Tables for Statisticians and Bionietnciam [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 /•(, 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 



a + h 



c+d 



a+c \ b+d ! N 



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 + rf)/iV = i (I - (z,), T,' = (c + d)IN = i (1 - «^). 



then djX=T^,rJ + TjT-,'r + T„TJr- + ... + T„T„'r" + (xx.wii) 



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

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

 Ti, T, ... Te, and further of h, the ratio of the abscissa of the dichot.omic line to the 

 standai-d 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„ = hji^Tn-i - qnTn-2 (xxxviii), 



where p„=l\^n, 7,, = (« - ■2),'v'» (« - 1) (xxxix). 



The following table gives the values of 2>,i and (/„ from n = 7 to 24. 



n 



Pn 



?n 



n 



Pn 



In 



7 



•37796 



•771.'i2 



Hi 



•2.i000 



•00370 



8 



•35355 



•80178 



17 



■24254 



■90951 



9 



•33333 



■82496 



IS 



■23570 



■91466 



10 



•31623 



•84327 



19 



■22942 



■91925 



11 



•30151 



•85812 



20 



■22361 



•92338 



IS 



•28868 



•87039 



n 



■21822 



■92711 



IS 



•27735 



•88070 



22 



■21320 



■93048 



U 



•26726 



•88950 



2S 



•20851 



■93356 



IS 



•25820 



•89709 



24 



•20412 



■93638 



