Correlation coefficient

A correlation coefficient is a coefficient that illustrates a quantitative measure of some type of correlation and dependence, meaning statistical relationships between two or more random variables or observed data values.

Types of correlation coefficients include:

• Pearson product-moment correlation coefficient, also known as r, R, or Pearson's r, a measure of the strength and direction of the linear relationship between two variables that is defined as the (sample) covariance of the variables divided by the product of their (sample) standard deviations.
• Intraclass correlation, a descriptive statistic that can be used when quantitative measurements are made on units that are organized into groups; describes how strongly units in the same group resemble each other.
• Rank correlation, the study of relationships between rankings of different variables or different rankings of the same variable
  • Spearman's rank correlation coefficient, a measure of how well the relationship between two variables can be described by a monotonic function
  • Kendall tau rank correlation coefficient, a measure of the portion of ranks that match between two data sets.
  • Goodman and Kruskal's gamma, a measure of the strength of association of the cross tabulated data when both variables are measured at the ordinal level.

Related concepts:

• Goodness of fit, any of several measures that measure how well a statistical model fits observations by summarizing the discrepancy between observed values and the values expected under the model in the correlation coefficient has to be between –1.0 and 1.0