Correlation Coefficient Value

Context:
- It can (typically) signify a strong relationship when close to -1 and 1.
- It can (typically) signify a weak relationship when close to 0.
- It can range from being a Sample Correlation Coefficient to being a Population Correlation Coefficient.
- …
Example(s):
- a Pearson Product-Moment Correlation Coefficient, often denoted with [math]\displaystyle{ r }[/math].
- a Spearman Rank Correlation Coefficient.
- …
Counter-Example(s):.
- a Covariance Value.
See: Confusion Matrix, Correlational Relationship, Correlation Function.

References

(Wikipedia, 2015) ⇒ https://www.wikiwand.com/en/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.

(Dubnicka, 2006e) ⇒ Suzanne R. Dubnicka. (2006). “Random Vectors and Multivariate Distributions - Handout 5." Kansas State University, Introduction to Probability and Statistics I, STAT 510 - Fall 2006.
- QUOTE: Suppose that X and Y are random variables with variances 2 X and 2 Y, respectively. The correlation between X and Y is given by Corr(X,Y) = X,Y = Cov(X,Y) X Y . The quantity X,Y is also called the correlation coefficient between X and Y .
(Starbird, 2006) ⇒ Michael Starbird. (2006). “Meaning from Data: Statistics Made Clear.” The Teaching Company
- QUOTE: The quantification of the strength of linear association that exists between two numeric variables. The correlation coefficient takes values between -1 and 1, where negative correlations mean that as the value of one variable rises, the other falls, and positive correlations mean that the values of the two variables rise together. Values of the correlation coefficient near 1 or -1 indicate a strong linear relationship between the two variables. Values near 0 indicate no linear relationship between the two variables.