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Correlation refers to the relationship between two or more variables. Many different forms of correlation exist, but they all reflect a quantitative, statistical means for describing relationships. A correlation statistic is inherently bivariate (i.e., two variables) in nature.
Correlation speaks to whether or not variables are systematically related in some predictable fashion. For example, assuming no irrigational intervention, annual rainfall is likely related to growth in agricultural crops, such that crops receiving more rain likely will be more productive. Of course, this relationship probably varies somewhat depending on the type of crop, amount of sunlight, and many other variables.
Scatterplots can be used to graphically display the relationship, where each axis represents one of the variables and the paired data for each observation are plotted. Perfect linear relationships result in the formation of a line by the plotted observations. As the relationship weakens, the plotted points will diverge from a straight line to form a more circular pattern.
The most common manifestation of bivariate correlation is the Pearson product-moment correlation coefficient, which was named after Karl Pearson (1857—1936), who popularized the statistic originally introduced by Francis Galton (1822—1911). The statistic is more commonly known as Pearson r or just r. A large section of statistical work can be traced to the simple correlation coefficient.
Pearson r ranges from + 1to — 1, inclusive. A coefficient of 0 would represent no relationship. Coefficients of +1 would represent a perfect, positive (i.e., direct) relationship and those of — 1 would represent a perfect, negative (i.e., indirect, inverse) relationship. Thus, the absolute value of the coefficient speaks to the strength of the relationship and the sign indicates directionality, either positive or negative. Importantly, r can be squared to yield an effect size statistic indicating the amount of shared variance between two variables.
- Henson, R. K. (2000) Demystifying parametric analyses: illustrating canonical correlation as the multivariate general linear model. Multiple Linear Regression Viewpoints 26 (1): 11—19.
- Hinkle, D. E., Wiersma, W., & Jurs, S. G. (2003) Applied Statistics for the Behavioral Sciences, 5th edn. Houghton Mifflin, Boston, MA.