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Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. [a] The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution.
The Spearman correlation coefficient is defined as the Pearson correlation coefficient between the rank variables. [6]For a sample of size , the pairs of raw scores (,) are converted to ranks [], [] , and is computed as
The point biserial correlation coefficient (r pb) is a correlation coefficient used when one variable (e.g. Y) is dichotomous; Y can either be "naturally" dichotomous, like whether a coin lands heads or tails, or an artificially dichotomized variable.
In statistics, the interclass correlation (or interclass correlation coefficient) measures the relationship between two variables of different classes (types), such as the weights of 10-year-old sons and their 40-year-old fathers.
Formally, the partial correlation between X and Y given a set of n controlling variables Z = {Z 1, Z 2, ..., Z n}, written ρ XY·Z, is the correlation between the residuals e X and e Y resulting from the linear regression of X with Z and of Y with Z, respectively.
In statistics, the autocorrelation of a real or complex random process is the Pearson correlation between values of the process at different times, as a function of the two times or of the time lag.
For continuous functions and , the cross-correlation is defined as: [1] [2] [3] () ¯ (+) which is equivalent to () ¯ where () ¯ denotes the complex conjugate of (), and is called displacement or lag.