120 The Correlation Coefficient of a Polychoric Table 
§ 11. Formulae for Computation. 
The forms found for S are not convenient for computation. The following have 
been found more expeditious. Various other formulae are also collected for reference : 
X., = Nz {h„ h, r) = ^=^e 2(1 -r^) (134), 
277 V 1 — r- 
— A^i + -Bs( — 1, 
when no quadrantal suffix is used a is understood. 
'Sn-ii = n„^«u + ^n^c,i + _ ^ (135), 
and similarly for aSi2-i2» ^^c., 
.(136), 
'5ii.2i = rill ^21^11 
(137), 
^lin22''^12 ^11^21 
+ yiii^22«13 
/S1I.22 = niin22«ll + 5111122^21 + Bi^B^^n^i 
(138), 
+ ^lin22>^12 •P1I-P22 
+ ^11^22**13 ^ 
'S'12-21 = ni2n2i^hi 
+ 5i2n2i«2i + 512521^31 
+ n 12 ^21*^12 + -Sl2-^21*'^22 _ -Pl2 ^21 (139') 
+ ^12^21^3 ^ 
/S12.22 = HiaHaa ('«ii + »h2) + -212 022 (^21 + "22) + 51,522 (*^31 + %2) 
+ A2^2ni3 - ^'f''- (140), 
^21-22 = 11211122 (^lll + "21) + B.^iB^^n^-^ 
P 
.(Ml) 
+ ^211122 (^^12 + ^22) B21P22 
^21 ^22 ( "13 + %3) ^ 
XstXs'f^stOs't'Bsfs't' = ^sfs't' (1-12), 
I? _ ^st-s't' 
. . J^st * s't' — 
= ^ - (143). 
"^^st'st^s't' -s't' 
