72 



BELL SYSTEM TECHNICAL JOURNAL 



this way we can transform the integral curve into a straight line by 

 choosing an .v-scale proportional to the integral from to x of the 

 probability curs'e." When plotted in this way, a normal distribution 

 appears as a straight line on such paper. At first it may appear very 

 simple to determine whether or not the data conform to a straight 

 line, but in practice this is not always so easy. Thus, we have seen 

 that the distribution of shots presented in Fig. 5 is not normal, but 



DiSTEIBUTIOM OT TDOO 5HDT5 





Fig. 9 



when these results are plotted on probability paper we ha\e the 

 curve given in Fig. 9. The reader should be cautioned that in such 

 a case there is a temptation to consider that the obser\-ed points are 

 approximately well fitted by the straight line, although this is not 

 the case. 



Probability paper could be ruled for difterent theoretical distrilni- 

 tions, but in its present form it serves only to determine whetlier or 

 not the distribution is approximately normal. Its use leaves much 

 to be desired in the way of a quantitative measure of the degree ol 

 fit between the theoretical and observed distributions. 



Cakiilation of a, fii = 'Vk, and fi«. Let us consider what informa- 

 tion can be obtained as to the best theoretical distribution from only 

 a consideration of the first four moments of the observed frequencies. 

 Let us consider the values of k and (3; presented in Table V. These 

 have been calculated for the point binomial (/>+<?)" where p, q and n 

 have been given different values. For the normal law corresponding 

 to p = q and m = «, we have k = and /32 = 3. Thus, if in a practical 



" Whipple, G. C. — ^The Elements of Chance in Sanitation — Franklin Inslitulc 

 Journal, Vol. 182, July, December, 1916— pp. 37-59 and 205-227. 



