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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.
Statistical significance measures the probability that an observed result occurred by chance. If this probability, known as...
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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:
H0: The two variables (factors)...
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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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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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Test for Homogeneity

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The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can...
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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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A two-step hierarchical hypothesis set testing framework, with applications to gene expression data on ordered

Yihan Li, Debashis Ghosh1

  • 1Department of Statistics, Pennsylvania State University, University Park, State College, Pennsylvania 16802, USA. ghoshd@psu.edu.

BMC Bioinformatics
|April 16, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces a new framework for multi-dimensional multiple testing, controlling overall false discovery rate (OFDR) and mixed-directional false discovery rate (mdFDR) in large-scale experiments like gene expression studies.

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Area of Science:

  • Biostatistics
  • Genomics
  • Bioinformatics

Background:

  • Large-scale experiments involve numerous features and multiple hypotheses per feature, creating multi-dimensional multiple testing challenges.
  • Gene expression studies, particularly time-course or dose-response experiments, require testing differential expression across categories for each gene.

Purpose of the Study:

  • To develop a general framework for testing multiple sets of hypotheses in complex experimental settings.
  • To control the overall false discovery rate (OFDR) and introduce the mixed-directional false discovery rate (mdFDR) for hypothesis set testing.

Main Methods:

  • A two-step hierarchical hypothesis set testing procedure is proposed, controlling OFDR under independence.
  • The procedure is extended to incorporate directional decisions for two-sided alternatives, addressing mdFDR.
  • The framework is applied to microarray time-course/dose-response experiments, yielding three specific procedures.

Main Results:

  • Simulation studies confirm OFDR and mdFDR control under independence and positive correlations.
  • Two novel procedures demonstrate higher statistical power compared to existing methods.
  • The methodology identified 17 β-estradiol sensitive genes in breast cancer cells from a dose-response study.

Conclusions:

  • The proposed framework offers a versatile platform for multiple testing procedures in large-scale experiments with multiple sources of multiplicity.
  • Procedures derived from this framework effectively control OFDR and mdFDR, crucial for hypothesis set testing.
  • The methods are validated through simulations and real-world data, showing improved power and adaptability.