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  2. Pearson correlation coefficient - Wikipedia

    en.wikipedia.org/.../Pearson_correlation_coefficient

    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.

  3. Covariance and correlation - Wikipedia

    en.wikipedia.org/wiki/Covariance_and_correlation

    [1] [2] Both describe the degree to which two random variables or sets of random variables tend to deviate from their expected values in similar ways. If X and Y are two random variables, with means (expected values) μ X and μ Y and standard deviations σ X and σ Y, respectively, then their covariance and correlation are as follows: covariance

  4. Correlation - Wikipedia

    en.wikipedia.org/wiki/Correlation

    Some correlation statistics, such as the rank correlation coefficient, are also invariant to monotone transformations of the marginal distributions of X and/or Y. 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).

  5. Correlation coefficient - Wikipedia

    en.wikipedia.org/wiki/Correlation_coefficient

    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 .

  6. p-value - Wikipedia

    en.wikipedia.org/wiki/P-value

    In null-hypothesis significance testing, the p-value [note 1] is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. [2] [3] A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis.

  7. Spearman's rank correlation coefficient - Wikipedia

    en.wikipedia.org/wiki/Spearman's_rank_correlation...

    Stata implementation: spearman varlist calculates all pairwise correlation coefficients for all variables in varlist. MATLAB implementation: [r,p] = corr(x,y,'Type','Spearman') where r is the Spearman's rank correlation coefficient, p is the p-value, and x and y are vectors. [21]

  8. Partial correlation - Wikipedia

    en.wikipedia.org/wiki/Partial_correlation

    The value –1 conveys a perfect negative correlation controlling for some variables (that is, an exact linear relationship in which higher values of one variable are associated with lower values of the other); the value 1 conveys a perfect positive linear relationship, and the value 0 conveys that there is no linear relationship.

  9. Distance correlation - Wikipedia

    en.wikipedia.org/wiki/Distance_correlation

    The classical measure of dependence, the Pearson correlation coefficient, [1] is mainly sensitive to a linear relationship between two variables. Distance correlation was introduced in 2005 by Gábor J. Székely in several lectures to address this deficiency of Pearson's correlation, namely that it can easily be zero for dependent variables.