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THE AMEBIC AN NATURALIST [Vol. L 



combinations are given. Methods for the rapid formation of 

 symmetrical tables from which either correlation or contingency 

 coefficients may be calculated 10 and for the formation of con- 

 densed tables from which correlation coefficients 11 only may be 

 deduced greatly reduce the necessary labor in such cases. For 

 the testing of linearity of regression in the case of these intra- 

 class and inter-class correlations, tables are essential. The use of 

 such coefficients would, however, be greatly facilitated if calcula- 

 tion could be carried out directly from moments computed from 

 the classes themselves. Harris 12 has given an exhaustive series 

 of formulae by which this can be accomplished, with examples 

 showing the wide applicability of such coefficients. For example, 

 these formulae fulfil more adequately the purpose of Boas's 

 second formula (loc. cit.). 



These intra-class correlation formulae have been thrown into a 

 form suitable for measuring substratum heterogeneity in experi- 

 mental cultures. 13 



If the x and y character of a pair are differentiated, spurious 

 values of the correlation coefficient must result from the render- 

 ing symmetrical of the correlation surface. Pearson many years 

 ago recognized the difficulty in dealing with groups in which 

 there is orderly differentiation due, for example, to growth. 14 

 Attention has recently been directed 15 to difficulties arising when 

 differentiation within the class may exist, but it may be difficult 

 or impossible to arrange the individuals by any character out- 

 side of themselves to obtain the constants necessary for deter- 

 mining the true correlation from the spurious values deduced 



10 Harris, J. Arthur, ' ' On the Formation of Correlation and Contingency 

 Tables when the Number of Combinations is Large," Amer. Nat., 45: 566- 

 571, 1911. 



u Harris, J. Arthur, ' ' The Formation of Condensed Correlation Tables 

 when the Number of Combinations is Large," Amer. Nat., 46: 477-486, 

 1912. 



12 Harris, J. Arthur, ' ' On the Calculation of Intra-class and Inter-class 

 Coefficients of Correlation from Class Moments when the Number of Pos- 

 sible Combinations is Large," Biometrika, 9: 446-472, 1913. 



is Harris, J. Arthur, "On a Criterion of Substratum Homogeneity or 

 Heterogeneity in Field Experiments," Amer. Nat., 49: 430-454, 1915. 



i* Pearson, K., ' « On Homotyposis in Homologous but Differentiated Or- 

 gans," Proc. Boy. Soc. Lond., 71 : 288-313, 1903. 



is Harris, J. Arthur, "On Spurious Values of Intra-Class Correlation 

 Coefficients Arising from Disorderly Differentiation within the Classes," 

 Biometrika, 10: 412-416, 1914. 



