Correlation coefficient
A correlation coefficient is a
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.
Types
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,
Pearson
The
Intra-class
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
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 coefficientis 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.
Tetrachoric and polychoric
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:
- The two variables were measured on a continuous scale, instead of as ordered-category variables.
- The two continuous variables followed a bivariate normal distribution.
When both variables are
See also
- 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
Notes
- ^ Correlation coefficient: A statistic used to show how the scores from one measure relate to scores on a second measure for the same group of individuals. A high value (approaching +1.00) is a strong direct relationship, values near 0.50 are considered moderate and values below 0.30 are considered to show weak relationship. A low negative value (approaching -1.00) is similarly a strong inverse relationship, and values near 0.00 indicate little, if any, relationship.[1]
References
- ^ "correlation coefficient". NCME.org. National Council on Measurement in Education. Archived from the original on July 22, 2017. Retrieved April 17, 2014.
- ISBN 0-935702-75-X. Archived from the original(PDF) on 15 February 2019. Retrieved 14 February 2019.
- ISBN 978-0-470-74664-6.
- ^ Weisstein, Eric W. "Statistical Correlation". mathworld.wolfram.com. Retrieved 2020-08-22.