\\.\VII \LI 



clxxxxii 



t.li.-.t PearKMl '\\\><- VII a.,. I 'l\\- IV nirvrs, with their n.oimmt-coeffici. nt~, 

 will ivpivsrnl ;uli .jiiately the triir sampling distrilmtion.s at tli.-ir two probability 



level*. 



//Inanition. In a sample ..f .",00 i h,. following v:ihios an- found : 



Is it possible that the sampled population was normal? 



The table shows that in 5 / of random samples from a normal population V#] 

 may be expected to be less than - '170 and in 1 % less than - -255. The observed 

 value falls in between these limits. For $ 2 we see that only 1 % of samples can be 

 expected to give a # 2 greater than 3'60, and the observed value lies outside this 

 limit. The test therefore provides a doubtful answer when applied to Vtfi but a 

 decisive one when applied to # 2 , and we may therefore conclude that it is practically 

 certain that the sample has not been drawn at random from a normal (xipulation. 



TAHLKH XXXVIII XLI. 



Moment-Coefficients of Asymptotic Frequency Distributions. (Gertrude K. Pearee, 

 Biometrika, Vol. XX A . pp. 314 355.) 



Pearson and Pairman have discussed the formulae for correction of moment- 

 coefficients when the frequency curve rises abruptly at one or both terminals from 

 its base or from a vertical, i.e. when there is not, what Sheppard's corrections 

 suppose, high contact at the terminals*. These authors then passed to the con- 

 sideration of cases in which the frequency curve, instead of rising abruptly from the 

 base, asymptotes to the vertical at one or both terminals, i.e. when it is a true 

 J- or 7-curve. The corrections to be made to the moments in all such cases as the 

 above are termed abruptness-coefficients. We may distinguish the two cases as non- 

 asymptotical ly abrupt curves and asymptotically abrupt curves. 



In the second part of the Pearson and Pairman paper wherein x to x = T P 

 is the total range and N is the total frequency , the form 



Z= yda; = N[l +tf(A+Bx + Co? + Do?+Ea*)] ............ (i) 



Jx 



was proposed as a suitable auxiliary curve in the case of asymptotically abrupt 

 Biometrika, Vol. xn. pp. 231 et seq. The two forms are thus 



(i) 



abruptly from base at A 

 All these forms occur in the Pearson Type Curves. 



Springing from vertical at /.' 



