SECTION V. DISSECTION INTO COMPONENT CURVES. 



I shall next consider the possibility of .statistical dissection of 

 our frequency curve. It might be possible that the sample con- 

 sisted of two (statistically) different strains. If this were so then it 

 would be possible to break up the frequency distribution into two 

 component normal distributions. 



The fundamental memoir on this subject is K. Pearson : " On 

 the Dissection of Asymmetrical Frequency Curves." l Pearson has 

 discussed the application of the theory in several 2 actual cases 

 and 3 has given the fundamental equations in a somewhat better 

 form in a paper li On the Problem of Sexing Osteometric Mate- 

 rial ".* I have followed the notation of the fundamental memoir, 

 excepting in one or two instances, where I have used a slightly 

 modified notation. 



•But before proceeding to a full discussion of the subject it 

 will be useful to apply some simpler tests of homogeneity. 



Agreement of Sub-samples. 



The whole group of two hundred cards were arbitrarily 

 divided into two sub-groups of 100 cards each. The Frequency 

 Constants were calculated for each of these two sub-groups and 

 compared. 



The unit of grouping adopted was 50 mm. in each case. 



Mean : — 



1st group of 100 = 16 5875 + 4-64 36 mm. 

 2nd group of 100 = 16 57-00 + 4*94 14 



Difference = 175 + 678 08 6 



Standard Deviation : — 



2nd group = 73.26 ±3'49 mm - 



1st group = 68*85 ±3*28 



Difference = 4'4 X ±479 



1 Phil. Trans. Vol. 1S4A (1894), pp. 71 — no. 



2 K. Pearson: "On the Applications of the Theory of Chance to Racial 

 Differentiation," Phil. Mag. 1901, p. 110. 



3 K. Pearson : " On the Probability that two Independent Distributions of 

 Frequency are really Samples of the Same Population, with Special Reference 

 to Recent Work on the Identity of Trypanosome Strains." Biometrika Vol. 

 10 (1915), p. 123 ff. 



* Biometrika Vol. IO (1915), pp. 479 — 487. 



root 



5 It is well known that the P.E. of a sum or a difference is given by square 

 of the sum of the squares of P. E. (see Yule Statistics, p. 211). 



