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Related Concept Videos

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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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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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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Calibration Curves: Correlation Coefficient01:10

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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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Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
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Correlation Coefficients for a Study with Repeated Measures.

Guogen Shan1, Hua Zhang2, Tao Jiang3

  • 1Epidemiology and Biostatistics Program, School of Public Health, University of Nevada Las Vegas, Las Vegas, NV 89154, USA.

Computational and Mathematical Methods in Medicine
|April 18, 2020
PubMed
Summary
This summary is machine-generated.

For repeated measures, a mixed-effects model provides the most accurate correlation estimates. This approach accounts for within-subject variability, unlike traditional Pearson correlation, offering reliable trajectory analysis.

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Area of Science:

  • Biostatistics
  • Longitudinal Data Analysis

Background:

  • Repeated measures are common in studies to track changes over time.
  • Determining the correlation between measures in such studies is a key initial step.
  • Traditional methods like Pearson correlation may be inappropriate for longitudinal data.

Purpose of the Study:

  • To compare five methods for calculating correlation in repeated-measure studies.
  • To evaluate the accuracy and reliability of different correlation calculation techniques.
  • To identify the most suitable method for analyzing correlated longitudinal data.

Main Methods:

  • Comparison of five correlation calculation methods: Pearson correlation, correlation of subject means, partial correlation for subject effect, partial correlation for visit effect, and a mixed-effects model approach.
  • Evaluation based on average correlation and mean squared error.
  • Analysis of correlation structures within mixed-effects models, specifically the compound symmetric structure.

Main Results:

  • Pearson correlation, while sometimes close, may not be theoretically sound for repeated measures due to ignoring within-subject correlations.
  • Mixed-effects models offer a more appropriate framework by accounting for the correlation structure.
  • The mixed-effects model with a compound symmetric structure demonstrated correlations close to the nominal level with minimal mean squared error.

Conclusions:

  • The mixed-effects model approach, particularly with a compound symmetric structure, is recommended for correlation analysis in repeated-measure studies.
  • This method provides more accurate and reliable correlation estimates compared to traditional methods.
  • Accurate correlation estimation is crucial for understanding the trajectory of measures over time in longitudinal research.