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Related Concept Videos

Correlation and Regression00:53

Correlation and Regression

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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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Calibration Curves: Correlation Coefficient01:10

Calibration Curves: Correlation Coefficient

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In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the...
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Correlation01:09

Correlation

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In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
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Correlations02:20

Correlations

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Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
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Coefficient of Correlation01:12

Coefficient of Correlation

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The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the...
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Correlation and Causation01:27

Correlation and Causation

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Statistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. An indirect relationship of the variables signifies a correlation, while a direct relationship shows causation. If it is determined that no connection exists between the variables, then the correlation is a coincidence.
Correlation versus Causation
If the dependent variable increases or decreases when the independent variable increases, there is a positive or negative...
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Related Experiment Video

Updated: Apr 11, 2026

Author Spotlight: Unlocking New Insights in fNIRS Studies - A Novel Framework for Inter-Brain Synchrony Analysis
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Integrative correlation: Properties and relation to canonical correlations.

Leslie Cope1, Daniel Q Naiman2, Giovanni Parmigiani3

  • 1The Sidney Kimmel Comprehensive Cancer Center, The Johns Hopkins University School of Medicine, United States.

Journal of Multivariate Analysis
|June 2, 2015
PubMed
Summary

This study explores the integrative correlation coefficient for validating gene expression microarray data. It reveals unique statistical properties, enhancing reproducible gene identification in meta-analyses.

Keywords:
BioinformaticsCorrelationCross-study validationGene expressionReproducibilityStatistics

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Area of Science:

  • Bioinformatics
  • Statistical Genetics
  • Computational Biology

Background:

  • Validating gene expression microarray results across diverse datasets and platforms is crucial for reliable biological insights.
  • Identifying reproducibly measured genes is essential for robust meta-analyses in genomics.

Purpose of the Study:

  • To investigate the mathematical and statistical properties of the integrative correlation coefficient.
  • To analyze the implications of these properties for identifying reproducible genes in meta-analyses.

Main Methods:

  • Development and analysis of the integrative correlation coefficient.
  • Exploration of its unique permutation-based null distribution.
  • Investigation of its behavior with increasing sample size.

Main Results:

  • The integrative correlation coefficient possesses a unique permutation-based null distribution.
  • A key finding is that its variance does not decrease with increasing sample size.
  • These properties offer insights into reproducible gene identification methods.

Conclusions:

  • The mathematical and statistical properties of the integrative correlation coefficient are significant for its application.
  • Understanding these properties is vital for accurate interpretation and use in meta-analysis.
  • The coefficient provides a valuable tool for identifying reproducibly measured genes across studies and platforms.