clxii Tables for Statisticians and Biometricians [XXXII XXXIV 



The student must be warned that to obtain a Pearson curve with a good fit he 

 must deduce that curve by aid of the first four moments, not by fitting through a 

 knowledge of the range and mean. He must disregard the fact that the curve may 

 have a range non-coincident with the correlation range 1 to + 1. Frequencies, if 

 any, outside the correlation range will as a rule be wholly negligible*. 



The process of fitting with a Pearson curve is easy and rapid if we know the 

 mean, standard deviation, and fti, ft z of the r-distribution. Table XXXII contains 

 these at the foot for the range of small samples n = 3 to 25 and for various higher 

 values of n. But since this table also gives the ordi nates for these cases, the need 

 for curve fitting arises only in special instances for these values of n. Outside 

 these, when we need a curve for the distribution of r, we have no table of the 

 means, standard deviations and /3's for the various values. These constants of the 

 distribution must be computed from the original formulae, which give the first four 

 moments about r = of the r-frequency in converging series, and which for n > 25 

 are relatively easily evaluated. These moments must then be transferred to the 

 mean by the usual process and r, o>, r /3i, r (3?t determined. 



The requisite formulae are as follows, the first having been already cited, p. cxlviii : 



rf-,-,^!*, 12 ' 12 - 3 <" 



.'-i- Efc- 



3!(n+l)(n + 3)(n + 5)8 

 where o> 2 = u 2 ' r 2 . 



...) ...(iii), 



+ ...) ...(iv), 



'=r- .*!ln 



' 



3 2 .5 2 .7 2 p 6 



" ' 



where p: 3 = ^ - S/j^' r + 2r 3 . 



4 2 p 2 4 2 . 6 2 



4 2 . 6 2 . 8 2 p 6 



" l ~3!(w + 3)(n + 5)(?t + 7)8" i 

 where /t 4 = /* 4 ' 4t/j. 3 'r + 6p, 2 ' f 2 3r 4 . 



The student must bear in mind that if p be positive, //, 3 will be negative. 

 In the above formulae 



/Jr _ 

 sm"" 1 <f)d<f), 

 i 



* As in the case of a stature frequency when represented by a normal curve. 



