Inference about the mean difference of two non-normal populations based on independent samples: a comparative study

Abstract

Inference about the mean difference of two non-normal populations is considered. The usual procedures based on the large sample distribution of the t-test and various modifications of it as well as the approach based on the empirical likelihood are studied. The various procedures are compared using simulation techniques. The comparison was made in terms of the attainment of the nominal confidence levels, test sizes and powers. The results show that the bootstrapped empirical likelihood inference procedures are superior with accurate test sizes and confidence levels even for very small samples from considerably skewed, heavy-tailed or differently shaped parent populations.

Keywords:

• Bootstrap
• Empirical likelihood
• Non-normal populations
• ttest
• Mean difference
• The two-sample problem