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A closed testing procedure for comparison between successive variances.

Navdeep Singh¹, Parminder Singh¹

¹Department of Mathematics, Guru Nanak Dev University, Amritsar, India.

Journal of Applied Statistics

|June 16, 2022

Summary

This summary is machine-generated.

This study introduces a stepwise statistical test to identify significant differences in variances between successive normal populations. The proposed method offers improved power and strongly controls the family-wise error rate compared to single-step approaches.

Keywords:

Type I family-wise error rate critical constant power comparison single-step procedure step-wise procedure

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Area of Science:

Statistics
Statistical Inference
Hypothesis Testing

Background:

Comparing variances of successive normal populations is crucial in statistical analysis.
Existing methods may not adequately control error rates or offer optimal power for sequential comparisons.

Purpose of the Study:

To propose a novel stepwise test procedure for simultaneously comparing variances of successive normal populations.
To ensure strong control of the family-wise error rate.
To extend the procedure for comparing scale parameters of exponential populations.

Main Methods:

Development of a stepwise hypothesis testing procedure for variance differences.
Numerical computation and tabulation of critical constants.
Monte Carlo simulation for power comparison.
Extension to two-parameter exponential distributions.

Main Results:

The proposed stepwise procedure effectively controls the family-wise error rate.
Tabulated critical constants facilitate practical application.
Monte Carlo simulations demonstrate superior power compared to single-step procedures.
The method is successfully extended to exponential populations.

Conclusions:

The developed stepwise procedure provides a statistically robust and powerful method for comparing variances of successive normal populations.
It offers a significant advantage over traditional single-step methods, particularly in controlling error rates and enhancing detection power.
The extension to exponential populations broadens its applicability in analyzing related data structures.