Using Kurtosis for Selecting One-Sample T-Test or Wilcoxon Signed-Rank Test

Aims / Objectives: To introduce a statistical test, which is mixture of the one-sample t-test and Wilcoxon signed-rank test depends on sample kurtosis, using data from symmetric univariate distribution with finite variance.
 Study Approach: Computer simulation coverage probabilities power calculations either or based software R.
 Methodology: Data are generated differing sizes Normal, Uniform, student-t small degrees freedom, Laplace distributions. Coverage compared t-test, three proposed tests select kurtosis being significantly low high either. Nonstandard values t, probability Type I error, selected to account for discrete nature allowing fair comparisons among tests.
 Results: The false positive rate simulated these nine distributions both two-sided one-sided tests, five testing procedures.
 Conclusion: When dataset sampled distribution, then in comparison equal preference Normal fact more preferable non-Normal tested herein. For sizes, preferred over but otherwise all tests.