Apply Kendall's two-sided test based on (8.10) to the data of Table 8.12. Compare your result with the result of Problem 56.

Problem 56

The data in Table 8.12 are a subset of the data obtained by Shen et al. (1970) in an experiment concerned with the hypothesis that diabetes mellitus is not simply a function of insulin deficiency and that perhaps insulin insensitivity could play an important role in the hyperglycemia of diabetes. One of the purposes of the study was to investigate the relation between the response to a glucose tolerance test and glucose impedance, a quantity describing the body tissues' resistance to glucose and expected to be constant for a given individual throughout the experimental range of glucose uptake rate in the author's study. The seven subjects represented in Table 8.12 were volunteers recently released from a minimum security prison and characterized by low plasma glucose response to oral glucose. Table 8.12 gives the weighted glucose response to an oral glucose tolerance test (X) and the glucose impedance reading (Y) for each of the seven subjects.

Use procedure (8.88) to test for impedance of weighted glucose response and glucose impedance. (Recall that procedure (8.88) is designed to detect all alternatives to the hypothesis of independence. However, if one has prior reasons or evidence to suspect that the weighted glucose response is positively correlated with glucose impedance, it would be more appropriate to focus on alternatives of positive association by using the one-sided procedure, based on Kendall's K, given by (8.8).)