Methods of correlation
In previous chapters methods have been presented by which the differences between sets of sample data can be tested as regards their statistical significance. The aim in all these cases was to assess whether the differences that were observed could have occurred by chance sufficiently frequently for some doubt to be cast on the validity of the apparent differences, or whether the probability of their having happened by chance was so slight that these observed differences could legitimately be accepted as justified and significant. In all these cases it was the overall characteristics of the various sets of data that were under consideration rather than the detailed characteristics and their changes. In many problems, however, there is the need to compare sets of data in terms of the extent to which a change in one is or is not reflected by a change in the other set-the focus is not upon differences but upon degrees of association. This necessarily implies that the individual items of the two sets of data co-exist either in time or space, such that the possibility of interrelated changes can be considered. In such a problem an index is required that reflects the degree to which changes in direction ( + or -) and magnitude in one set of data are associated with comparable changes in the other set. Indices of this sort are termed correlation coefficients and are designed to range from + 1 (perfect positive correlation) through zero to -1 (perfect negative correlation). In the following pages coefficients will be employed in the study of several problems, two of the coefficients being linked to ordinal data and one to interval and ratio data.