NOTES AND LITERATUEE 



BIOMETRICS 

 An Important Contribution to Statistical Theory 



One of Pearson's most valuable contributions to statistical 

 theory is his test for goodness of fit. 1 It enables one, with the 

 aid of Elderton's 2 tables, easily to determine the probability that 

 a given system of observed frequencies does or does not differ 

 significantly from a series of theoretical frequencies supposed to 

 graduate the observations. The significance of this criterion in 

 MemMi.-m work has recently been pointed out by Harris. 3 



Hitherto this criterion has found an important limitation in 

 the fact that, as originally developed by Pearson, it was appli- 

 cable only to frequency systems. It could be used to test good- 

 ness of fit only where the observations were counts of the number 

 of times particular classes of events occurred. But, of course, 

 frequency systems comprise only one kind of observational data 

 to which one has occasion to fit* curves. Much more often there 

 is need for a criterion of goodness of fit where the observations 

 are of the nature of true ordinates, rather than frequencies. 

 Such cases include all data of the sort where a mean y is deter- 

 mined for each x, as in a growth curve: or in the regression 

 observed in a correlation table, where for each successive value 

 of one of the variables the mean value of the correlated variable 

 is calculated. There has been no method of testing the good- 

 ness of fit for such curves. From a visual inspection of the 

 plotted regression line one has been compelled to form his judg- 

 ment as to whether it was or was not a good fit. 



Recently a Russian statistician, E. Slutsky, 4 has extended 



i Pearson, K., "On the Criterion that a Given System of Deviation from 

 it Can be Reasonably Supposed to Have Arisen from Kan.lom Sampling," 



- lUom, tnka. Vol. I. pp. l".-]63. 



3 Harris, J. A., "A Simple Test of the Goodness of Fit of Mendelian 

 Ratios," Amer. Nat., Vol. 46, 1912, pp. 741-745, 1912. 



* Slutsky, E., "On the Criterion of Goodness of Fit of the Regression Lines 

 and on the Best Method of Fitting Them to the Data," Jour. Boy. Stat. Soc., 

 Vol. LXXVII, Part I (December, 1913), issued 1914, pp. 78-84. 



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