Stratified Sampling

Proportionate Stratification

A sample with proportionate stratification is chosen such that the distribution of observations in each stratum of the sample is the same as the distribution of observations in each stratum within the population. The sampling fraction, which refers to the size of the sample stratum divided by the size of the population stratum (nh/Nh), is [Page 1452]equivalent for all strata. Proportionate stratification is primarily useful when a researcher wishes to estimate values in a population and believes that different groups within the population differ on the variable of interest. For example, suppose a university administrator wants to measure attitudes about imposing a new student fee among students at a university with 10,000 students, including 4,500 in the humanities, 3,000 in the sciences, and 2,500 in business. If the administrator wanted a sample of 200 (2% of the students), she would randomly sample 90 humanities majors (2% of 4,500), 60 science majors (2% of 3,000), and 50 business majors (2% of 2,500). It is essential that the stratification factor be related to the variable of interest. Stratification by major will improve the precision of the estimate of attitude in the population to the extent that students in different majors have different attitudes about the fee increase and relatively similar attitudes to other students within their major.

Disproportionate Stratification

In disproportionate stratification, the sampling fraction is not the same across all strata, and some strata will be oversampled relative to others. Disproportionate stratification is primarily useful when a researcher wants to make comparisons among different strata that are not equally represented in the population. For example, a researcher in the United States who is interested in comparing learning outcomes among children of different ethnic backgrounds might use disproportionate stratification to ensure that the sample includes an equal (or at least sufficient) number of children from minority groups. Suppose that a school district of 10,000 children is 80% Caucasian (8,000 children), 15% African American (1,500 children), and 5% Asian American (500 children). If a researcher draws a simple random sample of 100 children (1% of the population), the sample is likely to contain about 15 African American and 5 Asian American children, but by random chance those groups could be considerably smaller. To ensure adequate samples of African American and Asian American children, the researcher can increase the sampling fraction of these subgroups. Say the researcher decides to include 40 students from each group in the sample. In this case, the sampling fraction for Caucasians is 40/8,000 = .005, for African Americans, it is 40/1,500 = .03, and for Asian Americans it is 40/500 = .08.

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