Data Analysis with R, Second Edition - Second Edition

Correlation coefficients

A solution to this quirk of covariance is to use Pearson's correlation coefficient instead. Outside its colloquial context, when the word correlation is uttered—especially by analysts, statisticians, or scientists—it usually refers to Pearson's correlation.

Pearson's correlation coefficient is different from covariance in that, instead of using the sum of the products of the deviations from the mean in the numerator, it uses the sum of the products of the number of standard deviations away from the mean. These number-of-standard-deviations-from-the-mean are called z-scores. If a value has a z-score of 1.5, it is 1.5 standard deviations above the mean; if a value has a z-score of -2, then it is 2 standard deviations ...