Compute a rank correlation between change in weight and change in HgbA1c, each over 1 year. Use this measure to directly test the hypothesis that change in weight over 1 year is related to change in HgbA1c. Report a two-tailed p-value, and provide a 95% confidence interval for the underlying rank correlation?

Diabetes

A group of 10-year-old boys were first ascertained in a camp for diabetic boys. They had their weight measured at baseline and again when they returned to camp 1 year later. Each time, a serum sample was obtained from which a determination of hemoglobin A1c (HgbA1c) was made. HgbA1c (also called glycosylated hemoglobin) is routinely used to monitor compliance with taking insulin injections. Usually, the poorer the compliance, the higher the HgbA1c level will be. The hypothesis is that the level HgbA1c is related to weight. The data in Table 11.28 were obtained.

Table 11.28: Relationship between weight change and change in HgbA1c among diabetic boys

 

Transcribed Image Text:

1st visit 2nd visit HgbA1c 2nd visit - HgbA1c 1st visit (%) Weight 2nd visit - weight 1st visit (kg) Woight (kg) Weight (kg) HgbA1c HgbA 1c (%) (x) ID no. x) (x) 9.9 + 5.0 40.5 45.5 8.4 -1.5 11.3 43.2 47.0 9.2 + 3.8 -2.1 + 5.7 -0.8 3 36.3 10.4 42.0 9.6 + 0.7 4 30.8 7.4 35.3 8.1 +4.5 29.9 -1.9 9.8 33.2 7.9 + 3.3 -0.8 39.7 8.5 46.1 7.7 + 6.4 37.8 + 0.9 + 0.6 + 0.4 36.9 7.3 7.7 36.4 8. 7.8 37.0 8.4 + 0.6 34.3 -0.2 + 1.8 34.5 7.8 9.6 5.7 + 3.2 + 0.8 10 35.2 38.4 6.5 11 43.0 7.4 48.6 7.4 + 5.6 12 38.4 6.5 42.7 7.0 +4.3 + 0.5 13 42.0 7.1 48.0 7.4 + 6.0 + 0.3 -0.8 14 34.1 8.9 41.3 8.1 + 7.2 9.3 15 43.5 51.4 7.4 + 7.9 -1.9 Mean 37.63 8.34 41.91 8.03 4.28 -0.31 sd 5.73 4.35 1.56 0.90 2.40 1.18 15 15 15 15 15 15