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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 .
With any number of random variables in excess of 1, the variables can be stacked into a random vector whose i th element is the i th random variable. Then the variances and covariances can be placed in a covariance matrix, in which the (i, j) element is the covariance between the i th random variable and the j th one.
Pearson/Spearman correlation coefficients between X and Y are shown when the two variables' ranges are unrestricted, and when the range of X is restricted to the interval (0,1). Most correlation measures are sensitive to the manner in which X and Y are sampled. Dependencies tend to be stronger if viewed over a wider range of values.
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.
[12] [13] [clarification needed] After calculating the cross-correlation between the two signals, the maximum (or minimum if the signals are negatively correlated) of the cross-correlation function indicates the point in time where the signals are best aligned; i.e., the time delay between the two signals is determined by the argument of the ...
In statistics, Goodman and Kruskal's gamma is a measure of rank correlation, i.e., the similarity of the orderings of the data when ranked by each of the quantities.It measures the strength of association of the cross tabulated data when both variables are measured at the ordinal level.
A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. [1] If one considers the correlation function between random variables representing the same quantity measured at two different points, then this is often referred to as an ...
The concordance correlation coefficient is nearly identical to some of the measures called intra-class correlations.Comparisons of the concordance correlation coefficient with an "ordinary" intraclass correlation on different data sets found only small differences between the two correlations, in one case on the third decimal. [2]