KUNGL. SV. VET. AKADEMIENS HANDLINGAR. BAND 58. N:0 3. 



43 



The following examples we take from Pearsojsts memoir on Skew Correlation 

 and non-linear regression. They are all examples used by him as illustrations of his 

 regression formulae. Thus a very interesting comparison is afforded, as we shall also 

 record Pearson's results. As will be seen the comparison is in no way to our dis- 

 advantage minding that in two of the examples the distribution is really not of the 

 ^4-type and considering that our curves include only moments of up to the fourth order, 

 while Pearson's theory, if cubical regression formulae are required, must include also 

 moments of the fifth and generally even of the sixth order. As the moment >v> is not 

 recorded by Pearson we cannot examine also the scedastic curves. 



Example 5. Pearson's illustration /I. 1 On the skew correlation between the 

 number of branches to the whorl and position of the whorl on spray in case of 

 Asperida od orata. 



As the correlation table is of rather special form we reproduce it here. 



Table V 





Number of 



branches in vvhovl 







Whorl 









Totals 



•'.'/ 





4 5 



6 7 



8 





First 



3 



66 42 



39 



150 



6,780 



Second 



3 



61 47 



39 



150 



6,813 



Third 



6 



60 40 



44 



150 



6,813 



Fourth 



1 12 



68 39 



22 



142 



6,486 



Fifth 



1 13 



53 10 



10 



87 



6,172 



Totals 



2 37 



308 178 



154 



679 





The characteristics needed in (34*) we derive from Pearson's moments. They 

 are not corrected for grouping. 



M, = 6,6663 

 ff, =0,8978 



i>'ci — —0,02 17 

 ,^ 12 = + 0,0736 



»• 03 = + 0,0601 



r — 0,207 6 



VI, = 2,802 6 

 O 2 =l,3 3 6'.i 



/V 04 = — 0,048 8 

 (? I3 = + 0,034 1 



r 04 = — 0,oo64 



Hence we derive using (35) II 



r v = 6,7093 — 0,1 4 i i{y — m 2 ) — 0, 03 o 2(2/ — m 2 ) 2 4- 0, 00 o 5(1/ — wi,) r '. 



1 We may mentiou that our r 3n = — —s and our r 40 = - : ~ in Pearson's notation. 



