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Related Concept Videos

Statistical Hypothesis Testing01:16

Statistical Hypothesis Testing

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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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Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This...
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When performing a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis and the decision to reject or not.
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Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances
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HYPOTHESIS TESTING FOR HIGH-DIMENSIONAL SPARSE BINARY REGRESSION.

Rajarshi Mukherjee1, Natesh S Pillai2, Xihong Lin3

  • 1Department of Statistics, Stanford University, Sequoia Hall, 390 Serra Mall, Stanford, California 94305-4065, USA.

Annals of Statistics
|August 7, 2015
PubMed
Summary
This summary is machine-generated.

This study explores hypothesis testing for rare genetic variants in high-dimensional binary regression. We identified a new detection boundary phenomenon influenced by data sparsity and signal strength, crucial for association studies.

Keywords:
Higher CriticismMinimax hypothesis testingbinary regressiondetection boundarysparsity

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Area of Science:

  • Statistics
  • Genetics
  • High-dimensional data analysis

Background:

  • Hypothesis testing is crucial for identifying genetic variants associated with diseases.
  • High-dimensional and sparse binary regression models present unique challenges in statistical inference.
  • Existing methods may not fully capture the complexities of rare variant detection in sparse genetic data.

Purpose of the Study:

  • To investigate the detection boundary for minimax hypothesis testing in high-dimensional, sparse binary regression.
  • To understand the impact of design matrix sparsity on hypothesis testing power.
  • To develop and evaluate optimal tests for detecting rare variant effects.

Main Methods:

  • Derivation of the detection boundary as a function of design matrix sparsity index and signal strength.
  • Analysis of asymptotic power for different sparsity levels.
  • Development of an extended Higher Criticism Test for sparse regimes.
  • Comparison with the generalized likelihood ratio test in dense regimes.

Main Results:

  • A novel phenomenon in detection boundary behavior specific to sparse binary regression was observed.
  • The detection boundary is critically dependent on the design matrix sparsity index and signal strength.
  • For high sparsity, tests become asymptotically powerless regardless of signal strength.
  • The extended Higher Criticism Test is shown to be rate optimal and sharp in the sparse regime.

Conclusions:

  • The study provides a theoretical framework for understanding hypothesis testing in sparse binary regression.
  • Optimal testing strategies depend heavily on the sparsity characteristics of the genetic data.
  • The proposed extended Higher Criticism Test offers an effective solution for rare variant detection in sparse settings.