8 - Interrelationships of Quantitative Variables

Summary

Kinds of information and relationships

There are two main kinds of information that we may have about a series of individuals or samples. One kind consists of measurements, counts, scores, etc., which take the form of a numerical assessment. We call this quantitative information. The other kind consists of a classification of the individuals or samples into a series of qualitatively different categories. We call this qualitative information. We can examine interrelationships for any of the three possible combinations thus, qualitative/qualitative, qualitative/quantitative, and quantitative/ quantitative. As we shall see, in practice, the situation is more complex because the categories used in the qualitative classification may form a semi-quantitative series. Again, even when a numerical assessment is not made, it may still be possible to arrange the individuals or samples in order on the basis of a particular criterion, i.e. to rank them.

Qualitative/qualitative data

Interrelationship based on qualitative information is usually called association and examined by means of a c × r table as described in Chapter 7. We calculate χ² with (c - 1)(r - 1) degrees of freedom and this permits us to test the association for significance. The χ² value itself is not a good measure of the closeness of association as its magnitude depends on the total number of observations. To compare the levels of association for two tables with the same number of degrees of freedom we use χ²/n, the ‘mean-square contingency’.