xl Tables for Statisticians and Biometricians [XXIII — XXIV 



p. xxxiv. Both ?> and Q give very high results for (4) aud (5), and this is in accord- 

 ance with the view elsewhere expressed that for extreme dichotomies Q is not to 

 be trusted. It may further be doubted, whether for such dichotomies the theory 

 of the distribution of deviations on which /> is based can in its turn be accepted. 

 On the whole r, seems to me the most satisfactory coefficient of association, to be 

 controlled by results for ?> in the cases where neither the dichotomies 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. 



Abacs XXI and XXII (pp. 33—34). 

 See after Tables XXIII and XXIV. 



Tables XXIII and XXIV 



Tables for determining approximately the probable error of a tetrachoric 

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

 Julia Bell, M.A.) 



Given a tetrachoric table 



a+6 



(7 ' c-\-d 



SO arranged that a + c>b + d and a \-h >c-\-d, 



then if ^ (1 + a,) = (« + b)lN, \{\+ a,) = {a + c)IN, 



and I't be the correlation, we have approximately ; 



Probable error of ?•( = Xi ■ Xr, • Xa, ■ Xa„j 

 where Xi = ■67449/ViV, 



and is tabled in Table V, p. 12, 



s/i(l + a,)i(l-«,) 'J^(l'+a.)\{l -cu) ... 



Xa, = -JJ . Xa.=— ^ ...(XXXIII), 



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



Xr, = ^l-'>'y 1 -(^^^0^) (xxxiv), 



sin~'?'( being read in degrees, x^ aud Xa, '^^'^ tabled in Table XXIV and Xr in 

 Table XXIII (p. 35). 



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

 siderabl}' from the true value* for extreme dichotomies. lu such cases the full 

 formula must be used. 

 • Phil. Tram. Vol. 195, p. 14. Xn '° formula (I) should of course uot be included under the radical. 



