THE CRITERION OF GOODNESS OF FIT OF 
PSYCHOPHYSICAL CURVES. 
By GODFREY H. THOMSON, D.Sc, Armstrong College, 
ill the University of Durham. 
CONTENTS 
PAGE 
(1) Introduction 216 
(2) Peculiarities of P.sj'cliophysical Data 218 
(3) The Constant Process, a Process for titting a Normal Curve to Data with 
Uncentred Tails 220 
(4) The Probability of a certain Category of Judgment . .... 221 
(5) Pearson's Criterion of Goodness of Fit 223 
(6) Numerical E.xaniplc 226 
(7) Urban's Incorrect Method of comparing Goodness of Fit. . . . 226 
(8) The Probable Errors of tlie Criteria of Fit 228 
(9) Summary of the Rules for testing Goodness of Fit of Psychophysical 
Curves ,229 
Api»endix . 230 
(1) Introduction. 
The object of the present paper is to inquire what is the proper method of 
examining psychophysical curves as to their goodness of fit. In psychophysics 
various mathematical processes are employed for fitting theoretical curves of 
"ogive" form* (known to psychologists as psychometric functions, but really error 
functions), to data of a certain kind, usually threshold measurements collected by 
the " Method of Right and Wrong Cases." The best known of these mathematical 
processes is the Miiller "Constant Process," using the probability integral f. To 
make the material in which we are about to work understandable, it is necessary 
first to go into some detail as to the nature of the experiments which supply 
the data to be fitted, and as to the theories which have led to such mathematical 
curves being drawn through these data. 
Most of the experiments in question have for their object the determination of 
the conditions of our experiences of equality and diftei'ence. For example, suppose 
we compare two weights, one of which is 100 grams, by lifting them in succession 
by the right hand with a number of experimental precautions, into which we need 
* The term in this connexion is Galton's. 
t G. T. Fechner, FAcmentc dcr Fsycliophysik, 1860; G. E. Miiller, " Ueber die Maassbestimmungen 
des Ortsinnes der Haut mittels der Metliode der richtigen und falschen Falle," Pjlilijers Archiv fiir die 
gei<. Pliysiologie, 1879, xix, pp. 191 — 235, especially par. 5 et acq.; G. E. Miiller, Die Gesichtspiinkte und 
die Thatsachen der Psychophysischen Metliodik, Wiesbaden, 1904, par. 11; F. M. Urban, "Die Psycho-, 
physischen Massmethoden," Archiv fiir die yes. Psychologie, 1909, xv, p. 287; G. H. Thomson, "The 
Accuracy of the 0(7) Process," Brit. Journal of Psychol., 1914, vii, p. 46, and in various text-books, 
e.g. Titchener's Experimental Psychology, and W. Brown's Essentials of Mental Measurement. 
