274 
On Theories of Association 
First Brother. 
3—4 
4—5 
6—7 
2 g 
/ £ • >\J<J'.' I V.' 1 t — 
V= -6214 ±-0170 
t.— -3761 + "0184 
Q= -4920 ±-0230 
,. .94.28+ -0919 
$= -3434 ± -0304 
$=■3653 ±-0383 
3—4 
= -3761 + -0184 
$=-4920± -0230 
r t = -5185+ -0160 
$=•6229 ±-0165 
r ( = -3524+ -0196 
$=-4603± -0232 
r,= -2777 + -0230 
$=•3963+ -0301 
4—5 
r,= -2428+ -0212 
$=•3434 ±"0304 
r t = -3524 ± -0196 
$=•4603+ -0232 
?•(= -3677+ -0209 
$=•5089 ±-0231 
r ( = -2978+ -0246 
$=■4306 ±-0301 
6—7 
■/•< = -2373+ -0240 
§=•3653 ±-0383 
r t = -2777 ±'0230 
$ = -3963 ± -0301 
r t = -2978+ -0246 
$ = -4306 ± "0301 
r ( = -3128+ -0276 
$= -4705 ± -0326 
0> 
— 
o 
S-i 
pq 
S3 
O 
o 
a; 
02 
and Second Brother in terms of First, and the repetition of the same numbers in 
a second cell does not give those numbers double weight. Had we worked our 
tables for Elder Brother and Younger Brother, each cell would have had 
independent weight, but adding them reversed we have lost one-half of the 
non-diagonal independent frequencies, and we must not still retain the same 
number of independent weights. Relative to Mr Yule's method of procedure, this, 
in our opinion, true method of weighting emphasises in symmetrical tables the 
diagonal columns and would correspondingly better tetrachoric r t as against Q. 
But we have not used what we consider the true weighting, because it might be 
said that it had been adopted with a view to bettering our position. Arranging as 
before we have the following results for the 16 coefficients : 
Weighted Mean 
Tetrachoric r t 
•3474 
Association $ 
•5083 
Weighted 
Standard Deviation 
■0931 
•0952 
Thus the positions of r t and Q are just reversed by proper weighting*. The 
coefficient of variation has no meaning, we hold, in the case of mere numerics like 
r t and Q, both of which may range from - 1 to + 1 in the general case. Indeed 
the case is more complex than can be accurately determined even by weighted 
standard deviations. For Q, although nominally ranging between + 1, is for any 
given case numerically greater than the corresponding tetrachoric r t , and thus 
their variabilities if not functionally related are related by limitations. For 
reasons already given we see no advantage in considering the probable error of 
* Mr Yule (loc. cit. p. 634) gives them as -084 and -081. If we take into account all the reasonably 
possible divisions 36 in number, i.e. 1-2, 2-3, 3-4, 4-5, 6-7, 7-8, the standard deviations are respectively 
<r,.= "121 and <tq= '130, while the ranges, on which Mr Yule appears to lay stress, take for r t the value : 
•59 and for Q : the value -92 ! 
