Correlation coefficient#Interpreting correlation coefficient values

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, or categorical.

The Pearson product-moment correlation coefficient, also known as {{mvar|r}}, {{mvar|R}}, or Pearson's {{mvar|r}}, is a measure of the strength and direction of the linear relationship between two variables that is defined as the covariance of the variables divided by the product of their standard deviations.{{Cite web|last=Weisstein|first=Eric W.|title=Statistical Correlation|url=https://mathworld.wolfram.com/StatisticalCorrelation.html|access-date=2020-08-22|website=mathworld.wolfram.com|language=en}} 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:

• Spearman's rank correlation coefficient is a measure of how well the relationship between two variables can be described by a monotonic function.
• The Kendall tau rank correlation coefficient is a measure of the portion of ranks that match between two data sets.
• Goodman and Kruskal's gamma is a measure of the strength of association of the cross tabulated data when both variables are measured at the ordinal level.

The polychoric 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:

1. The two variables were measured on a continuous scale, instead of as ordered-category variables.
2. The two continuous variables followed a bivariate normal distribution.

When both variables are dichotomous instead of ordered-categorical, the polychoric correlation coefficient is called the tetrachoric correlation coefficient.

The correlation between two variables have different associations that are measured in values such as {{mvar|r}} or {{mvar|R}}. Correlation values range from −1 to +1, where ±1 indicates the strongest possible correlation and 0 indicates no correlation between variables.{{cite book |last1=Taylor |first1=John R. |title=An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements |date=1997 |publisher=University Science Books |location=Sausalito, CA |isbn=0-935702-75-X |page=217 |edition=2nd |url=http://faculty.kfupm.edu.sa/phys/aanaqvi/Taylor-An%20Introduction%20to%20Error%20Analysis.pdf |access-date=14 February 2019 |archive-url=https://web.archive.org/web/20190215050550/http://faculty.kfupm.edu.sa/phys/aanaqvi/Taylor-An%20Introduction%20to%20Error%20Analysis.pdf |archive-date=15 February 2019 |url-status=dead }}

• Correlation disattenuation
• Coefficient of determination
• Correlation and dependence
• Correlation ratio
• Distance correlation
• 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
• Multiple correlation
• Partial correlation

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Category:Correlation indicators

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