ON THE PEOBABLE ERROR OF BISERIAL v. 
By KARL PEARSON, F.R.S. 
(1) In a paper in Biometriha, Vol. vii, pp. 248-257, entitled "On a New 
Method of determining Correlation where one Variable is given by alternative and 
the other by multiple Categories," I gave in 1910 the process of determining what 
is now generally termed "biserial tj." 
Let X be the alternative, y the multiple variate, Ir^, the distance from the division 
between the alternative categories of the mean of the array of x's corresponding to 
a given value of y, yO.j. its standard deviation and n.y its frequencv. Let x, and 
N be the corresponding quantities for the marginal total. Then, if 
I showed that 
-,S\n 
1 
and explained that rj might be found from the usual tables of the probability 
integral. I did not publish the probable error of this method of determining 
"biserial 77" at the time, and it has remained one of the few outstanding cases 
where probable errors were still wanting. I now add the determination of the 
probable error, and owing to the kindness of my colleagues. Miss Ethel M. Elderton 
and Miss B. M. Cave, am able to give a table for its fairly easy computation. 
(2) I take as my biserial table the following: 
nil 
«21 
^1 
«i 
«2 
N 
Here stands for tiy, and the y variate is the horizontal or multiple category 
variate. We shall write 
" ^S{n,y,% y^=^(x/a,r (ii), 
and thus 
^ 1 + k2 
1 +y2 
.2- 
