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The k-in-a-row up-and-down design, revisited
1Department of Statistics, University of Washington, Seattle, WA 98195-4322, U.S.A. assaf.oron@gmail.com
Statistics in Medicine
|April 21, 2009
Summary
The k-in-a-row (KR) experimental design, widely used for estimating percentiles, is confirmed to have a unique stationary mode. This study demonstrates KR
Area of Science:
- Psychology
- Statistics
- Sensory Science
Background:
- The k-in-a-row (KR) design is a widely adopted up-and-down method for estimating non-median percentiles, particularly in sensory studies.
- Despite its prevalence, the statistical properties of the KR design, including the existence of a unique mode in its asymptotic distribution, have been debated.
Purpose of the Study:
- To revisit and clarify the fundamental properties of the k-in-a-row (KR) experimental design.
- To confirm the existence of a unique stationary mode for the KR design and evaluate its operational characteristics compared to other up-and-down designs.
Main Methods:
- Revisiting the theoretical underpinnings of the k-in-a-row (KR) design.
- Presenting supporting proofs and numerical calculations to validate findings.
- Analyzing an anesthesiology experiment to illustrate design properties.
Main Results:
- The k-in-a-row (KR) design is confirmed to generate a unique stationary mode near the target percentile.
- KR demonstrates superior operational characteristics compared to two other extensively studied up-and-down designs.
- The study highlights the advantages of the up-and-down design family through a practical example.
Conclusions:
- The k-in-a-row (KR) design is statistically sound and possesses a unique mode, validating its use in percentile estimation.
- KR offers practical advantages over alternative up-and-down methods, making it a robust choice for experimental design.
- The findings support the continued application and understanding of KR in fields requiring precise percentile estimation.
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