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Related Concept Videos

Types of Hypothesis Testing01:11

Types of Hypothesis Testing

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There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed that the null hypothesis is a neutral statement against which the alternative hypothesis is tested. The alternative hypothesis is a claim that instead has a certain direction. If the null hypothesis claims that p = 0.5, the alternative hypothesis would be an opposing statement to this and can be put either p > 0.5, p < 0.5, or p...
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Errors In Hypothesis Tests01:14

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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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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.
Statistical significance measures the probability that an observed result occurred by chance. If this probability, known as...
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Accuracy and Errors in Hypothesis Testing01:13

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Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
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Multiple Comparison Tests01:13

Multiple Comparison Tests

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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.
It would be easy to compare two samples using a significance alpha level of 0.05. In other words, there is only one sample pair to be compared. However, it would be difficult to identify a significantly different sample if the number...
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Confounding in Epidemiological Studies01:27

Confounding in Epidemiological Studies

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Confounding in statistical epidemiology represents a pivotal challenge, referring to the distortion in the perceived relationship between an exposure and an outcome due to the presence of a third variable, known as a confounder. This variable is associated with both the exposure and the outcome but is not a direct link in their causal chain. Its presence can lead to erroneous interpretations of the exposure's effect, either exaggerating or underestimating the true association. This...
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CONFOUNDER ADJUSTMENT IN MULTIPLE HYPOTHESIS TESTING.

Jingshu Wang1, Qingyuan Zhao1, Trevor Hastie2

  • 1Department of Statistics, The Wharton School, University of Pennsylvania, 400 Huntsman Hall, 3730 Walnut St, Philadelphia, Pennsylvania 19104, USA.

Annals of Statistics
|August 24, 2019
PubMed
Summary
This summary is machine-generated.

This study unifies statistical methods for large-scale hypothesis testing, addressing bias from confounding factors. New estimators offer powerful, accurate results, controlling errors even with strong confounding in big data analysis.

Keywords:
Empirical nullPrimary 62J15batch effectrobust regressionsecondary 62H25surrogate variable analysisunwanted variation

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Area of Science:

  • Statistics
  • Bioinformatics
  • Genomics

Background:

  • Large-scale studies involve numerous simultaneous significance tests, susceptible to bias from latent confounding factors like batch effects.
  • Confounding variables can correlate with primary variables (e.g., treatment, phenotype) and outcomes, compromising hypothesis testing integrity.
  • Existing statistical methods aim to adjust for confounders but lack a unified framework for complex scenarios.

Purpose of the Study:

  • To unify and generalize existing statistical methods for adjusting hypothesis testing in the presence of confounding factors.
  • To extend methods to accommodate multiple primary and nuisance variables.
  • To analyze the statistical properties and provide theoretical guarantees for adjusted hypothesis testing procedures.

Main Methods:

  • Developed a unified statistical framework encompassing various confounder adjustment methods.
  • Generalized existing techniques (RUV-4, LEAPP) to handle multiple primary and nuisance variables.
  • Provided theoretical guarantees for estimators under different identification conditions (negative controls, sparse non-nulls).

Main Results:

  • Proposed estimators based on RUV-4 and LEAPP demonstrate asymptotic power comparable to oracle estimators when confounding is strong.
  • Asymptotic z-tests derived from these estimators effectively control Type I error rates in hypothesis testing.
  • Numerical experiments confirm that the Benjamini-Hochberg procedure controls the false discovery rate with sufficiently large sample sizes.

Conclusions:

  • The unified framework and new estimators provide robust solutions for hypothesis testing in large-scale studies with confounding.
  • Theoretical guarantees and empirical results support the reliability and power of the proposed methods.
  • These advancements are crucial for accurate interpretation of results in complex biological and data-intensive research.