Correlation is a term that refers to the strength of a relationship between two variables. A strong, or high, correlation means that two or more variables have a strong relationship with each other while a weak, or low, correlation means that the variables are hardly related. Correlation coefficients can range from -1.00 to +1.00. The value of -1.00 represents a perfect negative correlation while a value of +1.00 represents a perfect positive correlation. A value of 0.00 means that there is no relationship between the variables being tested.
The most widely used type of correlation coefficient is the Pearson r, which is also referred to as linear or product-moment correlation. This analysis assumes that the two variables being analyzed are measured on at least interval scales. The coefficient is calculated by taking the covariance of the two variables and dividing it by the product of their standard deviations.
Interpreting The Correlation Coefficient
A value of +1.00 implies that the relationship between variables X and Y is perfectly linear, with all data points lying on a line for which Y increases and X increases. Conversely, a negative value of implies that all data points lie on a line for which Y decreases as X increases.
For example, let’s suppose we were looking at variables age and income. If the correlation coefficient was +0.80, this means that as age increases, income increases as well.
StatSoft: Electronic Statistics Textbook. (2011). http://www.statsoft.com/textbook/basic-statistics/#Crosstabulationb