226 Criterion of Goodness of Fit of Psychoplnjsical Curves 
(6) Numerical Example. 
Let us apply these formulae to the example already cited. The calculations 
are carried out in the following table. The theoretical j/q's should be used, clearly, 
as denonjinators of the terms of ■)(^. 
p' 
9' 
p'q' 
•0088 
•9912 
•00872 
•00021025 
•0241 
■04.38 
•9562 
■04198 
•00029241 
•0070 
■1489 
•8511 
■12673 
•00103684 
•0082 
■3544 
•6456 
•22880 
•00000529 
•0000 
■G155 
•3845 
•23665 
•00003025 
•0001 
•8319 
•1681 
•13983 
•00264196 
•0189 
•9483 
•0517 
•04903 
•00033489 
•0069 
•0652 = *9(,t-7pY) 
The number of experiments was the same for each p, viz. 300, therefore 
^- = ^S' = 300 X •0652 = 19-5G* 
The Table XII in Pearson's Tables to find P has to be entered with and 
v' = (n + 1), where n is the number of variates, here the number of pa, i.e. 7. We 
find there 
n' = 8, %== 19, -008187 = 7-^, x- = 20, •005570 = P. 
It is unnecessary, with data such as we are here handling, to interpolate elaborately. 
Clearly, for ^- = 19^56, P is of the order 
P = -007. 
That is to say, in only seven cases in a thousand should we expect to get our 
present observed p's from our theoretical p"s by random sampling. It is therefore 
not at all probable that the equation (1) truly represents the, "psychometric 
function " for this subject and this reaction. 
(7) Urban s incorrect method of comparing Onodness of Fit. 
In the article from which the above example is taken, Professor Urban was 
inter alia, desirous of comparing various hypotheses of the " psychometric function " 
among themselves. Those which he fully works out are (1) the above assumption 
that it is the integral of the normal probability curve, and (2) the assmnption that 
it is an "arctan." curve (tan~' 6). (It is needless to point out surely that the latter 
hypothesis is in itself most unlikely ; however, we are here concerned with an 
empirical comparison of the two hypotheses, and it is important that the method 
should be correct since it will be necessary to compare other and more likely 
theories, as for example Pearson's curves.) 
* Compare Appendix. 
