Correlation Coefficient: Association between Two Continuous Variables

Many statistical analyses can be undertaken to examine the relationship between two continuous variables within a group of subjects. Two of the main purposes of such analyses are: To assess whether the two variables are associated. There is no distinction between the two variables and no causation is implied, simply association. To enable the value of one variable to be predicted from any known value of the other variable. One variable is regarded as a response to the other predictor (explanatory) variable and the value of the predictor variable is used to predict what the response would be. For the first of these, the statistical method for assessing the association between two continuous variables is known as correlation, whilst the technique for the second, prediction of one continuous variable from another, is known as regression. Correlation and regression are often presented together and it is easy to get the impression that they are inseparable. In fact, they have distinct purposes and it is relatively rare that one is genuinely interested in performing both analyses on the same set of data. However, when preparing to analyse data using either technique it is always important to construct a scatter plot of the values of the two variables against each other. By drawing a scatter plot it is possible to see whether or not there is any visual evidence of a straight line or linear association between the two variables. This tutorial will deal with correlation, and regression will be the subject of a later tutorial.