In statistics the pearson correlation coefficient pcc pronounced p ir s n also referred to as pearsons r the pearson product moment correlation coefficient ppmcc or the bivariate correlation is a measure of the linear correlation between two variables x and y. For a gaussian bivariate distribution the distribution of correlation coefficients is given by 1 where is the population correlation coefficient is a hypergeometric function and is the gamma function kenney and keeping 1951 pp 217 221. If as the one variable increases the other decreases the rank correlation coefficients will be negative it is common to regard these rank correlation coefficients as alternatives to pearsons coefficient used either to reduce the amount of calculation or to make the coefficient less sensitive to non normality in distributions. The histograms approximate the sampling distribution of the correlation coefficient for bivariate normal samples of size 20 for the various values of the population correlation the distributions are not simple notice that the variance and the skewness of the distributions depend on the value the underlying correlation in the population
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