Abstract
Inferring the difference between means of two independent normal distributions with unknown variances, which is called the Behrens–Fisher problem, is common in statistical studies. The performance of classical methods for the Behrens–Fisher problem is a little liberal or conservative for small sample sizes. Moreover, classical methods are not easy to understand for students. In this article, we present a simple approximation method for the Behrens–Fisher problem, which is suitable for small sample sizes. The proposed method demonstrated shortened expected widths (EWs) while maintaining the coverage probabilities (CPs). The proposed method is a competitive alternative methods for small sample sizes. All methods were illustrated using three real examples. We recommended several methods for use in practice according to their performance in both CPs and EWs.
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