Acorrelation coefficient is anumerical measure of some type oflinearcorrelation, meaning alinear function between twovariables.[a] The variables may be two columns of a givendata set of observations, often called asample, or two components of amultivariate random variable with a knowndistribution.[citation needed]
Several types of correlation coefficient exist, each with their own definition and own range of usability and characteristics. They all assume values in the range from −1 to +1, where ±1 indicates the strongest possible correlation and 0 indicates no correlation.[2] As tools of analysis, correlation coefficients present certain problems, including the propensity of some types to be distorted byoutliers and the possibility of incorrectly being used to infer acausal relationship between the variables (for more, seeCorrelation does not imply causation).[3]
There are several different measures for the degree of correlation in data, depending on the kind of data: principally whether the data is a measurement,ordinal, orcategorical.
ThePearson product-moment correlation coefficient, also known asr,R, orPearson's r, is a measure of the strength and direction of thelinear relationship between two variables that is defined as thecovariance of the variables divided by the product of their standard deviations.[4] This is the best-known and most commonly used type of correlation coefficient. When the term "correlation coefficient" is used without further qualification, it usually refers to the Pearson product-moment correlation coefficient.
Intraclass correlation (ICC) is a descriptive statistic that can be used, when quantitative measurements are made on units that are organized into groups; it describes how strongly units in the same group resemble each other.
Rank correlation is a measure of the relationship between the rankings of two variables, or two rankings of the same variable:
Thepolychoric correlation coefficient measures association between two ordered-categorical variables. It's technically defined as the estimate of the Pearson correlation coefficient one would obtain if:
When both variables aredichotomous instead of ordered-categorical, thepolychoric correlation coefficient is called the tetrachoric correlation coefficient.
The correlation between two variables have different associations that are measured in values such asr orR. Correlation values range from −1 to +1, where ±1 indicates the strongest possible correlation and 0 indicates no correlation between variables.[5]
| r orR | r orR | Strength or weakness of association between variables[6] |
|---|---|---|
| +1.0 to +0.8 | -1.0 to -0.8 | Perfect or very strong association |
| +0.8 to +0.6 | -0.8 to -0.6 | Strong association |
| +0.6 to +0.4 | -0.6 to -0.4 | Moderate association |
| +0.4 to +0.2 | -0.4 to -0.2 | Weak association |
| +0.2 to 0.0 | -0.2 to 0.0 | Very weak or no association |
