1 IAPT: The correlation coefficient

The correlation coefficient Correlation coefficients are used to measure the strength of the relationship or association between two quantitative variables. For example, Table 1 shows height, muscle strength and age in 41 alcoholic men. We will begin with the relationship between height and strength. Figure 1 shows a plot of strength against height. This is a scatter diagram. Each point represents one subject. If we look at Figure 1, it is fairly easier to see that taller men tend to be stronger than shorter men, or, looking at the other way round, that stronger men tend to be taller than weaker men. It is only a tendency, the tallest man is not the strongest not is the shortest man the weakest. Correlation enables us to measure how close this association is. The correlation coefficient is based on the products of differences from the mean of the two variables. That is, for each observation we subtract the mean, just as when calculating a standard deviation. We then multiply the deviations from the mean for the two variables for a subject together, and add them. We call this the sum of products about the mean. It is very like the sum of squares about the mean used fo