222 Criterion of Goodness of Fit of Psythophysical Curves 
matical process. To avoid this mental confusion I have elsewhere * suggested that 
the two words Metliod and Process should in psychophysics be consistently used in 
the way in which they are employed in the above sentence, viz. Method of collecting 
data, and Process of calculating. Frequently the Constant Process has been called 
the phi-gamma method, from the use of the name phi-gamma for the probability 
function. 
In 1909, F. M. Urban {ojx cit.) suggested alterations to the Muller weights, or 
rather suggested the necessity of another set of weights in additionf. These 
alterations arise from the notion of comparing the judgments heavier with the 
drawing of black balls from a bag containing black balls and white balls. The 
analogy is in detail as follows. 
(1) From a bag containing black balls and white balls 300 drawings are made, 
one at a time, the ball being returned each time before the next drawing is made. 
107 black balls are observed out of the 300. 
(2) A subject on performing a certain experiment with weights sometimes 
gives the answer heavier, sometimes some other answer. On one occasion, when 
the weights were 100 grams standard and 96 grams unknown, this experiment was 
repeated 300 times, with due precautions against fotigue, etc., and the answer 
heavier was returned 107 times out of the 300. 
Now a -p is the observed proportion (here 107/300) of black balls in a bag, then 
the j)i'obable error of p is known to vary with "J p{l —p)t- With the same sized 
sample, a result p = '5 has a larger probable error than a result = '8. say. If 
anything similar holds, as the analogy suggests, for the psychometric experiment, 
then the n equations (1) or (5) are not equally reliable, even although based on the 
same number, 300, of experiments each. In addition to the weights AT they need 
other weights 
^ (9) 
4<p{l -p) 4<pq ^ ^ 
to allow for this new variation in reliability. The combined weights M/4<pq are 
known as Urban's weights, and a table of these is usually given in psychophysical 
textbooks alongside the ordinary Muller weights. Urban discusses the matter at 
some length in his already cited article, and a discussion will also be found in 
Wirth's Psychophysik (Leipzig, 1912) where on page 151 the actual scatter of 
various p'& is given in a diagram. 
* Brit. Jourii. Psychol. 1912, v, p. 203. 
t There are many errors in the article of Urban's quoted. See my articles in the Brit. Journ. Psychol., 
1913, VI, p. 217, and 1914, vii, p. 44. But tliese errors, though making Urban's conclusions in that 
article invalid, do not touch the point here raised, in which I think Urban's suggestion marks an advance. 
+ Really the true values of and 1 -p should be used but this is the best we can do. And further, 
the expression, probable error, ceases to have an accurate meaning when is too close to zero or unity 
and the distribution in consequence is very skew. But these refinements do not matter at this stage of 
our argument. 
