On powerful exact nonrandomized tests for the Poisson two-sample setting.

Area of Science:

• Statistics
• Biostatistics
• Hypothesis Testing

Background:

• Comparing two independent Poisson distributions often involves testing the ratio of population means.
• Existing conditional tests are optimally powerful only with randomized decisions at the boundary.
• There is a need for nonrandomized, powerful tests in this domain.

Purpose of the Study:

• To adapt Boschloo's method for constructing a powerful nonrandomized test for Poisson distributions.
• To introduce the Poisson-Boschloo test and evaluate its performance.
• To extend the methodology to two-sided equivalence testing.

Main Methods:

• Adapted Boschloo's 1970 approach for binomial data to the Poisson case.
• Developed the Poisson-Boschloo test based on a cutoff for the observed total number of events.
• Analyzed power loss compared to the randomized Uniformly Most Powerful Unbiased (UMPU) test.
• Extended the construction for two-sided equivalence testing.

Main Results:

• The Poisson-Boschloo test achieves power nearly equivalent to the randomized UMPU test.
• Sample size calculations for the Poisson-Boschloo test can use existing UMPU test procedures.
• Approximate sample size calculation methods are rendered unnecessary.
• The test construction successfully extends to two-sided equivalence testing.

Conclusions:

• The Poisson-Boschloo test provides a powerful and practical nonrandomized alternative for comparing Poisson distributions.
• It simplifies sample size determination, making it more accessible.
• The methodology is adaptable for equivalence testing, offering similar advantages.