A. Ritchie-Scott 
iir 
§ 9. The Standard Deviation of Polychoric r in special cases. 
The value of the standard deviation when r = 0 is of interest and may be got 
as follows. 
Assuming r = 0 throughout : 
Agt = (kf) = -~ , 
and writing w'^. = N ~ mg. and m'.^ = N — m.^, then 
p _ m',.m'.t 
Substituting these values in the S's, we have after reduction 
^11-11 = ]p mi.wi.iw^.m'.i (104), 
'S'i2-i2 = ^ m-^.m.2m\.m' (105), 
'S21-21 = m.2.m.im'.^.m'.:^ (106), 
'^22.22 = j^3-'"'2-'«.2»*'2-»^'-2 (1*^*7), 
'5ii.j2= WH.?H.im'i."^'.2 (108), 
*5u.2i = ^ ?ni.m.iTO'2.»i'.i (109), 
Si2-2i = '5ii-22 = nij^.7ii.im'2.m' .2 (110), 
'Si2-22 = ^ m-^.m.^vi'^.m' .2 (Ill), 
'§^21-22 = ^^2-»*-l^>^'2-™'-2 (112). 
From these values we get the ct's and i^'s. 
