15G 
On Polycliorie Coefficients of Correlation 
is one of fitting the " best " normal surface to the data subject to the limitation 
that the marginal totals are exactly reproduced, and this limits the genei'ality. 
An example has been given of the process, but it is seen from this example that 
the heavy arithmetic does not lead us to any more accurate value for the correlation 
than far simpler methods. Thus : 
Correlation from product-moment = '5189 ± •0100. 
Polychoric Correlation Coefficient " Best Fit " = -5034. 
Polychoric Correlation Coefficient " Product Moment " = ■5204. 
Mean Square Contingency, Corrected for Class Indices = '5179. 
Correlation Ratio from means of arrays = "5218. 
The latter method, which has been long in use in the Biometric Laboratory, is 
thus, when used with due precaution, seen to be justified by the theoretically 
preferable polychoric method. If a method could be discovered of finding uniquely 
the mean of a columnar array, i(sing all its cells at the same time, this method 
woulfl still more effectively replace the polychoric correlation coefficient. 
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