A progressive shift alternative to evaluate nonparametric tests for skewed data

When the power of different nonparametric tests is evaluated by simulation, the alternative hypothesis should be carefully designed to ensure validity of the results in the specific research field. In the paper, we propose a probit-based progressive shift alternative that is more realistic than the simple shift alternative for skewed non-negative data that occur in many research areas. Our motivation comes from parasitology. The progressive shift alternative is used to compare the power of 6 location-scale tests and 7 commonly used location tests for several skewed theoretical and empirical parasite distributions. It is shown that location-scale tests are more powerful than location tests. The results are relevant also in other fields where skewed distributions are common, e.g. in the analysis of financial, health care, or treatment cost data. The methods studied in the paper are available in a free and user friendly web tool.

When the power of different nonparametric tests is evaluated by simulation, the alternative hypothesis should be carefully designed to ensure validity of the results in the specific research field. In the article, we propose a probit-based progressive shift alternative that is more realistic than the simple shift alternative for skewed non-negative data that occur in many research areas. Our motivation comes from parasitology. The progressive shift alternative is used to compare the power of six location-scale tests and seven commonly used location tests for several skewed theoretical and empirical parasite distributions. It is shown that location-scale tests are more powerful than location tests. Programs for applying the methods studied in the article are freely available for download.