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Related Concept Videos

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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Correlations02:20

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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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Correlation01:09

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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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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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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.
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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.
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Meta-analyzing dependent correlations with correction for artifacts that multiplicatively attenuate the true

Shu Fai Cheung1, Darius K-S Chan2, Rong Wei Sun3

  • 1Department of Psychology, Faculty of Social Sciences, University of Macau, Avenida da Universidade, Taipa, Macau, China. sfcheung@umac.mo.

Behavior Research Methods
|August 24, 2018
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Summary

New methods improve meta-analysis of dependent correlations by correcting for artifacts. These samplewise-adjusted procedures provide accurate estimates of population mean correlation, unlike previous methods.

Keywords:
Correction for artifactsDependent effect sizesMeta-analysis

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Area of Science:

  • Psychometrics
  • Statistical Methodology
  • Meta-Analysis

Background:

  • Existing meta-analysis methods for dependent correlations can distort effect size variation.
  • Samplewise-adjusted procedures improve dependent correlation meta-analysis but lack artifact correction.
  • Artifact correction (e.g., unreliability) is increasingly vital in meta-analytic research.

Purpose of the Study:

  • To extend samplewise-adjusted procedures for meta-analyzing dependent correlations with artifact correction.
  • To evaluate the performance of new procedures under various conditions via Monte Carlo simulation.

Main Methods:

  • Monte Carlo simulation was employed to assess meta-analytic procedures.
  • Simulated data varied in correlation dependence, heterogeneity, sample size, and number of studies.
  • Procedures were compared based on bias and confidence interval coverage for population parameters.

Main Results:

  • Previous methods, including uncorrected samplewise procedures, produced biased estimates and poor confidence interval coverage.
  • Bias and undercoverage worsened with larger sample sizes and more studies.
  • Newly developed samplewise-adjusted procedures with artifact correction demonstrated negligible bias in estimating mean population correlation.

Conclusions:

  • Accurate meta-analysis of dependent correlations necessitates artifact correction for attenuation.
  • The proposed samplewise-adjusted procedures offer a robust solution for this challenge.
  • Further research can explore conditions for enhancing these improved meta-analytic techniques.