Tables for Statisticians and Biometricians [XXIX 



Table XXIX (pp. 42—51) 



Tables of the Tetrachoric Functions. (P. F. Everitt, Biometrika, Vol. VII. 

 pp. 437—451.) 



The purpose of these tables is to expedite the calculation of tetrachoric r t , the 

 correlation coefficient from a four-fold table, when we suppose the variates to be 

 Gaussian in the law of their frequency. 



Let the table be 



where a is the quadrant in which the mean falls, then b + d and c + d are clearly 

 each less than ±N. Let 



t = (b + d)jN = i (1 - aO, < - (o + d)/N = A ( 1 . - «,), 



then d/N= t t ' + Tit/?- + t 2 t./?-' j + . . . + TnT„'r" + (xxxvii) 



is the equation to determine r the tetrachoric correlation, and Table XXIX gives 

 the values for given t , i.e. ^(1— a) of the following six tetrachoric functions 

 ii, To ... t 6 , and further of h, the ratio of the abscissa of the dichotomic line to the 

 standard deviation of the corresponding variate. 



It is occasionally needful to go beyond the first six tetrachoric functions. In 

 this case the following finite difference formula is available : 



t„ = /tp„T„_, - f] fl T M (xxxviii), 



where p n =l/'Jn, q n = (n - 2)/Vn(rc — 1) (xxxix). 



The following table gives the values of p n and q n from n = 7 to 24. 



