Self-reported BMI Self-reported measures are often unreliable. For example, people tend to understate their weight and overstate their height, resulting in understatement of one’s body mass index or BMI (weight divided by height squared). Analyses based on understated BMIs may overstate health risks of overweight status. The following table shows estimated counts in the entire Canadian population (based on a sample) where the true height, weight, and BMI were accurately measured and compared with self-reported measures for each individual. The counts are in thousands, but just ignore the three extra zeroes in any calculations. (Due to rounding to nearest 1000, column entries may not add perfectly to totals.)

a) Give the conditional distribution of self-reported BMI for each of the three measured overweight classes.

b) Give the conditional distribution of measured BMI for each of the three self-reported overweight classes.

c) Why do you know in advance that the two categorical variables in this study will not be independent? How is this clear by visual inspection of the table?

d) What have you learned about self-reported measures of overweight?

e) Name another (categorical) variable that it might be wise to incorporate into such an analysis, for example, breaking up the data according to values of such a variable prior to analysis.

f) This analysis shows a general underestimation of overweight. How does this affect our estimates of the health risk (for diabetes, etc.) to Canadians of being overweight when self-reported data are used? Will risk of overweight to health be over- or underestimated?

Self-reported BMI Measured BMI category (kg/m) Underweight Normal weight Overweight Obese class I Obese class II/III (less than 18.5) (18.5 to 24.9) (25.0 to 29.9) (30.0 to 34.9) (35 or more) '000 % '000 % '000 % '000 % '000 % category (kg/m) Total 402 100 10 859 100 8 746 100 4 288 100 1 562 100 Underweight 271 67 308 3 1 0 6 0 0 0 (less than 18.5) Normal weight 131 33 10 163 94 2651 30 120 3 4 0 (18.5 to 24.9) Overweight 0 0 388 4 5851 67 1894 44 134 9 (25.0 to 29.9) Obese class I 0 0 0 0 244 3 2247 32 52 603 39 (30.0 to 34.9) Obese class II/III 0 0 00 00 22 1 822 53 (35.0 or more) Source: Adapted from Statistics Canada, Estimates of obesity based on self-report versus direct measures, Health Reports, 82-003XIE2008002, vol 19 no. 2, May, 2008. www.statcan.gc.ca/bsolc/olc-cel/olc-cel?catno-82-003-XWE&lang=eng.