. THEORY OF STATISTICS. 
only a part of the information afforded by the original data or 
the correlation table. The correlation table itself, or the original 
data if no correlation table has been compiled, should always be 
given, unless considerations of space or of expense absolutely 
preclude the adoption of such a course. 
REFERENCES. 
The theory of correlation was first developed on definite assumptions 
as to the form of the distribution of frequency, the so-called ‘‘ normal 
distribution ” (Chap. XVI.) being assumed. In (1) Bravais introduced 
the product-sum, but not a single symbol for a coefficient of correlation. 
Sir Francis Galton, in (2), (3), and (4), developed the practical method, 
determining his coefficient (Galton’s function, as it was termed at first) 
graphically. Edgeworth developed the theoretical side further in (5), 
and Pearson introduced the product-sum formula in (6)—both memoirs 
being written on the assumption of a “normal” distribution of fre- 
quency (¢f. Chap. XVI.). The method used in the preceding chapter 
is based on (7) and (8). 
(1) BRAVATS, A., ‘‘ Analyse mathématique sur les probabilités des erreurs de 
situation d’un point,” Acad. des Sciences : Mémoires présentés par divers 
savants, 11, série, t. ix., 1846, p. 255. 
(2) Garton, FrANcis, ‘‘ Regression towards Mediocrity in Hereditary 
Stature,” Jour. Anthrop. Inst., vol. xv., 1886, p. 246. 
(8) GarToN, FrANcis, ‘‘ Family Likeness in Stature,” Proc. Roy. Soc., 
vol. x1., 1886, p. 42. 
(4) Garton, Francis, ‘Correlations and their Measurement,” Proc. Roy. 
Soc., vol. xlv., 1888, p. 135. 
(5) EpcEworTH, F. Y., “On Correlated Averages,” Phil. Mag., 5th Series, 
vol. xxxiv., 1392, p- 190. 
(6) PEarsoN, KARL, ‘Regression, Heredity, and Panmixia,” Phil. Trans. 
Roy. Soc., Series A; vol. clxxxvii., 1896, p. 253. 
(7) YuLg, G. U., “On the significance of Bravais’ Formule for Regression, 
etc., in the case of Skew Correlation,” Proc. Roy. Soc., vol. 1x., 1897, 
pr 477. 
(8) Yur, G. U., “On the Theory of Correlation,” Jour. Roy. Stat. Soc., 
vol. 1x., 1897, p. 812. 
(9) DarpISHIRE, A. D., “Some Tables for illustrating Statistical Correla- 
tion,” Mem. and Proc. of the Manchester Lit. and Phil. Soc., vol. li., 
1907. (Tables and diagrams illustrating the meaning of values of the 
correlation coefficient from 0 to 1 by steps of a twelfth.) 
Reference may also be made here to— 
(10) EpcewortH, F. Y., “On a New Method of reducing Observations 
relating to several Quantities,” Phil. Mag., 5th Series, vol. xxiv., 1887, 
p- 222, and vol. xxv., 1888, p. 184. (A method of treating correlated 
variables differing entirely from that described in the preceding 
chapter, and based on the use of the median: the method involves 
the use of trial and error to some extent. For some illustrations see 
F. Y. Edgeworth and A. L. Bowley, Jour. Roy. Stat. Soc., vol. 1xv., 
1902, p. 341 et seq.) 
References to memoirs on the theory of non-linear regression are given 
at the end of Chapter X. 
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