Step-up multiple comparison procedure for comparing several normal variances

Abstract

The article deals with a step-up multiple comparison procedure for testing the homogeneity of all the subsets of scale parameter of $k\mathrm{ }\left(k\ge 2\right)\mathrm{ }$distributions indexed by location and scale parameters. The methods of computation of exact critical constants for $k=3$ and simulated critical constants for $k>3$ are discussed and critical constants are tabulated for selected configurations. Using Monte Carlo simulation, it is shown that the proposed procedure has more power than the single-step procedure and the Newman-Keuls type step-down procedure. Application of the proposed procedure to exponential probability model is discussed.

Keywords:

• Type I family-wise error
• Power comparison
• Single step procedure
• Stepwise procedure
• Critical constants
• Closed testing procedure

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F03

Disclosure statement

No potential conflict of interest was reported by the authors.

Table 1. The values of exact critical constants $d_2$ and $d_3$.

Table 2. Simulated critical constants of the step up test procedure for $\alpha =.05$.

Table 3. Power comparison at $\alpha =.05$.