ON THE PROBABLE ERROR OF A COEFFICIENT OF 
CORRELATION AS FOUND FROM A FOURFOLD 
TABLE. 
By KARL PEARSON, F.R.S. 
Let the fourfold table be 
a 
b 
a + b 
c 
d 
c + d 
a + c 
b + d 
N 
Then on tbe assumption that the frequency distribution is normal, we can by aid 
of Everitt's Tables of the Tetrachoric Functions* rapidly find r. I have shown in 
a paper published in the Phil. Trans, in 1900f that found in this way 
Probable error of r 
= -67449 \(a + d)(c + b) % (a + c)(d + b) (a + b)(d + c) 
n , . ad — be , ah — cd ac — bd\ i 
+ 2 rm — — y* — Yi 
wh 
ere 
Yi — -7= e * 2 dz, y,, — ~r-— 
V27r-'o v'IttJq 
1 
1 N* J 
i 
/c — r/i 
Vl - r 2 
2tt Vl - ?- s 
e 
•0), 
* Biometrika, Vol. vn, p. 436, and Vol. vm, p. 385. 
t P/«7. Trans. Vol. 195 A, p. 14. Owing to the carelessness of the printers my xo was put as V%^ 
and the last N' 2 in the denominator as N 3 . 
