Extensions of empirical likelihood and chi-squared-based tests for ordered alternatives.

Area of Science:

• Statistics
• Hypothesis Testing

Background:

• Existing methods for comparing k populations assess equal distributions but vary in alternative hypotheses.
• Focus on two key alternative hypotheses: monotone and umbrella ordering.

Purpose of the Study:

• Propose new families of test statistics for comparing k populations.
• Develop powerful tests for monotone and umbrella orderings.

Main Methods:

• Introduce two new families of test statistics.
• Adapt existing and propose new tests for monotone ordering.
• Adapt these families for testing umbrella ordering.
• Compare test performance using simulations for power and Type I errors.

Main Results:

• Two known tests and two novel powerful tests are included under monotone ordering.
• The proposed families are effective for testing umbrella ordering.
• Comparative analysis of test members reveals performance differences in power and Type I errors across simulations.

Conclusions:

• The new test statistics provide effective tools for comparing k populations under specific orderings.
• The methods are validated through simulations and illustrated with real-world data applications.