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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.
The size of the correlation r indicates the...
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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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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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Wilcoxon Signed-Ranks Test for Matched Pairs01:09

Wilcoxon Signed-Ranks Test for Matched Pairs

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The Wilcoxon signed-rank test for matched pairs evaluates the null hypothesis by combining the ranks of differences with their signs. It essentially tests whether the median of the differences in a population of matched pairs is zero. Since the test incorporates more information than the sign test, it generally yields more trustable conclusions. This test also does not require the data to follow a normal distribution, but two conditions must be met for it to be applicable: (1) the data must...
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Correlation and Regression00:53

Correlation and Regression

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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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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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Related Experiment Video

Updated: Mar 1, 2026

A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment
12:18

A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment

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Optimal classifier for imbalanced data using Matthews Correlation Coefficient metric.

Sabri Boughorbel1, Fethi Jarray2, Mohammed El-Anbari3

  • 1Systems Biology Department, Sidra Medical and Research Centre, Doha, Qatar.

Plos One
|June 3, 2017
PubMed
Summary

A new classifier optimizes the Matthews Correlation Coefficient (MCC) for imbalanced biomedical data, outperforming standard methods. This approach offers a simpler, more efficient solution for binary classification challenges where data is unevenly distributed.

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Related Experiment Videos

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Area of Science:

  • Biomedical data analysis
  • Machine learning in healthcare
  • Bioinformatics

Background:

  • Data imbalance is a common problem in biomedical applications, leading to poor classifier generalization.
  • Traditional resampling methods are ineffective with very small classes.
  • Standard metrics like accuracy are inadequate for imbalanced datasets.

Purpose of the Study:

  • To develop a novel classifier optimized for the Matthews Correlation Coefficient (MCC) to address imbalanced data.
  • To create a classifier that handles data imbalance effectively without relying on resampling.

Main Methods:

  • Derived an optimal Bayes classifier for MCC using Frechet derivative.
  • Validated optimality using simulated data across all possible binary classifiers.
  • Evaluated the proposed MCC-classifier on 64 imbalanced datasets.

Main Results:

  • The proposed MCC-classifier demonstrated comparable performance to imbalanced SVM (SVM-imba).
  • The MCC-classifier showed superior CPU efficiency compared to SVM-imba.
  • Theoretical analysis confirmed the consistency property of the proposed algorithm.

Conclusions:

  • The novel MCC-classifier provides an effective and efficient solution for imbalanced data in biomedical binary classification.
  • Optimizing for MCC is a viable strategy to improve classifier performance on imbalanced datasets.
  • The proposed method offers a simpler alternative to complex techniques like imbalanced SVM.