Mar. 15, 1924 
Measurement of Linkage Values 
885 
results in a very material simplification. Thus Woodworth's formula 
(2) for two characters segregating in the ratios 3 : 1 and 15 : 1 which 
is given as 12^+11 (^+2 rs) : 3 r 2 - f-4 (^+2 rs) : s 2 +2 rs : r 2 , becomes 
11 + p 2 : 4— p 2 : 1 — p 2 : p 2 , and the formula for evaluating p from an 
observed zygotic distribution becomes 
. P = - y/ 
8 (AB + ab) 
n 
5-5 
Formulae for calculating p for some of the zygotic distributions most 
frequently encountered are given below: 
. ,2 ( Ab + aB ) 
3 : 1 and 1 : 1 p = . . .5 
, 2 32 (AB + ab) 
63 : 1 and 3 : 1 p 2 = ° - ---23. 5 
ib 
A .2 3 2 {AB + ab) q 
15 : 1 and 15 : 1 p 2 =- — ---28 
^ ^ r n 
15 : 1 and 3 : 1 p 2 = - -- ---5-5 
n 
9 : 7 and 3 : 1 p 2 = 
9 : 7 and 9 : 7 p 2 = 
9 : 7 and 15 : 1 p 2 = 
16 (i 4 B + a6)— 7n 
6n 
32 (Aff+afr) — 14W 
yn 
32 (AB + afc) — 17ft 
3 n 
HALDANE'S METHOD 
The method proposed by Haldane may be written in the form: 
where 
34^1 + (2 + 4 ) 4 
2+4 4 
(4) 
4=^-2 
4 - 
n 
4.ab 
n 
h+U 
4 is an approximate value and when the observed classes are wide de¬ 
partures from expected Mendelian ratios it is necessary to make a further 
approximation by substituting T for 4 in formula (4). 
The method used in deriving the formula is to determine the most 
probable value of p 2 for an observed population where the departures 
from expected Mendelian ratios are the result of errors of sampling. 
The probable error is given by Haldane (5, p. 295) as: 
(2 +p 2 ) (1 -f) i 
(1+2 p 2 )n 
