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Related Concept Videos

Microsoft Excel: Pearson's Correlation01:18

Microsoft Excel: Pearson's Correlation

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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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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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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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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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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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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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More Voodoo correlations: when average-based measures inflate correlations.

Andrew Brand1, Michael T Bradley

  • 1a King's College London.

The Journal of General Psychology
|May 20, 2014
PubMed
Summary
This summary is machine-generated.

Using averaged measures in correlational designs can inflate correlation estimates significantly, by up to 76%. A simple analysis exists to prevent this inflation, safeguarding research integrity.

Keywords:
averagingcorrelationeffect sizeinflationreliability

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Area of Science:

  • Psychometrics
  • Statistical Modeling

Background:

  • Correlational research designs are widely used in scientific inquiry.
  • Average-based measures are frequently employed in these designs.
  • Potential inflation of correlation estimates using averaged measures is not well understood.

Purpose of the Study:

  • To quantify the inflation of correlation estimates when using average-based measures in common correlational designs.
  • To assess the real-world impact of this inflation by re-analyzing existing study data.
  • To identify a straightforward method to mitigate this statistical artifact.

Main Methods:

  • Conducted a Monte Carlo simulation to model the effect of averaged measures on correlation estimates.
  • Re-analyzed data from two independent, previously published studies.
  • Employed statistical analysis to determine the degree of correlation inflation.

Main Results:

  • Monte Carlo simulations demonstrated substantial inflation of correlation estimates, reaching up to 76%.
  • Re-analysis of two studies showed correlation estimates were inflated by over 50% in both cases.
  • Identified a simple analytical technique to correct for this inflation.

Conclusions:

  • The use of average-based measures can lead to misleadingly high correlation estimates in research.
  • This inflation is a significant issue, impacting previously published findings.
  • A readily available statistical method can effectively prevent and correct for this correlation inflation.