GoDFRp^Y H. Thomson 
217 
not here enter. We wish to know under what conditions the unknown weight 
appears lighter than, equal to, or heavier than the standard weight. An impijrtant 
condition is of course the " actual " weight of the unknown weight, as measured in 
the usual manner. But this is by no means the only important condition. The 
order in which the weights are lifted (whether standard first or unknown first) ; the 
luimber of categories into which our judgments have to be classified; the order of 
succession of the several unknown weights, whether rising or falling or at random ; 
the range over which the succession of unknown weights stretches, whether or no 
it contains any which are quite easily distinguished from the standard ; all these 
and many other conditions are of great importance. Steps can however be taken 
to eliminate some of these factors, by means of judicious experimental precautions, 
and the attempt can be made to keep the others as constant as possible during 
a series of trials. The judgments which are given by the subjects then dc'pend 
mainly on the difference between the standard stimulus and the variable stimulus ; 
in the case of our example on the difference between the standard weight and the 
variable weight. Among other points of importance in the fitting of the curves is 
the possibility of deciding by means of the goodness of fit whether the experimental 
conditions have really been kept as constant as has been hoped, for lack of constancy 
in this respect will lead to heterogeneity which will show itself by the necessity of 
using a compound curve to obtain a good fit. 
To fix ideas, it is desirable at this point to have an actual set of data to refer to. 
In some very carefully conducted experiments on weight-lifting. Professor F.M. Urban 
(op. cit.) found that, with one of his subjects, under certain experimental conditions, 
the standard weight being 100 grams, the following numbers of answers heavier 
were returned, out of 300 trials with each of the several unknown weights. It 
should be mentioned that the experimental method used involved that the unknown 
weights were presented to the subject in random sequence, accompanied each by 
the standard, so that the 300 trials referred to were not one after the other, but 
were separated from each other by trials with the other unknowns. Otherwise 
expectation and other psychological factors produce a considerable correlation between 
one judgment and the next, which is reduced to a minimum by Uiban's procedure. 
Moreover, precautions against fatigue and several other factors were taken. For the 
details the reader is referred to Urban's raem(jir, with the warning that much of 
the mathematical part thereof is incorrect. 
Grams .s 
Answers heavier 
Proportion p 
84 
7 out of 300 
0233 
88 
8 out of 300 
•0267 
92 
3.5 out of 300 
•1167 
96 
107 out of 300 
•3067 
100 
183 out of 300 
•6100 
104 
26.5 out of 300 
•8833 
108 
279 out of 300 
•9300 
It is to numbers such as these that the curves to be con.sidered are fitted. 
Biometrika xii 
15 
