The concept of correlation

This chapter is devoted to one of the central issues in the quantitative study of two variables: is there a relationship between them? Our aim is to explain the basic concepts, and then to obtain a measure of the degree to which the two variables are related. The statistical term for such a relationship or association is correlation, and the measure of the strength of that relationship is called the correlation coefficient.

We will deal first with the relationship between ratio or interval level (numerical) variables, and then look more briefly in §3.3 at the treatment of nominal and ordinal level measurements. In this initial discussion we ignore the further matters that arise because the results are usually based on data obtained from a sample. Treatment of this important aspect must be deferred until the issues of confidence intervals and hypothesis testing have been covered in chapters 5 and 6.

If there is a relationship between the two sets of paired variables (for example, between the level of relief expenditure (RELIEF) and the proportion of unemployed labourers (UNEMP) in each of the parishes, or between EMPFOR, the annual series for foreign employment and IRMIG, the number of immigrants from Ireland), it may be either positive or negative.