Two sociologist have grant money to study school busing in a particular city. Th

Question

Two sociologist have grant money to study school busing in a particular city. They wish to conduct an opinion survey using 624 telephone contacts and 362 house contacts. Survey company A has personnel to do 35 telephone and 13 house contacts per hour; survey company B can handle 23 telephone and 20 house contacts per hour. How many hours should be scheduled for each firm to produce exactly the number of contacts needed? How many hours should be scheduled for firm A to produce exactly the number of contacts needed? How many hours should be scheduled for firm B to produce exactly the number of contacts needed?

Explanation / Answer

"In the original National Science Foundation grant, support was given for a modified probability sample. Samples for the 1972 through 1974 surveys followed this design. This modified probability design, described below, introduces the quota element at the block level. The NSF renewal grant, awarded for the 1975--1977 surveys, provided funds for a full probability sample design, a design which is acknowledged to be superior. "Thus, having the wherewithal to shift to a full probability sample with predesignated respondents, the 1975 and 1976 studies were conducted with a transitional sample design, viz., one-half full probability and one-half block quota. The sample was divided into two parts for several reasons: 1) to provide data for possibly interesting methodological comparisons; and 2) on the chance that there are some differences over time, that it would be possible to assign these differences to either shifts in sample designs, or changes in response patterns. For example, if the percentage of respondents who indicated that they were 'very happy' increased by 10 percent between 1974 and 1976, it would be possible to determine whether it was due to changes in sample design, or an actual increase in happiness. There is considerable controversy and ambiguity about the merits of these two samples. Textbook tests of significance assume full rather than modified probability samples, and simple random rather than clustered random samples. In general, the question of what to do with a mixture of samples is no easier solved than the question of what to do with the 'pure' types. Investigators who have applied statistical tests to previous General Social Survey data should continue to apply those tests. Investigators who have refrained from applying such tests may now want to perform analyses on the probability subsample. This would, of course, reduce the number of cases by one half. Whatever choice investigators make, it should be remembered that the two subsamples represent the same universe. Having allowed for the appearance of all items in the transitional sample design, the General Social Survey then switched to a full probability sample for the 1977, 1978, 1980, and 1982--2008 surveys. The variable SAMPLE can be used to separate the block quota and full probability samples on the 1975 and 1976 surveys" (2188) (Source: Davis, James Allan; Smith, Tom W.; and Marsden, Peter V. General Social Surveys, 1972--2008: Cumulative Codebook / Principal Investigator, James A. Davis; Director and Co-Principal Investigator, Tom W. Smith. Chicago: National Opinion Research Center, 2009. 2,656 pp., 28cm. -- (National Data Program for the Social Sciences Series, no. 18).)

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