XIV] 



In particular from (ii) we have 



\cill 



(v). 



Here o- Mp , o-^ and o-/j a are "standard errors," i.e. the standard deviations of /*,,, ft 

 and ft in long series of large samples of size N, where we must write the sample 

 values of p^ and the /S's in our ignorance of the parent population values. 



The samples must be very considerable for the /A'S and ft'a to be normally 

 distributed even with rough approximation. When they are such we may use 

 "probable errors" and equations (v) may be written 



67449 



67449 



P.E. 



67449 



P.E. of 4 = _ 



.(vi). 



Equations (vi) should certainly not be used for samples under 50, and the inferences 

 from them should be guarded, even when the sample runs up to several hundreds. 

 They are limiting expressions "when N -* oc ." 



Illustration. The following table gives the distribution of Enteric Fever in 

 8689 cases* : 



The following moments were obtained using abruptness corrections "j*: 

 & = 3-821,776, n* = 7-595,118, /* 4 = 63-51882, 

 ft = 1-033,412, ft = 4-348,825. 



* See Phil. Tram. Vol 186, A, pp. 390392, and Biometrika, Vol. xvm. pp. 288289. 

 t Biometrika, Vol. xn. pp. 231258. 



