pearson product-moment correlation coefficient

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pearson product-moment correlation coefficient

A researcher calculates the Pearson product-moment correlation coefficient for a dataset.

Definition

Noun: - A statistical measure: The Pearson product-moment correlation coefficient is a specific numerical index that quantifies the strength and direction of a linear relationship between two continuous variables. It is the most standard and widely used method for calculating such a correlation.

Usage

This term is used in formal, academic, and professional contexts, primarily in statistics, data science, psychology, and the social and natural sciences. It describes the result of a specific calculation. - It is often abbreviated as Pearson's r, r, or the correlation coefficient. - It is calculated as the covariance of the two variables divided by the product of their standard deviations. - Its value always ranges from -1 to +1.

Examples
  • In a research paper: "The between study hours and exam scores was calculated to be r = 0.85, indicating a strong positive relationship."
  • In data analysis: "We used the to assess the linear association between age and reaction time."
  • In reporting results: "A significant was found (r = -0.62, p < .01), suggesting that increased stress levels are linearly associated with lower job satisfaction."
Advanced Usage
  • Interpretation of values:
    • r = +1: A perfect positive linear relationship.
    • r = -1: A perfect negative linear relationship.
    • r = 0: No linear relationship.
    • Values closer to +1 or -1 indicate stronger linear relationships.
  • Assumptions: Its proper use assumes that the variables are continuous, approximately normally distributed, and have a linear relationship with homoscedasticity (constant variance of errors).
Variants and Related Words
  • Pearson's r (n): The common abbreviation for the Pearson product-moment correlation coefficient.
    • The scatterplot and a Pearson's r of 0.9 both confirm a very strong linear trend.
  • Correlation coefficient (n): A more general term for any measure of statistical relationship; the Pearson version is the most common type.
    • Several types of correlation coefficients exist for different kinds of data.
  • Covariance (n): A related measure of how two variables change together, which forms the numerator in the calculation of Pearson's r.
  • Linear correlation (n): The type of relationship measured by this coefficient.
Synonyms
  • Pearson's r
  • Product-moment correlation
  • Bivariate correlation (when referring specifically to the correlation between two variables)
Related Phrases
  • To compute/calculate the Pearson product-moment correlation coefficient: The action of performing the statistical calculation.
    • The software will compute the Pearson product-moment correlation coefficient for the selected variables.
  • The magnitude of the coefficient: Refers to the absolute value (strength) of 'r', ignoring its sign.
    • The magnitude of the coefficient was large, regardless of its negative direction.
Notes
  • This is a technical term. In many practical contexts, it is simply called the "correlation" or "correlation coefficient," with the Pearson method being the default assumption unless specified otherwise (e.g., Spearman's rank correlation).
  • It measures only relationships. Two variables may have a strong non-linear relationship but a Pearson 'r' near zero.
pearson product-moment correlation coefficient

A researcher calculates the Pearson product-moment correlation coefficient for a dataset.

Noun
  1. the most commonly used method of computing a correlation coefficient between variables that are linearly related