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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Applebaum, R., Mehdizadeh, S.: Long-Term Care in Ohio: A Longitudinal Perspective. Scripps Gerontology Center, Oxford, OH (2001)
Applebaum, R.A., Straker, J.K., Geron, S.M.: Assessing Satisfaction in Health and Long-term Care. Springer, New York (2000)
Castle, N.: A literature review of satisfaction surveys. J. Health Soc. Policy (in press)
Freund , J.E.: Mathematical Statistics. Prentice Hall (1992)
Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.: Bayesian Data Analysis. Chapman & Hall (1995)
Geron, S.M., Smith, K., Tennstedt, S., Jette, A., Chassler, D., Kasten, L.: The home care satisfaction measure: A client-centered approach to assessing the satisfaction of frail older adults with home care services. J. Gerontol. Ser. B Psychol. Sci. Soc. Sci. 55B(5), S259–S270 (2000)
Johnson, NL, Kotz S.: Discrete Distributions. Houghton Mifflin Company. (1969)
Kane, R.A., Kling, K.C., Bershadsky, B., Kane, R.L., Giles, K., Degenholtz, H.B., Liu, J., Cutler, L.J.: Quality of life measures for nursing home residents. J. Gerontol. Ser. B Psychol. Sci. Soc. Sci. 58, M240–M248 (2003)
MEDSTAT Group, Participant Experience Survey Elderly/Disabled (E/D) Version Users’ Guide. Version 1.0. Thomson MEDSTAT. 2003
Scheaffer, R.L., Mendenhall, W., Ott, L.: Elementary Survey Sampling, WWS-Kent Publishing (1990)
Skellam, J.G.: A probability distribution derived from the binomial distribution regarding the probability of success as a variable between sets of trials. J. Roy. Stat. Soc. Ser. B. 10, 257–261 (1948)
Uman, G.C., Urman, H.N., Young, R.: Using consumer surveys in long term care today for a better tomorrow. Consult. Diet. 22(3), 11–14 (1998)
Wright, T.: Exact Confidence Bounds when Sampling from Small Finite Universes. Springer-Verlag (1991)
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Noble, R.B., Bailer, A.J., Kunkel, S.R. et al. Sample size requirements for studying small populations in gerontology research. Health Serv Outcomes Res Method 6, 59–67 (2006). https://doi.org/10.1007/s10742-006-0001-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10742-006-0001-4