76 BELL SYSTEM TECHNICAL JOURNAL 



criterion has Ijccn cie\elopeci by Prof. Pearson " in a series of articles 

 in the Philosophical Magazine. It is true that this test for goodness 

 of fit cannot be used indiscriminately. In fact the application of this 

 criterion is subject to numerous limitations clearly set forth in the 

 original papers by Pearson and in more recent articles on the mathe- 

 matics of statistics. In the use of the method it is necessary that 

 these be kept in mind by the individual making the original analysis 

 of the data. Irrespective of these facts, however, the method itself is 

 one of the most useful tools available for measuring in a quantitative 

 way the "goodness of fit" between two distributions. The significance 

 of the values of P given in Figs. 5, 6, and 8 now become evident. 



Engineering Judgment. The fourth very practical and one of the 

 most useful methods of comparing the theoretical with the observed 

 distribution is that of applying common sense or engineering judgment. 

 To quote from a recent article of Prof. Wilson'" we have: "And as 

 the use of the statistical method spreads we must and shall appreciate 

 the fact that it, like other methods, is not a substitute for, but a 

 humble aid to the formation of a scientific judgment." Even with the 

 use of all the statistical methods known to the art, it remains im- 

 possible to determine the true nature of the complex of causes which 

 control a set of observations. We can present plausible explanations, 

 but we can never be sure that they are right. Sometimes we can 

 present two plausible explanations and then we must fall back on 

 engineering judgment or common sense to decide between them. A 

 striking illustration of this fact is presented in the following paragraph. 



Prof. Pearson ■"- has recently presented measurements of the cephalic 

 index of a certain group of skulls. The object of the investigation 

 was to determine if variation had gone on to such an extent as to 

 indicate the survival of the fitter inside a homogeneous population, 

 or the survival of two races both of which were in existence many ages 

 in the past. Pearson shows that, by a solution of a nonic equation. 



"If \vc divide the entire range of variation into s equal intervals for which 



the observed frequencies are /i, /:, /j and the corresponding theoretical 



frequencies are /i , f,', /', Pearson calculates the function 



-2 



y 



from which he is able to determine the probability that a series of deviations 

 as large as, or larger than, that found to exist could have arisen as a result 

 of ran<lom sampling. Tables have lieen prepared which give the probability of 

 fit in terms of the ninnbcr of intcr\als into which the entire range has been 

 divided and of the value of x. 



" Wilson, E. B. — The Statistical Significance of Kxpcrimcntal Data — science 

 —New Series, \o\. 58, 1493, October 10, 1923, pp. 93-100. 



" Philosofhical Magacine, Vol. I, 1901— pp. 110-124. 



