xl Tables for Sfallxtin'mi* <nnl l{!innt'tr'n-i<iiix \\\\\\ \\ IV 



p. xx\i\. Until r,. anil (} i;i\e \>v\ hi^'h results (i>r ( 4) ;IIK| (o ), ami tins i- in a>-<-onl- 

 aiicc with the view elsewhere expressed lli.it I'm- r\tivnn- dichotomies (J is not to 

 be trusted. It may further he ili>nl>i>-<|, whether lor such dichotomies the theory 

 of the distribution of deviations on which ;-,. is based can in its turn be accept* d. 

 (In the whole /, se,-m-> to mi- i he most .sit isl'ad 01 \ cot-tlien-iit of association, to be 

 controlled by results for r,. in the casrs win-re iK-itlier the tlichotomies are extreme, 

 nor the numbers so large or so small as to fall outside the moderate range of 

 Tables XVIII XX or Abacs XXI and XXII. 



AI-.A.S XXI AND XXII (pp. 3334). 

 See after Tables XXIII and XXIV. 



TAIIUSS XXIII AND XXIV 



Tables fur determining approximately the probable error of a tetracliurir 

 correlation. (Pearson, Bwmctriku, Vol. IX. pp. 22 27. Tables calculated by 

 Julia Bell, M.A.) 



Given a tetrachoric table 



so arranged that a + c> b + <l and a \-b >c + d, 



then if |(1 + a,) = (a + b)/N, i ( 1 + a,) = (o + c)/N, 



and ?-, be the correlation, we have approximately : 



Probable error of r t = Xi Xr t Xo, Xo,- 

 where K = '67449/VF, 



and is tabled in Table V, p. 12, 



a t ff a.,- 



H and K being found from the z column of Table II, p. 2, and 



.1,1-0,) 



ll )> 



-, snr 

 ~^ 



sin~'r, being read in degrees. ^ a and ^ a are tabled in Ta'nle XXIV and \ r in 

 Table XXIII (p. 35). 



This value of the probable error is only approximate and may diverge con- 

 siderably from the true value* for extreme dichotomies. In such cases the full 

 formula must be used. 

 I'liil. Traiu. Vol. 195, p. 14. Xn > formula (I) should of course not be inclucii-.l un.i. r the radical. 



