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Abstract:
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Two-sample comparisons belonging to basic class of statistical inference is extensively applied in practice. There is a rich statistical literature regarding different parametric methods to address these problems. In this context, most of the powerful techniques are assumed to be based on normally distributed populations. In practice, the alternative distributions of compared samples are commonly unknown. In this case, one can propose a combined test based on the following decision rules: (a) the likelihood-ratio test (LRT) for equality of two normal populations and (b) the Shapiro-Wilk (S-W) test for normality. The rules (a) and (b) can be merged by, e.g., using the Bonferroni technique to offer the correct comparison of the samples distribution. Alternatively, we propose the exact density-based empirical likelihood (DBEL) ratio test. We develop the tsc package as the first R package available to perform the two-sample comparisons using the exact test procedures: the LRT; the LRT combined with the S-W test; as well as the newly developed DBEL ratio test. The Monte Carlo results and a real data example are also presented too.
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