Estimating the power of the two-sample Wilcoxon test for location shift

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Calculating statistical test power typically requires knowing the probability distribution's shape.
• Unknown distribution shapes present a challenge for traditional power analysis methods.

Purpose of the Study:

• To introduce a bootstrap method for approximating statistical test power for location shift.
• To demonstrate the method's reliability and accuracy without distribution shape assumptions.

Main Methods:

• A bootstrap method was developed to estimate power using observed or pilot data.
• The method was applied to the Wilcoxon two-sample test for location shift.
• Simulation studies were conducted to compare the bootstrap method with traditional approaches.

Main Results:

• The bootstrap method reliably approximates power for location shift tests.
• The proposed method showed higher accuracy than a benchmark traditional approach in simulations.
• The bootstrap method was successfully applied to a real-data example.

Conclusions:

• The bootstrap method offers a robust alternative for power calculations when distribution shape is unknown.
• This approach can inform sample size determination and the selection of optimal statistical tests.