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.

Noun

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