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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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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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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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In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a...
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Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...
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Highly efficient hypothesis testing methods for regression-type tests with correlated observations and heterogeneous

Yun Zhang1, Gautam Bandyopadhyay2, David J Topham3

  • 1J Craig Venter Institute, 4120 Capricorn Lane, La Jolla 92037, CA, USA.

BMC Bioinformatics
|April 17, 2019
PubMed
Summary

We developed computationally efficient PB-transformed tests for hypothesis testing with correlated, high-throughput data. These methods outperform weighted LMER tests, offering faster analysis and more biologically relevant findings in cancer studies.

Keywords:
Hypothesis testingMatrix decompositionOrthogonal transformationRNA-seqRotated test

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Area of Science:

  • Biostatistics
  • Genomics
  • Bioinformatics

Background:

  • Practical hypothesis testing often involves correlated data with heterogeneous variance.
  • Weighted linear mixed-effects regression (LMER) accounts for complex covariance but is computationally intensive and prone to convergence issues.
  • High-throughput data analysis demands efficient and stable statistical methods.

Purpose of the Study:

  • To propose computationally efficient parametric and semiparametric hypothesis testing methods.
  • To address the limitations of existing methods for correlated and high-throughput data.
  • To introduce the PB-transformation for simplifying complex hypothesis testing problems.

Main Methods:

  • Developed specialized matrix techniques, the PB-transformation, to simplify hypothesis testing.
  • The PB-transformation reduces the original problem to an equivalent one-sample hypothesis testing problem.
  • Transformed data achieve a scalar variance-covariance matrix, enabling the use of one-sample Student's t-test or Wilcoxon signed rank test.

Main Results:

  • Proposed methods demonstrated superior performance over alternatives in simulations under various distributions.
  • The PB-transformed t-test significantly outperformed the weighted LMER test in high correlation scenarios, with drastically reduced computational cost (3s vs. 933s).
  • Application to RNA-seq data from a breast cancer study revealed more biologically relevant findings using the PB-transformed t-test compared to the weighted LMER test.

Conclusions:

  • PB-transformed tests serve as fast, numerically stable alternatives to the weighted LMER test for complex, high-throughput data.
  • These methods are suitable for datasets with both independent and matched/repeated samples, avoiding data subsetting or ignoring correlations.
  • The PBtest R package is available for practical implementation of these advanced statistical techniques.