Human behaviour at both the individual and social level is characterized by great complexity, a complexity about which we understand comparatively little, given the present state of social research. One approach to a fuller understanding of human behaviour is to begin by teasing out simple relationships between those factors and elements deemed to have some bearing on the phenomena in question. The value of correlational research is that it is able to achieve this end.
Much of social research in general, and educational research more particularly, is concerned at our present stage of development with the first step in this sequence—establishing interrelationships among variables. We may wish to know, for example, how delinquency is related to social class background; or whether an association exists between the number of years spent in full-time education and subsequent annual income; or whether there is a link between personality and achievement. Numerous techniques have been devised to provide us with numerical representations of such relationships and they are known as ‘measures of association’. We list the principal ones in Box 10.1. The interested reader is referred to Cohen and Holliday (1982, 1996), texts containing worked examples of the appropriate use (and limitations) of the correlational techniques outlined in Box 10.1, together with other measures of association such as Kruskal’s gamma, Somer’s d, and Guttman’s lambda.
Look at the words used at the top of the Box to explain the nature of variables in connection with the measure called the Pearson product moment, r. The variables, we learn, are ‘continuous’ and at the ‘interval’ or the ‘ratio’ scale of measurement. A continuous variable is one that, theoretically at least, can take any value between two points on a scale. Weight, for example, is a continuous variable; so too is time, so also is height. Weight, time and height can take on any number of possible values between nought and infinity, the feasibility of measuring them across such a range being limited only by the variability of suitable measuring instruments.
A ratio scale includes an absolute zero and provides equal intervals. Using weight as our example, we can say that no mass at all is a zero measure and that 1,000 grams is 400 grams heavier than 600 grams and twice as heavy as 500. In our discussion of correlational research that follows, we refer to a relationship as a ‘correlation’ rather than an ‘association’ whenever that relationship can be further specified in terms of an increase or a decrease of a certain number of units in the one variable (IQ for example) producing an increase or a decrease of a related number of units of the other (e.g. mathematical ability).
Turning again to Box 10.1, we read in connection with the second measure shown there (Rank order or Kendall’s tau) that the two continuous variables are at the ‘ordinal’ scale of measurement. An ordinal scale is used to indicate rank order; that is to say, it arranges individuals or objects in a series ranging from the highest to the lowest according to the particular characteristic being measured. In contrast to the interval scale discussed earlier, ordinal numbers assigned to such a series do not indicate absolute quantities