Rank-based tests for interactions in a two-way design when there are ties

Area of Science:

• Statistics
• Non-parametric methods
• Hypothesis testing

Background:

• Non-parametric methods for interaction testing in two-way designs are valuable due to their robustness.
• Patel and Hoel's rank-based method is appealing for its invariance and lack of main effect assumptions.
• Wilcox compared three standard error estimation methods for Patel and Hoel's approach, with limited success.

Purpose of the Study:

• To extend Patel and Hoel's non-parametric interaction testing method to accommodate tied data.
• To compare the performance of the extended method against Wilcox's recommended approach, focusing on Type I error rates.

Main Methods:

• The study extends Cliff's work on tied values to the context of interaction hypothesis testing in two-way designs.
• Simulations were used to compare the Type I error rates of the extended method and Wilcox's method.

Main Results:

• One of Wilcox's methods showed satisfactory Type I error rates but assumed no tied values.
• The extended method, incorporating Cliff's findings, provides a viable solution for handling tied values in interaction testing.

Conclusions:

• The extended non-parametric method effectively addresses the issue of tied values in two-way interaction hypothesis testing.
• This extension offers improved Type I error control in the presence of ties, enhancing the reliability of non-parametric analyses.