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Related Concept Videos

Coefficient of Correlation01:12

Coefficient of Correlation

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 strength of the linear...
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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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Calibration Curves: Correlation Coefficient01:10

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Correlation and Regression00:53

Correlation and Regression

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 negative...
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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 that as one...

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Should Pearson's correlation coefficient be avoided?

Richard A Armstrong1

  • 1School of Life and Health Sciences: Ophthalmic Research Group, School of Optometry, Aston University, Birmingham, UK.

Ophthalmic & Physiological Optics : the Journal of the British College of Ophthalmic Opticians (Optometrists)
|August 20, 2019
PubMed
Summary
This summary is machine-generated.

This study surveyed statistical methods in ophthalmic literature, finding limited adherence to Pearson

Keywords:
Pearson's correlation coefficient (r)bivariate normal distributioncorrelationcurvilinear regressionpartial correlationrange restriction

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Area of Science:

  • Ophthalmic research
  • Statistical analysis
  • Biometry

Background:

  • Pearson's correlation coefficient (r) is frequently used in ophthalmic literature.
  • Understanding the limitations and appropriate application of statistical methods is crucial for valid research.
  • The use of correlation coefficients requires careful consideration of data distribution and assumptions.

Purpose of the Study:

  • To assess the application of Pearson's correlation coefficient (r) in ophthalmic journals.
  • To identify limitations associated with the use of Pearson's r.
  • To recommend alternative statistical methods when appropriate.

Main Methods:

  • Systematic search of online archives for Ophthalmic and Physiological Optics, Optometry and Vision Science, and Clinical and Experimental Optometry.
  • Keywords used included 'correlation' and 'Pearson's r'.
  • Analysis of the frequency of use for various correlation coefficients and related statistical concepts.

Main Results:

  • Pearson's r was frequently used, but assumptions like bivariate normality were rarely addressed.
  • Spearman's rank correlation and intra-class correlation coefficient (ICC) were also employed.
  • Limited attention was given to sample size issues and the interpretation of correlation as causality.

Conclusions:

  • Investigators should critically evaluate the assumptions and limitations of Pearson's r.
  • Consideration of non-linearity, data distribution, outliers, sample size, and causality is essential.
  • A more cautious approach to using Pearson's r and exploring alternative methods is recommended.