XXI XXIV] /////W//r//,,,, 



\\ln-n-.-i.s tin- ob.s.-rvrd \ahif i> ";:{. This SII-L;. >!-, that tin- analysis giving 22'H i* 

 of doubtful value; if it bo discarded 



w< - (26-6 - 23-9)/(-675) = 4-00. 



It will be seen that JT 4 for p = '02 is 4rl, so that the chance in slightly mon- than -02 

 that a range as great, as that, obst-m-d would be found in a wimple of 4. In this 

 case it would probably be felt d-siral>lr to make one or mon: further analyses. 



TABLES XXIII-XXIV. 



Tables of the Distribution of Range, Median and Mul-point betwm< KitreiM 

 Observations ("Centre") in Small Rumples. (E. S. Pearson and N. K. Adyan thuya, 

 Biometrika, Vol. XX A . pp. 359360.) 



(i) The Range. The frequency distributions of range upon which Tables XXIII 

 XXIV were based are those appropriate for samples from a Normal Population 

 (ft = 0, ft = 3). In certain problems the statistician may have clear evidence that his 

 population is of this form, but it may also happen that he is faced with one or other 

 of the following situations: (a) He has not sufficient data available to determine 

 the form of his population but is reasonably confident that no very great deviation 

 from normality exists. (6) He knows the form of his population distribution and 

 this is definitely not normal. In the first case he needs evidence that the distribu- 

 tions of range upon which the preceding tables have been based are not too sensitive 

 to changes in population form; in the second case he needs information about the 

 distribution of range in samples from populations of other forms. An exact equation 

 to the range curve has only been obtained in the case of the so-called Rectangular 

 Population* (ft = 0, ft = 1*8), but certain results of experimental sampling throw 

 some light on the position. 



Random samples of 2, 5, 10 and 20 were drawn from populations whose law of 

 distribution followed Pearson-type curves: 



Population Samples drawn 



8:2 



(3) Type VII ft = O'OO ft = 7 '07 1000 of 2, 1000 of 5, 500 of 10, 500 of 20. 



(4) Type III ft = 0'50 ft = 3'73 1000 of 2, 1000 of 5, 500 of 10, 1000 of 20. 



Table XXIII shows the frequency constants of the distributions of range 

 observed among these samples; the means and standard errors (s.E.) are given in 

 terms of the population standard deviation. Considering first the symmetrical 

 populations (ft = 0), it will be seen that the mean range changes very little with 

 the population ft for samples of 10 or less, but that at 20 there is a somewhat 

 greater change. The standard error of range changes however very considerably 



* That is to say a population in which individuals of each character value exist in equal numbers. 

 Very few populations in Nature are of this type; it is a theoretical limit to very platykurtio symmetrical 

 frequency distributions, before their transition into antimodal types, i.e. U-curves. 



