Question: Ryan et al. (1991) report results from the Ross Laboratories Mother's Survey, a national mail survey investigating infant feeding in the United States. Questionnaires asking mothers about the type of milk fed to their infants during each of the first 6 months and about socioeconomic variables were mailed to a sample of mothers of 6-month-old infants. The authors state that the number of questionnaires mailed increased from 1984 to 1989: "In 1984, 56,894 questionnaires were mailed and 30,694 were returned. In 1989, 196,000 questionnaires were mailed and 89,640 were returned." Low-income families were oversampled in the survey design because they had the lowest response rates. Respondents were divided into subclasses defined by region, ethnic background, age, and education; weights were computed using information from the Bureau of the Census.

a. Which was used: weighting-class adjustments or post stratification?

b. Oversampling the low-income families is a form of substitution. What are the advantages and drawbacks of using substitution in this survey?

c. Weighted counts are "comparable with those published by the U.S. Bureau of the Census and the National Center for Health Statistics" on ethnicity, maternal age, income, education, employment, birth weight, region, and participation in the Women, Infants, and Children supplemental food program. Using the weighted counts, the investigators estimated that about 53% of mothers had one child, whereas the government data indicated that about 43% of mothers had one child. Does the agreement of weighted counts with official statistics indicate that the weighting corrects the nonresponse bias? Explain.

d. Discuss the use of weighting in this survey. Can you think of any improvements?