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Related Concept Videos

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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Spearman's Rank Correlation Test01:20

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Spearman's rank correlation test, also known as Spearman's rho, is a nonparametric method for assessing the strength and direction of association between two variables. This test is particularly valuable when the data distribution is unknown or when the assumption of normality does not hold. Named after the English psychologist and statistician Dr. Charles Edward Spearman, it serves as the nonparametric counterpart to Pearson's correlation coefficient.
Spearman's test calculates correlation by...
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Microsoft Excel: Pearson's Correlation01:18

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Microsoft Excel is a powerful tool for statistical analysis, including calculating Pearson's correlation coefficient, which measures the strength and direction of a linear relationship between two continuous variables. Pearson's correlation coefficient, often denoted as "r," ranges from -1 to 1. A value close to 1 indicates a strong positive correlation, meaning as one variable increases, the other does too. A value close to -1 indicates a strong negative correlation, implying...
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Coefficient of Correlation01:12

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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.
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Correlation and Regression00:53

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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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Calculating and Interpreting the Linear Correlation Coefficient01:11

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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. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:
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Related Experiment Video

Updated: Apr 15, 2026

Studying Metabolic Brain Connectivity Using 2-Deoxy-2-[18F]Fluoro-D-Glucose Dynamic Positron Emission Tomography at the Single-subject Level
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cocor: a comprehensive solution for the statistical comparison of correlations.

Birk Diedenhofen1, Jochen Musch1

  • 1Department of Experimental Psychology, University of Duesseldorf, Duesseldorf, Germany.

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|April 4, 2015
PubMed
Summary

Researchers can now easily compare correlation magnitudes using the free R software package, cocor. This tool provides essential statistical tests for comparing independent and dependent correlations, enhancing data analysis capabilities.

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Area of Science:

  • Statistics
  • Computational Statistics
  • Psychometrics

Background:

  • Comparing correlation magnitudes requires specific statistical tests.
  • Many statistical software packages lack robust tests for the significance of the difference between correlations.
  • This gap hinders accurate interpretation of relationships in research.

Purpose of the Study:

  • Introduce cocor, a free R software package, to address the need for comparing correlation magnitudes.
  • Provide a comprehensive suite of statistical tests for various correlation comparison scenarios.
  • Enhance the R statistical computing environment with user-friendly tools for correlation analysis.

Main Methods:

  • Developed the cocor package for the R programming language.
  • Included tests for comparing independent and dependent correlations (overlapping and nonoverlapping variables).
  • Implemented Zou's confidence interval for all comparisons and provided graphical user interfaces (RKWard plugin, web interface).

Main Results:

  • The cocor package offers a wide range of statistical tests for comparing correlation magnitudes.
  • It supports comparisons of independent and dependent correlations with various variable overlaps.
  • Zou's confidence interval is integrated for all supported comparisons.

Conclusions:

  • The cocor package effectively closes the gap in statistical software for comparing correlation magnitudes.
  • It provides researchers with a convenient, user-friendly, and scriptable tool for robust correlation analysis.
  • Enhances the R statistical environment for advanced psychometric and statistical research.