xxxvi Tabltut Jni- Stalls! n-lmiK >im/ IHniiH-trlriinix I XVI I \\ 



and therefore log P = 1739 502, 



and P = 3179/10". 



In the first and third cases a different treatment must lie ust-d. For x*=l' 

 we use Table XII. 



We have for i' 4 : 



P = -801253 + -4393 [- 228846] - J (-4393) (-5607) [+ 480G4] 



= 6948. 

 Had we worked from Table XVII by Formula (i), we should have had 



P=-6950. 

 For = '7080, we can use Table XII, remembering that for %' = 0. f 



We have 



P = 1-000,000 + -708 [- 198,747] - } (-708) (-292) [- 30,099] 



= -8624. 



Had we worked from Table XVII by Formula (i), we should have had P = 

 close enough for practical purposes. 



The true value of P worked from 

 P. 



=2 { i f%-ix' d + JL e -i^ 1 



lV2irJ x * V27T 



by using Table II is P = '8713. See p. xxxviii. 



Examining the values of P we see that having regard to the errors of random 

 sampling we can only say that there is no relation between rural and urban 

 districts and houses building or built ; there is clearly no ' distinct association,' 

 for in 69 out of 100 cases in sampling from independent material we should get 

 more highly associated results. There is likewise no association on the given 

 material in the Datura characters. The other three cases have clearly very marked 

 association, quite independent of any influence of random sampling. If we regard 

 these three tables the order of ascending association judged by either <f> or C t is 

 (4), (5), (2), as against Mr Yule's (2), (4), (5). If we disregard the non-significance 

 and take merely intensity of association, without regard to random sampling, the 

 order is (3), (4), (1), (5), (2), as against Mr Yule's order (1), (2), (3), (4), (5). 



The best method of inquiry at present for relative association in the case of 

 four-fold tables is, I hold, first to investigate P and throw out as not associated 

 those cases like the 'Houses, built and building" above. Then to use either 

 " tetrachoric r t " or C t according as we are justified in considering the variates 

 as continuous or not r p (see p. xxxvii) may be used as control. 



TABLES XVIII XX (pp. 3132) 



Tables for deterniinin;/ t/ie. Hijiiiprobable Tetraclioric Correlation r r . (Pearson 

 and Bell : On a Novel Method of regarding the Association of two Variates classed 



