Affsortatire Mathxj !v Mtiv 



485 



sho-w so dose an agreement as to justify thc boliuf tJiat tlio system of groupiiig 

 adopted is within wide limits iinnintorial : 



(ö) Adniitting that the units of age adopted have no sensible eftect on the 

 result, the eorrelation observed may be due to small environmental influences, 

 affecting the gi'oup of persons frorn one parish in a district differently from those 

 in other paiishes. If such an effect existed, the niixture of records from different 

 parishes would exhibit a spuriou.s eorrelation, due to the heterogeneity of the 

 material uscd. Such a spurions eorrelation would be independent of any real 

 eorrelation between actual husbauds and wives, and if it existed it would be equall}' 

 appareut if the men and women from each parish were arranged in couples at 

 randoni, the couples so formed for every parish in tho district being then added 

 togethcr ; accordingly F. E. Lutz took the records from each graveyard in the 

 Wensleydale district, and arranged them in a series, after which a randora couple 

 was formed by taking with each man the wife of the man ten places removed from 

 him in the series ; this process being gone through for every graveyard in the 

 district, the random couples formed were added together and arranged in Table II, 

 from which it is found that the eorrelation between the age at death of one member 

 of such a random couple and that of the other is 0-0086 ± 0-0228, a value ditfering 

 from zero by less than half thc probable error of the determination. This is 

 sufficient proof that the observed eorrelation between actual husbands and wives 

 is not due to environmental effects which act differently upon the married 

 population of the diftercnt villages in the district. 



(6) A further environmental eftect reniains to be considered : a husband and 

 a wife live to a large extent in a similar environment, peculiar to themselves ; they 

 have on the whole the same nourishmont, they live under similar sanitary eon- 

 ditions, and are probably subject to niore nearly identical risk of zymotic disease 

 than any random couple of individuals ; lastly, the death of husband or wife is a 

 shock aftecting the survivor more intensely than anyone eise, and offen causing a 

 sudden change in financial and other environmental conditions. All these circum- 

 stances, resulting directly from marriage, may be considered likely to produce 

 a eorrelation between the age at death of husband and wife. This possibility was 



Biometrika ii 02 



