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Hypothesis testing is a critical statistical procedure facilitating informed, evidence-based decisions. It begins with a hypothesis, which is a tentative explanation, or a prediction about a population parameter. This hypothesis can be either a null hypothesis (H0), indicating no effect or difference, or an alternative hypothesis (Ha), suggesting an effect or difference.
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The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
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Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
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There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
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Multiple comparison test, abbreviated as MCT, is a post hoc analysis generally performed after comparing multiple samples with one or more tests. An MCT will help identify a significantly different sample among multiple samples or a factor among multiple factors.
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Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...
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Bayesian Hidden Markov Models for Dependent Large-Scale Multiple Testing.

Xia Wang1, Ali Shojaie2, Jian Zou3

  • 1Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221, U.S.A.

Computational Statistics & Data Analysis
|October 31, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a flexible Bayesian multiple hypotheses testing method for dependent data. It effectively manages test dependencies and distribution uncertainties, optimizing error rates for better decision-making.

Keywords:
Bayesian hierarchical modelDirichlet mixture process priorFalse discovery rateHidden Markov modelMultiple hypotheses testing

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Area of Science:

  • Statistics
  • Biostatistics
  • Computational Biology

Background:

  • Multiple hypotheses testing is crucial in data analysis but faces challenges with dependent data.
  • Ignoring data dependence can lead to inefficient and biased statistical decisions.
  • Incorrectly specifying non-null distributions can cause significant false positive and false negative errors.

Purpose of the Study:

  • To develop an optimal and flexible multiple hypotheses testing procedure for dependent data using Bayesian techniques.
  • To address the challenges of dependence structure and non-null distribution misspecification in hypothesis testing.
  • To optimize the false negative rate (FNR) while controlling the false discovery rate (FDR).

Main Methods:

  • Utilized Hidden Markov Models to model the dependence structure among hypotheses tests.
  • Applied Dirichlet mixture process priors to the non-null distribution to prevent misspecification.
  • Developed a Bayesian testing algorithm for both pointwise and clusterwise analyses.

Main Results:

  • The proposed Bayesian procedure effectively handles dependent data and distribution uncertainties.
  • Demonstrated improved performance in controlling error rates compared to existing methods.
  • Validated through simulations and real-world data applications.

Conclusions:

  • The developed Bayesian multiple hypotheses testing procedure offers an optimal and flexible solution for dependent data.
  • It successfully mitigates issues arising from dependence and distribution misspecification.
  • The method provides a robust framework for accurate statistical inference in complex data scenarios.