*Dependence *refers to any statistical relationship between two random variables. Correlation refers to any statistical relationship involving *dependence*. In a correlation study, the Six Sigma practitioner would be looking for a *correlation coefficient*. The probability runs from -1 to +1. In other words, if two random variables are 100% correlated, the correlation coefficient would be +1 or -1. If there is no correlation, the correlation coefficient would be zero (0).

Use: Understanding the formula Y = (function) of x (or multiple x’s) means that if there are a number of factors (x’s), you might want to know if one of the factors (factor A) will have an effect on your response of interest (response Y). For example, if you wanted to know whether the probability of rain is dependent upon the level of humidity, you might plot various levels of humidity against various probabilities of rain using paired comparisons.

Let’s say the favorable response is for more rain (Y). You want more rain because you are a farmer and the crops need rain. The humidity level is (x). You might find that there is a *positive* correlation – meaning that as the level of humidity rises, the probability of rain goes up. You also might find that there is a *negative* correlation, meaning that as the level of humidity goes up, the probability of rain decreases. You also might find that there is no correlation between the level of humidity and the probability of rain.