Search tips
Search criteria 


Logo of jepicomhJournal of Epidemiology and Community HealthVisit this articleSubmit a manuscriptReceive email alertsContact usBMJ
J Epidemiol Community Health. 1984 March; 38(1): 85–88.
PMCID: PMC1052324

Simple exact analysis of the standardised mortality ratio.


The standardised mortality ratio is the ratio of deaths observed, D, to those expected, E, on the basis of the mortality rates of some reference population. On the usual assumptions--that D was generated by a Poisson process and that E is based on such large numbers that it can be taken as without error--the long established, but apparently little known, link between the Poisson and chi 2 distributions provides both an exact test of significance and expressions for obtaining exact (1-alpha) confidence limits on the SMR. When a table of the chi 2 distribution gives values for 1-1/2 alpha and 1/2 alpha with the required degrees of freedom, the procedures are not only precise but very simple. When the required values of chi 2 are not tabulated, only slightly less simple procedures are shown to be highly reliable for D greater than 5; they are more reliable for all D and alpha than even the best of three approximate methods. For small D, all approximations can be seriously unreliable. The exact procedures are therefore recommended for use wherever the basic assumptions (Poisson D and fixed E) apply.

Full text

Full text is available as a scanned copy of the original print version. Get a printable copy (PDF file) of the complete article (575K), or click on a page image below to browse page by page. Links to PubMed are also available for Selected References.

Selected References

These references are in PubMed. This may not be the complete list of references from this article.
  • Livre blanc 1976. Chirurgiens-dentistes et société. Chir Dent Fr. 1976 Jun 16;46(309):22–31. [PubMed]
  • Dement JM, Harris RL, Jr, Symons MJ, Shy C. Estimates of dose-response for respiratory cancer among chrysotile asbestos textile workers. Ann Occup Hyg. 1982;26(1-4):869–887. [PubMed]
  • Ederer F, Mantel N. Confidence limits on the ratio of two Poisson variables. Am J Epidemiol. 1974 Sep;100(3):165–167. [PubMed]
  • LIDDELL FD. The measurement of occupational mortality. Br J Ind Med. 1960 Jul;17:228–233. [PMC free article] [PubMed]

Articles from Journal of Epidemiology and Community Health are provided here courtesy of BMJ Publishing Group