Godfrey H. Thomson 223 
Replacing in equation (7) therefore the weights M by the new Urban weights P, 
Urban found in the present instance 
,S = 98-24 grams, , 
/t= 0-1 17995. 
That is he represents the proportions p theoretically by using the hypothesis that 
the " psychometric function," as psychologists call it, is given by 
1 /-O-llTDiio (98-21 -s) 
p'=-7= e-^'-dx (10). 
W TT J -00 
The theoretical values ^j' thus calculated are compared with the actual values 7) in 
this table. 
Grams 
P 
P' 
Difference x 
84 
•0233 
•0088 
+ -Olib 
88 
■0267 
•0438 
- •oni 
92 
•1167 
•1489 
- -0322 
96 
•3567 
•3544 
+ -0023 
100 
•6100 
•6155 
- ^0055 
104 
•8833 
•8319 
+ •0514 
108 
•9300 
•9483 
- •0183 
The object of the present paper is to make clear the proper methods (a) of as- 
certaining, in all such cases, whether the theoretical numbers are a i-easonable fit 
to the observed numbers, or not, and (b) of comparing the fits obtained by different 
hypotheses, that is by different error functions. The psychohigist would e.xpress 
this by saying that he was comparing different psychometric functions. To the 
statistician the comparison is one of error functions, the natural procedure being to 
try first the normal curve, then members of Pearson's family of curves, then 
compound curves ; the conclusion in the latter case being that the material was 
not homogeneous. This work I have as a matter of fact already carried out, and 
have come to that conclusion ; but it is beyond the scope of the present paper, 
which hopes to interest psychologists in inodern statistical methods, and statisticians 
in modern psychology. 
(.5) Pearson's Criterion of Goodness of Fit. 
This problem, of comparing the goodness of fit of curves in psychophysics, 
although it has not as far as I am aware ever been correctly performed, is really 
very simple, and could be handled at once from first principles. For the sake how- 
ever of showing the connexion with other work it is advisable to treat it as a special 
case of the application of Pearson's Criterion of Goodness of Fit*, which is in brief 
as follows. 
* Kavl Pearson, Phil. Mag., July 1900 and April 191(j. 
