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Sample size determination in two-sided distribution-free treatment versus control multiple comparisons.

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This study provides methods for determining statistical power and sample size for distribution-free multiple comparison tests involving K treatments versus a control. The developed formulas accurately calculate power for various adjustment methods, aiding research design.

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Area of Science:

  • Statistics
  • Biostatistics
  • Experimental Design

Background:

  • Determining appropriate sample size and statistical power is crucial for the validity of multiple comparison tests.
  • Existing methods often rely on assumptions about data distribution, limiting their applicability.
  • Distribution-free tests offer an alternative when distributional assumptions are uncertain.

Purpose of the Study:

  • To develop and validate methods for power and sample size determination in distribution-free multiple comparison tests.
  • To address both per-pair and all-pairs power definitions for K treatments versus a control.
  • To provide practical tools applicable with known or unknown underlying distributions.

Main Methods:

  • Derivation of power formulas for joint and pairwise ranking mechanisms.
  • Explicit formulation of power for single-step, step-down, and step-up adjustment procedures.
  • Assessment of numerical integration methods, including quasi-Monte Carlo and Monte Carlo integration.
  • Validation through simulation studies.

Main Results:

  • Accurate power and sample size calculation formulas were derived for distribution-free multiple comparison tests.
  • Monte Carlo integration demonstrated superior accuracy for power calculations.
  • The methods are applicable whether underlying distributions are known or estimated from pilot data.

Conclusions:

  • The proposed methods offer a robust approach to power and sample size determination for non-parametric multiple comparisons.
  • Monte Carlo integration is recommended for its accuracy in these calculations.
  • The findings facilitate more reliable experimental design in comparative studies.