vi Tables for Statisticians and Biometricians 



where S should be the standard deviation in the parent-population, which is assumed 

 by them to be normally distributed. But not knowing 2, they replace it by the 

 value a computed from the sample, i.e. they use for standard error 



a- / _ 1\~* __o_ 

 V2^V n) "VlS 



Now since a is liable to differ from S by a quantity of the order 1/V, it is difficult 

 to see what justification there is for retaining terms like and its successors. 



Thus the n 1 in the original formula may be replaced by n, although an astronomer 

 (and many physicists) in reducing ten observations would certainly use n 1 = 9, 

 as if there were some logical reason for their doing so. Further illustrations of the 

 same method of finding F Ct by giving/!, / 2 , / 3 , etc. their single sample values and 

 still retaining terms in l/?i 2 , 1/w 3 , etc., can be found in the use of the formula of 

 Spearman and Holzinger for the standard error of a tetrad of correlation coefficients, 

 or in the use of that of Wishart for the standard error of a tetrad of product moments, 

 when terms in the higher powers of 1/n are retained and the sample values of the 

 coefficients inserted in these formulae. 



At the present time, when modern physics is becoming so largely a branch 

 of mathematical statistics although it may perhaps be doubted whether many 

 modern physicists have yet crossed the limits of classical probability it may not 

 be without interest to insist that statistical conclusions, whether drawn from organic 

 or inorganic data, whether biometrical or physical, are based on the same funda- 

 mental conception, namely that the experience of the past may be legitimately 

 projected into the future. The only reason for separating vital from physical 

 experience is that in the case of the inorganic it is easier to reproduce within 

 narrower limits of difference past conditions with regard to the "universe under 

 discussion." Our belief in the stability of statistical ratios, our belief that past 

 experience is a guide to future happenings, is as valid for biometric as for 

 physiometric experience. We can never assert that the sequences we recognise in 

 our perceptions must be repeated; there can be no logical proof that a law of 

 causation exists. But thought, and with thought conduct, would be impossible if 

 there were physically or biologically no such thing as the stability of statistical 

 ratios. Our knowledge of "things," their differentiation into classes, depends 

 solely on past statistical experience of their attributes their actions and reactions ; 

 and this is true of both organic and inorganic "things." Hence it comes about 

 that as science passes more and more from the descriptive to the metric stage, the 

 mathematical theory of statistics with its category of correlation (far wider than 

 that of causation) tends to become more and more a study essential to all 

 students of science. If these Tables for Statisticians and Biometricians, in any 



