Definition

Noun: A coefficient of correlation is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It is a single number that summarizes how closely the variables move together.

Usage

The term is used primarily in statistics, data analysis, economics, psychology, and scientific research to describe and measure associations. * Researchers calculated the coefficient of correlation between study hours and exam scores. * A high coefficient of correlation does not imply that one variable causes the other. * The report included a table showing the coefficient of correlation for each pair of economic indicators.

Examples

• The coefficient of correlation between temperature and ice cream sales is positive and strong.
• To validate the hypothesis, we must examine the coefficient of correlation.
• A coefficient of correlation near zero suggests no linear relationship.

Advanced Usage

• Pearson correlation coefficient: The most common measure, often simply called "the correlation coefficient," denoted by .
  • The Pearson coefficient of correlation is appropriate for data measured on an interval or ratio scale.
• Spearman's rank correlation coefficient: A nonparametric measure that assesses monotonic relationships, denoted by (rho).
  • For ordinal data, Spearman's coefficient of correlation is more suitable.

Variants and Related Words

• Correlation coefficient: A fully synonymous term.
• Correlation (r): In many contexts, especially when the type is implied (e.g., Pearson's), the single word "correlation" is used to mean the coefficient.
• R-squared (R²): The coefficient of determination, which is the square of the correlation coefficient, representing the proportion of variance shared.

Synonyms

• Correlation coefficient (exact synonym)
• Pearson's r (specific type)

Related Phrases

• Positive correlation: When the coefficient is greater than 0, indicating that as one variable increases, the other tends to increase.
• Negative correlation: When the coefficient is less than 0, indicating that as one variable increases, the other tends to decrease.
• No correlation: When the coefficient is approximately 0, indicating no linear relationship.

Noun

1. a statistic representing how closely two variables co-vary; it can vary from -1 (perfect negative correlation) through 0 (no correlation) to +1 (perfect positive correlation)
   • what is the correlation between those two variables?