Godfrey H. Thomson 
219 
and vice ?!e?'S(7, quantities analogous to the iii'h can be formed from the proportions 
p of the psychometric experiment, viz. : 
nio = (]h-ih)M, 
In the case of our example we should have: 
Below 84 grams, 
7 cases, 
/»/J/= -0233 
84— 88 „ 
1 
•0034 
88— 92 
27 „ 
■0900 
92— 96 
72 „ 
•2400 
90—100 
76 „ 
•2533 
100—104 
82 „ 
•2733 
104—108 
14 
•0467 
Above 108 „ 
21 „ 
„ -0700 
Totals 
300 „ 
1 •oooo 
There are however important differences which make the analogy inexact from the 
curve-fitting point of view. 
In the biometric histogram, if any one of the cells 111^ is larger than it ought to 
be, then any other nuist have a tendency to be smaller than it ought to be. There 
is a strong negative correlation between the numbers in the cells, a correlation, 
that is, from trial to trial. In the psychometric pseudohist(jgram however, formed 
from the jjroportions p, this is otherwise, because the ^^'s are measured quite 
separately from one another. 
In the biometric histogram the 711s, the numbers in each cell, are necessarily 
positive quantities. In the psychometric pseudohistogram they may be negative, 
if the p's do not rise steadily. In the biometric histogram the actual range found 
in a trial is as a rule known, that is the points where is zero and p is unity are 
known. In the psychometric case these points are as a rule not known, and there 
may be psychological reasons why extreme stimuli (such as would be required to 
find these points) should not be used. In our example we do not know whether 
the subject would have given no answers heavier at 80 grams, or whether at the 
other end he would have given only answers heavier at 112 grams. 
When we do know these points, or can assume them, in the psychometric case, 
we can fit our probability integral by forming the pseudohistogram, and calculating 
the mean and the standard deviation as though it were a real histogram *. This has 
been suggested by more than one writer, in England by Professor C. Spearman f, 
who does not however point out the difficulty that it cann(jt as a rule be done, 
because the points p = 0 and = 1 are not known. 
* The actual arithmetical formation of the histogram is uunecessary if a summation method of 
finding moments is employed. 
+ Brit. Journ. Psychol., 1908, ii, p. 227. 
15—2 
