Johnston] NAVAHO POPULATION 171 



of 39 J3er 1,000, which is about 19 percent higher than the official 

 rate reported for this year.^° 



It should be stressed that the relative merits of the alternative 

 populations which might be used as a base for calculating Navaho vital 

 rates is not at issue. The point to be noted is that each of these popu- 

 lations represents a particular definition of the universe "at risk," 

 and these alternative populations differ sufficiently in size to introduce 

 significant variation in the derived rates.^^ 



A word should be added, finally, in regard to the range of chance 

 variation that is associated with the vital rates that may be derived 

 from a population, such as the Navaho, whose size is 60 or 70,000 

 persons. If, for example, we have a base population of Y0,000 and a 

 reported crude birth rate of 35 per 1,000, the range of probable error 

 (at 95 percent confidence limits) is plus or minus 1.4 per 1,000. This 

 means that there is a 95 percent probability that the "true" rate lies 

 somewhere between 33.6 and 36.4 per 1,000 (see Appendix). 



Similarly, if we have a base population of 7,000 and a reported 

 crude death rate of 10 per 1,000, the range of probable error (or chance 

 variation), again with 95 percent confidence limits, is plus or minus 

 0.8 per 1,000, so that we have a 95 percent probability that the "true" 

 rate lies somewhere between 9.2 and 10.8 per 1,000. 



This last consideration introduces a measure of irreducible inde- 

 terminancy among the vital rates and other similar measures that can 

 be derived from populations whose size is as small or smaller than that 

 of the Navaho. One major conclusion can be drawn from this fact: 

 However accurate the basic data may be, all calculations derived from 

 these data (involving proportions or rates of occurrence) and the 

 inferences based thereon, should allow for the variation that is 

 necessarily associated with the small frequencies involved. 



Since 1944, annual summaries of Navaho deaths, by age and sex, 

 have been compiled from copies of death certificates forwarded to the 

 Navajo Agency at Window Rock, Ariz. The average number of re- 

 ported deaths, by age and sex, for the periods 1944^6, 1948-52, and 

 1953-57, is shown is table 34. For each of these periods, the esti- 

 mated Navaho population at midyear of the central year of the inter- 

 val is also shown, permitting calculation of age-specific death rates 

 for both sexes combined. 



Unless one accepts the implausible view that the reporting of deaths 

 among the Navaho has been progressively deficient in recent years, the 



^" Here also, an upward adjustment of the base figure (which pertains to the population 

 as of April 1, 1950) to provide an estimate of the population at midyear would reduce the 

 derived crude birth rate from 39.0 to about 38.8 per 1,000. 



" The corresponding variation in the crude death rates would be much less than that of 

 the crude birth rates, because of the lower magnitude of the former rates. For example, 

 applying the alternative base populations given in table 33 to an "official" crude death rate 

 of 10.0 per 1,000 would produce rates from 9.6 to 11.9 per 1,000. 



