Determining sample size for surveys with data analyzed by hierarchical linear models

There has been an upsurge in interest among behavioral and social scientists and education researchers in analyzing data in a way that accounts for the naturally occurring nested structure, for instance, in analyzing students nested within schools. Linear models appropriate for such data are called hierarchical or multilevel. In part, the increased interest has been sparked by the availability of new software that properly handles the nested structure and facilitates the analyses. There has also been a realization that one can take advantage of the nested structure to explore relationships not amenable to other approaches. Bryk and Raudenbush (1992), Goldstein (1987, 1995), and Longford (1993) are recommended for book-length discussions related to hierarchical linear models. To illustrate these models, an example of Bryk and Raudenbush (1992, Chapter 4) will be summarized. This example is based on data from a subsample of the 1982 High School and Beyond Survey, a survey of high school students in the United States by the U.S. National Center for Education Statistics. The socioeconomic status (SES) of the student is a variable computed from the income, education, and occupation of the student's parents. The MEAN SES is the average over the students in the school of the SES values for the students. The following questions, quoted from Bryk and Raudenbush (1992, p. 61), were being explored: