respect to its type error and power in all sample sizes. The modified test is applicable to small samples and is easy to compute and implement. The methods are also applied to two real-life examples.