Ryan et al. (1991) report results from the Ross Laboratories

Ryan et al. (1991) report results from the Ross Laboratories Mothers’ Survey, a national mail survey investigating infant feeding in the United States. Questionnaires asking mothers about type of milk fed to the infant during each of the first six months and about socioeconomic variables were mailed to a sample of mothers of six-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 U.S. Census Bureau.
a. What are the advantages and drawbacks of oversampling the low-income families in this survey? What implicit model is adopted for non response?
b. 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. The weighted counts estimated that about 53% of mothers had one child, while 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 non response bias? Explain.
c. Discuss the use of weighting in this survey. Can you think of any improvements?

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