Skip to main content
PMC home page
Health Services Research logoLink to Health Services Research
. 1992 Aug;27(3):267–294.

Testing the null hypothesis in small area analysis.

K C Cain 1, P Diehr 1
PMCID: PMC1069879  PMID: 1500287

Abstract

The goal of small area analysis is often to demonstrate that hospital admission rates or procedure rates vary greatly among regions, suggesting the occurrence of unnecessary admissions or procedures in some regions. Recent articles have shown that such variation may be largely due to chance, even if no underlying differences exist among the small areas; thus, it is important to test if the observed variation is larger than expected by chance. In this article we discuss how the appropriate method for testing the null hypothesis depends on the distribution of the number of admissions at the person level. If it is not possible for an individual to have more than one admission for a given procedure, the appropriate test is a simple chi-square test. If multiple admissions are possible, a modified chi-square test can be used to account for the excess variability due to multiple admissions. Failure to make the correct modification to the chi-square test in this latter case can result in spurious results. This underscores the importance of collecting data on multiple admissions in order to estimate the distribution of the number of admissions at the individual-patient level.

Full text

PDF
291

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Chassin M. R., Brook R. H., Park R. E., Keesey J., Fink A., Kosecoff J., Kahn K., Merrick N., Solomon D. H. Variations in the use of medical and surgical services by the Medicare population. N Engl J Med. 1986 Jan 30;314(5):285–290. doi: 10.1056/NEJM198601303140505. [DOI] [PubMed] [Google Scholar]
  2. Connell F. A., Day R. W., LoGerfo J. P. Hospitalization of medicaid children: analysis of small area variations in admission rates. Am J Public Health. 1981 Jun;71(6):606–613. doi: 10.2105/ajph.71.6.606. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Diehr P., Cain K., Connell F., Volinn E. What is too much variation? The null hypothesis in small-area analysis. Health Serv Res. 1990 Feb;24(6):741–771. [PMC free article] [PubMed] [Google Scholar]
  4. Diehr P., Grembowski D. A small area simulation approach to determining excess variation in dental procedure rates. Am J Public Health. 1990 Nov;80(11):1343–1348. doi: 10.2105/ajph.80.11.1343. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Kazandjian V. A., Durance P. W., Schork M. A. The extremal quotient in small-area variation analysis. Health Serv Res. 1989 Dec;24(5):665–684. [PMC free article] [PubMed] [Google Scholar]
  6. MANTEL N., HAENSZEL W. Statistical aspects of the analysis of data from retrospective studies of disease. J Natl Cancer Inst. 1959 Apr;22(4):719–748. [PubMed] [Google Scholar]
  7. McPherson K., Wennberg J. E., Hovind O. B., Clifford P. Small-area variations in the use of common surgical procedures: an international comparison of New England, England, and Norway. N Engl J Med. 1982 Nov 18;307(21):1310–1314. doi: 10.1056/NEJM198211183072104. [DOI] [PubMed] [Google Scholar]
  8. Pasley B., Vernon P., Gibson G., McCauley M., Andoh J. Geographic variations in elderly hospital and surgical discharge rates, New York State. Am J Public Health. 1987 Jun;77(6):679–684. doi: 10.2105/ajph.77.6.679. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Paul-Shaheen P., Clark J. D., Williams D. Small area analysis: a review and analysis of the North American literature. J Health Polit Policy Law. 1987 Winter;12(4):741–809. doi: 10.1215/03616878-12-4-741. [DOI] [PubMed] [Google Scholar]
  10. Pocock S. J., Cook D. G., Beresford S. A. Regression of area mortality rates on explanatory variables: what weighting is appropriate? J R Stat Soc Ser C Appl Stat. 1981;30(3):286–295. [PubMed] [Google Scholar]
  11. Tsutakawa R. K. Mixed model for analyzing geographic variability in mortality rates. J Am Stat Assoc. 1988 Mar;83(401):37–42. doi: 10.1080/01621459.1988.10478562. [DOI] [PubMed] [Google Scholar]
  12. Wolfe R. A., Griffith J. R., McMahon L. F., Jr, Tedeschi P. J., Petroni G. R., McLaughlin C. G. Patterns of surgical and nonsurgical hospital use in Michigan communities from 1980 through 1984. Health Serv Res. 1989 Apr;24(1):67–82. [PMC free article] [PubMed] [Google Scholar]

Articles from Health Services Research are provided here courtesy of Health Research & Educational Trust

RESOURCES