# Correlation

The correlation is any relationship statistics , causal or not, between two random variables or bivariate data. Correlation is any statistical association, although in common use it most often refers to how close the two variables are to having a linear relationship . Correlations are useful to indicate a predictive relationship that can be exploited in practice.

## Summary

[ hide ]

• 1 Correlation coefficient
• 2 Rank correlation
• 3 Types of correlations
• 5 Sources

## Correlation coefficient

A correlation coefficient is a numerical measure of some kind of correlation, which means a statistical relationship between two variables. Variables can be two columns of a given set of observational data, often called samples, or two components of a multivariable random variable with a known distribution.

There are several types of correlation coefficients, each with its own definition and range of usability and characteristics. All assume values ​​in the range of −1 to +1, where ± 1 indicates the strongest possible agreement and 0 indicates the strongest possible disagreement. As analysis tools, correlation coefficients present certain problems, including the propensity of some types to be distorted by outliers and the possibility that they may be used incorrectly to infer a causal relationship between variables.

## Range correlation

A rank correlation is any one of several statistics that measure an ordinal association: the relationship between the ranges of different ordinal variables or different ranges of the same variable, where a “range” is the assignment of the order labels “first”, ” second “,” third “, etc. to different observations of a particular variable. A rank correlation coefficient measures the degree of similarity between two classifications and can be used to assess the importance of the relationship between them. For example, two important common nonparametric methods that use rank correlation are the Mann-Whitney U-test and the Wilcox signed-rank test.

## Types of correlations

1 – Pearson’s Product Moment Correlation Coefficient (Pearson’s Correlation): This is just the standard function already in Excel , Pearson (1896).

2 – Spearman’s Rank Correlation Coefficient (Spearman’s Correlation): A member of the family of rank-based correlation coefficients, Spearman (1904).

3 – Quadrant Correlation Coefficient, or Quadrant Count Ratio: A member of the family of rank-based correlation coefficients, Blomqvist (1950).

4 – Kendall’s Tau Rank Correlation Coefficient (Kendall’s Tau Correlation): If ‘ties’ is set to TRUE, the macro calculates Kendall’s tau-b, adjusting the ties, Kendall (1949).

5 – Goodman and Kruskal’s Gamma Rank Correlation Coefficient (Goodman-Kruskal Gamma): A member of the family of rank-based correlation coefficients, Goodman and Kruskal (1954).

6 – Correlation Median Estimator: As discussed by Pasman and Shevylakov (1987).

7 – Tukey’s BiWeight Mid Correlation Coefficient (Tukey BiWeight MidCorrelation): A type of M-estimator or Estimator of the maximum likelihood type, Wilcox (1997).

8 – Fisher e Yates Normal Scores Correlation Coefficient (Fisher Yates Normal Scores): As described in Fieller and Pearson (1961).

9 – Bivariate Alpha-Trimmed Correlation Coefficient (Bivariate Alpha-Trimmed): As described in Wilcox (1994).

10 – Univariate Alpha-Winsorized Pearson Correlation Coefficient (Univariate Alpha-Winsorized): As described in Wilcox (1993).

11 – Median Correlation Coefficient: As discussed by Shevylakov (2011).

12 – MAD Gideon Correlation Coefficient (MAD Correlation, Gideon): As described by Gideon (2007).

13 – MAD Shevylakov Coefficient Correlation (MAD Correlation, Shevylakov): As discussed by Pasman and Shevylakov (1987).

14 – Absolute Value Correlation Coefficient (Absolute Value Correlation): As described by Gideon (2007).

15 – Spearman’s Footrule Rank Correlation Coefficient (Footrule Correlation): A member of the family of rank-based correlation coefficients, Spearman (1906).

16 – Percentage Bend Correlation (Percentage Bend Correlation): Requires a “curve” value between (0.1), Wilcox recommends = 0.2, Wilcox (1994).