A 14th Way to Look at a Correlation Coefficient: Correlation as the Proportion of Matches

Abstract An interpretation of the correlation coefficient is presented that describes the coefficient in terms of the proportion of matches in an idealized data set. This characteristic is then expressed as the result of the definition of the Pearson product-moment correlation. An expression is derived to relate the correlation coefficient to the proportion of times a second variable falls within a set range of the first. Both a simulation and a real data example are presented to show how this would be reflected in data.