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Sample size requirements for studying small populations in gerontology research

  • Robert B. Noble
  • A. John Bailer
  • Suzanne R. Kunkel
  • Jane K. Straker
Article

Abstract

Calculating sample sizes required to achieve a specified level of precision when estimating population parameters is a common statistical task. As consumer surveys become increasingly common for nursing homes, home care agencies, other service providers, and state and local administrative agencies, standard methods to calculate sample size may not be adequate. Standard methods typically assume a normal approximation and require the specification of a plausible value of the unknown population trait. This paper presents a strategy to estimate sample sizes for small finite populations and when a range of possible population values is specified. This sampling strategy is hierarchical, employing first a hypergeometric sampling model, which directly addresses the finite population concern. This level is then coupled with a beta-binomial distribution for the number of population elements possessing the characteristic of interest. This second level addresses the concern that the population trait may range over an interval of values. The utility of this strategy is illustrated using a study of resident satisfaction in nursing homes.

Keywords

Sampling strategies Consumer satisfaction Hypergeometric distribution Beta-binomial distribution Hierarchical model 

Notes

Acknowledgments

The authors would like to acknowledge support from the Ohio Long Term Care Project and the Ohio Department of Aging Nursing Home Family Satisfaction Survey Project.

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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Robert B. Noble
    • 1
  • A. John Bailer
    • 1
    • 2
  • Suzanne R. Kunkel
    • 2
  • Jane K. Straker
    • 2
  1. 1.Department of Mathematics and StatisticsMiami UniversityOxfordUSA
  2. 2.Scripps Gerontology CenterMiami UniversityOxfordUSA

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