The following data are from the Canada Health Survey, and given in Rao and Thomas
(1989, p. 107) . They relate smoking status (current smoker, occasional smoker, never smoked) to fitness level for 2505 persons. Smokers who had quit were not included in the analysis. The estimated proportions in the table below were found by applying the sample weights to the sample. The design effects are in brackets. We would like to test whether smoking status and fitness level are independent.

a. What is the value of X2 if you assume the 2505 observations were collected in a multinomial sample? Of G2? What is the p-value for each statistic under multinomial sampling, and why are these p-values incorrect?
b. Using (10.9) find the approximate expected value of X2 and G2.
c. Calculate the corrected statistics X2F and G2F for these data, and find p-values for the hypothesis tests. Does the clustering in the Canada Health Survey make a difference in the p-value you obtain?

Transcribed Image Text:

Fitness level Minimumm Recommended acceptable Unacceptable Smoking Status Current Occasional 0.023 13.45 0.010 .07 0 0.220 13.50 0.150 [4.59 0.17050 0.540 1.441 0.203 [3.49 0.099 [2.07 0.4 0416 [2.441 0.446 14.69 0.259 I5.96 0.295 11.7 1.000 001090044 12.321 Never Total