The correlation coefficient, often represented as "r" in mathematical equations, represents the relationship between two variables. This coefficient ranges in value from -1 to 1. "1" represents perfect correlation, meaning that given one variable you can exactly determine the other variable. On the other hand, "-1" means that the two variables have no relationship. For example, shoe size and age are two variables that would have a rather high correlation coefficient.
Sometimes, statisticians would like to compare the behavior or characteristics of two test groups or population. In this case, the correlation coefficient is based on the average, or mean, response of each group. The sum of means is the sum of the respective mean from each test group. This number can be used for further statistical testing. The sum of means is weight based on the size of the test group. So, if test group 1 was twice the size of test group 2, test group 1 would be weighted twice as much in the sum of means.
Because the correlation coefficient represents the relationship between the two variables or population groups, it also reflects the mean behavior or response of those two groups. The higher the coefficient value, the more closely the two groups are related in their behavior. As such, the higher the correlation coefficient the closer the sum of means gets to the means of each group individually.
There are unlimited uses for these statistical indicators. Specifically, correlation coefficients can illustrate important trends in many fields and industries. Marketers use these statistical tests to learn more about what people would like to buy and how much they are willing to pay for it. Scientists use these tests to better understand the environmental impact of certain chemicals. Doctors can use statistical analysis to determine whether a certain drug is effective as a treatment for a specific disease or condition. Once you understand the basics of statistics, there is no telling how many ways you may use them in the future.