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Related Concept Videos

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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Graphical Representation of Inequalities01:28

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The graph of the equation where y equals x squared forms a curve known as a parabola. This curve acts as a boundary in the coordinate plane, dividing it into distinct regions based on the relative position of points.When the equality sign in the equation is replaced with an inequality—such as greater than, less than, greater than or equal to, or less than or equal to—the graphical representation changes from a single curve into a broader shaded area that signifies the set of all...
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Collisions in Multiple Dimensions: Problem Solving01:06

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In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
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Collisions in Multiple Dimensions: Introduction01:05

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It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a...
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Sign Test for Median of Single Population01:20

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In general, the sign test serves as a nonparametric method to test hypotheses about the median of a single population when the data does not follow a known distribution. This simplicity makes it particularly useful for small sample sizes or when the assumptions of parametric tests cannot be met. The process begins with identifying a null hypothesis, typically stating that the population median equals a specific value. The alternative hypothesis could be that the median is either not equal to,...
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Test for Homogeneity01:23

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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Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances
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Efficient Test and Visualization of Multi-Set Intersections.

Minghui Wang1, Yongzhong Zhao1, Bin Zhang1

  • 1Department of Genetics and Genomic Sciences, Icahn Institute of Genomics and Multiscale Biology, Icahn School of Medicine at Mount Sinai, 1470 Madison Avenue, NY 10029, USA.

Scientific Reports
|November 26, 2015
PubMed
Summary
This summary is machine-generated.

Researchers developed SuperExactTest, a novel R package, to statistically assess and visualize intersections among multiple gene sets. This tool addresses limitations in current methods, enabling deeper insights into complex biological relationships.

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Area of Science:

  • Bioinformatics
  • Computational Biology
  • Statistical Genetics

Background:

  • Identifying shared features across multiple object sets is crucial in many scientific fields.
  • Analyzing multi-set intersections is key to understanding complex relationships but lacks statistical significance testing for three or more sets.
  • Existing visualization methods for multi-set intersections are not scalable.

Purpose of the Study:

  • To develop a theoretical framework and computational methods for assessing the statistical significance of intersections among three or more sets.
  • To create efficient and scalable techniques for visualizing multi-set intersections and their statistics.
  • To implement these methods in a user-friendly R software package, SuperExactTest.

Main Methods:

  • Developed a statistical framework based on combinatorial theory to compute distributions of multi-set intersections.
  • Designed an efficient procedure for calculating exact probabilities of multi-set intersections.
  • Created scalable visualization techniques for multi-set intersections and associated statistics.
  • Implemented the framework and visualization methods in the R package SuperExactTest.

Main Results:

  • Successfully developed and implemented the SuperExactTest R package, providing tools for statistical significance testing and visualization of multi-set intersections.
  • Demonstrated the utility of SuperExactTest through simulations and analyses of cancer gene sets and genome-wide association study (GWAS) gene sets.
  • The package enables efficient and scalable analysis of complex set intersections.

Conclusions:

  • SuperExactTest provides the first method to assess the statistical significance of intersections among three or more sets.
  • The developed visualization techniques are efficient and scalable, overcoming limitations of existing approaches.
  • SuperExactTest is expected to have broad applications in scientific data analysis across various disciplines.