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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. [citation needed]
However, the Pearson correlation coefficient (taken together with the sample mean and variance) is only a sufficient statistic if the data is drawn from a multivariate normal distribution. As a result, the Pearson correlation coefficient fully characterizes the relationship between variables if and only if the data are drawn from a multivariate ...
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.
If F(r) is the Fisher transformation of r, the sample Spearman rank correlation coefficient, and n is the sample size, then z = n − 3 1.06 F ( r ) {\displaystyle z={\sqrt {\frac {n-3}{1.06}}}F(r)} is a z -score for r , which approximately follows a standard normal distribution under the null hypothesis of statistical independence ( ρ = 0 ).
Cohen's Kappa, Krippendorff's Alpha, Intra-Class correlation coefficients, Correlation coefficients, Kendal's concordance coefficient, etc. are useful statistical tools. (B) Test-Retest Reliability: Test-Retest Procedure is estimation of temporal consistency of the test.
In the analysis of data, a correlogram is a chart of correlation statistics. For example, in time series analysis, a plot of the sample autocorrelations versus (the time lags) is an autocorrelogram. If cross-correlation is plotted, the result is called a cross-correlogram.
The coefficient of multiple correlation is known as the square root of the coefficient of determination, but under the particular assumptions that an intercept is included and that the best possible linear predictors are used, whereas the coefficient of determination is defined for more general cases, including those of nonlinear prediction and those in which the predicted values have not been ...
If the relationship between values of and values of ¯ is linear (which is certainly true when there are only two possibilities for x) this will give the same result as the square of Pearson's correlation coefficient; otherwise the correlation ratio will be larger in magnitude. It can therefore be used for judging non-linear relationships.