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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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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

Calibration Curves: Correlation Coefficient

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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

Calculating and Interpreting the Linear Correlation Coefficient

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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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Correlations02:20

Correlations

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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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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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Related Experiment Video

Updated: Feb 2, 2026

Easy Measurement of Diffusion Coefficients of EGFP-tagged Plasma Membrane Proteins Using k-Space Image Correlation Spectroscopy
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Modified Pearson correlation coefficient for two-color imaging in spherocylindrical cells.

Sonisilpa Mohapatra1,2, James C Weisshaar3

  • 1Department of Chemistry, University of Wisconsin-Madison, Madison, WI, 53706, USA. smohapa2@jhmi.edu.

BMC Bioinformatics
|November 18, 2018
PubMed
Summary

The Pearson Correlation Coefficient (PCC) inaccurately assesses protein correlations in 3D bacterial cells. A modified PCC (MPCC) is introduced to accurately quantify spatial distributions in spherocylindrical cell geometries.

Keywords:
Bacterial imagingFluorescence microscopyPearson correlation coefficientSuperresolution imagingTwo color imaging

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Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions
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Area of Science:

  • Microscopy and Cell Biology
  • Biophysics
  • Computational Biology

Background:

  • Superresolution microscopy allows detailed visualization of protein distributions in live cells.
  • Analyzing spatial correlations between different proteins is crucial for understanding cellular functions.
  • Standard correlation methods like PCC may not accurately represent 3D spatial data when projected to 2D.

Purpose of the Study:

  • To evaluate the accuracy of the Pearson Correlation Coefficient (PCC) for analyzing 3D protein distributions in spherocylindrical cells.
  • To develop and validate a new method for assessing spatial correlations that accounts for cell geometry.

Main Methods:

  • Utilized superresolution fluorescence microscopy to image protein distributions in live E. coli.
  • Applied the standard Pearson Correlation Coefficient (PCC) to 2D projections of 3D data.
  • Developed a modified Pearson Correlation Coefficient (MPCC) using a geometry-specific reference matrix.
  • Validated MPCC through numerical simulations and experimental data.

Main Results:

  • Demonstrated that PCC provides inaccurate correlation values for 3D spherocylindrical cell projections.
  • Showed PCC can yield identical positive correlation values for both truly correlated and uncorrelated 3D distributions.
  • MPCC accurately quantifies correlations, correctly assessing both positive and negative relationships between spatial distributions.
  • MPCC showed correct behavior on experimental data of HU and RNA polymerase in E. coli.

Conclusions:

  • The standard PCC is unreliable for analyzing spatial protein correlations in spherocylindrical cells due to projection artifacts.
  • The modified Pearson Correlation Coefficient (MPCC) offers a robust and accurate method for assessing protein colocalization in such geometries.
  • MPCC is a valuable tool for quantitative analysis in live-cell superresolution microscopy and may be adaptable to other cell shapes.