The following data are from Rao and Thomas (1988), and were collected in the Canadian Class Structure Survey, a stratified multistage sample collected in 1982–83 to study employment and social structure. Canada was divided into 35 strata by region and population size; two psus were sampled in 34 of the strata, and one psu sampled in the 35th stratum. Variances were estimated using balanced repeated replication using the 34 strata with two psus. Estimated design effects are in brackets behind the estimated proportion for each cell.

a. What is the value of X2 if you assume the 1463 persons were surveyed in a simple random 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. How many df are associated with the BRR variance estimates?
d. Calculate the first-order corrected statistics X2Fand G2F for these data, and find approximate p-values for the hypothesis tests. Does the clustering in the survey make a difference in the p-value you obtain?
e. The second-order Rao–Scott correction gave test statistic X2S = 38.4, with 3.07 df. How does the p-value obtained using the X2S compare with the p-value from X2F ?