In: Statistics and Probability
If you calculate a correlation of .954 can you say that the variable is a cause of the change in the other variable?
No. High positive correlation between two variable implies that with increase in one variable, the other variable also increases. But from that, we cannot conclude that one variable is the cause for other. This is because of the fact that correlation doesn't imply causation. In some cases, one variable can be the cause of other. But in some cases, the cause can be some other variable, which we are not counting in the study. Such hidden variables that are the real causative factors are called lurking variables.
Example 1: A typical example is number of visitors in a public swimming pool and ice cream sales. If we study these two variables, we will find high correlation. But ice cream sale increase is not a cause for swimming pool visit or swimming pool visit wont increase ice cream sale. The lurking variable is the average daily temperature (in general, season variation of temperature). In summers, people tend to visit pools more often and consumes more ice cream as well. So, we cannot conclude that correlation implies causation in the other variable.