On the Association of Attributes in Statistics: With Illustrations from the Material of the Childhood Society, &c

1. In the ordinary theory of statistical correlation, normal or otherwise, we are always supposed to be dealing with material susceptible of continuous variation, or at least of variation by a considerable number of discontinuous steps. The correlations of lengths or measurements on portions of the body form examples of the first kind; of numbers of children in families, petals or other parts of flowers, are examples of the second. Certain practical cases arise, however, where either no variation is thinkable at all, or else is not measured or possibly measurable. We may class a number of individuals into deaf and not deaf, blind and not blind, imbecile and not imbecile, without attempting to go further (although gradations of deafness, blindness, and imbecility occur), and demand on the basis of the enumeration a discussion of the association of the three infirmities. Or again the data may be the mortality from some disease with and without the administration of, say, a new antitoxin, the statistics giving number who died to whom antitoxin was administered, number who died to whom antitoxin was not administered; number who did not die to whom antitoxin was not administered, number who did not die to whom antitoxin was administered; and from these data a discussion of the value of the cure is required. Here there is no scale of “death”; there may be a scale of “antitoxin” if the dose varied, but not otherwise.