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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

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Simultaneous Critical Values For T-Tests In Very High Dimensions.

Hongyuan Cao¹, Michael R Kosorok

¹Department of Statistics and Operations Research, 318 Hanes Hall, CB 3260, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599.

Bernoulli : Official Journal of the Bernoulli Society for Mathematical Statistics and Probability

|May 17, 2011

Summary

This study introduces a novel data-driven method for multiple hypothesis testing using t-tests. It improves statistical power by directly using critical values, outperforming traditional p-value approaches in complex data analyses.

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Area of Science:

Statistics
Biostatistics
Genomics

Background:

Multiple hypothesis testing is crucial in analyzing large datasets, such as genomic data.
Traditional methods using p-values can lack power in complex scenarios.
Hidden models complicate the accurate control of error rates.

Purpose of the Study:

To develop a data-driven procedure for multiple hypothesis testing using t-statistics.
To control error rates like k-family wise error rate (k-FWER), false discovery rate (FDR), and tail probability of false discovery proportion (FDTP).
To enhance the power of statistical tests in high-dimensional data analysis.

Main Methods:

Utilizing one-sample and two-sample t-statistics under a two-state hidden model.
Developing an asymptotically valid data-driven procedure for critical value determination.
Introducing a new consistent estimator for the proportion of alternative hypotheses.
Employing moderate deviations properties of t-statistics with minimal moment conditions.

Main Results:

The proposed method provides asymptotically valid control of k-FWER, FDR, and FDTP.
A new consistent estimator for the proportion of alternative hypotheses was developed.
Simulation studies confirmed theoretical results and showed significant power improvements over p-value methods.
The procedure demonstrated effectiveness in a real-world leukemia microarray data analysis.

Conclusions:

The data-driven critical value approach offers superior statistical power in multiple hypothesis testing.
The method is robust, requiring only finite fourth moments and general population conditions.
This approach is applicable to large-scale genomic studies, such as cancer microarray data analysis.