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Convex hull test for ordered categorical data
V W Berger1, T Permutt, A Ivanova
1Food and Drug Administration, Center for Biologics Evaluation and Research, Rockville, Maryland 20852-1448, USA. bergerv@cber.fda.cov
Biometrics
|February 13, 1999
Summary
Researchers explored statistical tests for ordered contingency tables. The Smirnov and convex hull tests offer improved power compared to linear rank tests, especially under specific margin conditions, ensuring more reliable significance detection.
Area of Science:
- Statistics
- Biostatistics
- Data Analysis
Background:
- Testing for stochastic order in 2 x J contingency tables often involves setting significance cutoffs based on marginal distributions.
- Linear rank tests, while common, can exhibit zero power for certain alternatives given specific marginal conditions.
Purpose of the Study:
- To evaluate alternative statistical tests for stochastic order in ordered contingency tables.
- To identify tests that maintain power across various marginal conditions and alternatives.
Main Methods:
- Exact conditional power calculations were employed.
- Simulations were conducted to assess test performance.
- The study focused on Smirnov and convex hull tests in comparison to linear rank tests.
Main Results:
- Smirnov and convex hull tests effectively avoid the power drawback of linear rank tests.
- The convex hull test demonstrates admissibility, palindromic invariance, and optimal significance level minimization.
- These tests maintain power even when margins satisfy specific conditions.
Conclusions:
- The Smirnov and convex hull tests are superior to linear rank tests for detecting stochastic order in ordered contingency tables.
- The convex hull test offers robust performance and desirable statistical properties for hypothesis testing.
- These findings advocate for the use of Smirnov and convex hull tests in relevant statistical analyses.