Similarities between Cases
Several approaches to multivariate analysis begin by assessing the similarities of each case in a dataset to each other case in the dataset, basing the measure of similarity on the values of the set of variables that have been recorded for each case. Such measures of similarity are called similarity coefficients. The notion of similarity between cases in this instance is exactly what common sense implies. Two cases are quite similar if they have similar values for each of the variables measured and less similar if they have rather different values for each of the variables. Actual objects with physical measurements provide a clear illustration, for example the projectile point measurements in Table 22.1. Looking first at the length measurements for the four projectile points, we would easily recognize that Points 1, 2, and 3 are quite similar with regard to length, while Point 4 is rather different. Looking at thickness, however, we would equally quickly say that it is Point 2 that stands out as different from the group. Yet a different pattern emerges with regard to weight: here Points 1 and 4 are quite similar (identical in fact), and Points 2 and 3 are identical to each other but different from 1 and 4.