No. 498] 



NOTES AND LITERATURE 



H9 



with various points regarding the general theory of probable 

 errors. W. F. Sheppard, in a paper giving the mathematical 

 proof of his corrections for the moments of frequency distribu- 

 tions, 1 points out that theoretically the raw value of the second 

 moment rather than the value obtained by applying his correc- 

 tions should always be used in calculating the probable errors 'of 

 the mean and standard deviation. The present writer'- shows 

 by the consideration of concrete examples that the point made 

 by Sheppard is not likely ever to be of any pmcf ical significance 

 to the working biometrician. It makes no sensible difference in 

 the actual result whether one does or .Iocs not use the corrected 

 value of the second moment in determining these probable 

 errors. In the same paper it is shown that a very considerable 

 error may be made by using the formula ordinarily given for the 

 probable error of the standard deviation when the distribution 

 of variation differs considerably from the normal curve in cer- 

 tain particulars. One must always be cautious in assuming that 

 a deviation from normality will be of no consequence in cal- 

 culating probable errors. 



A novel and important point regarding the probable error of 

 a mean has been thoroughly investigated and solved by that 

 mysterious person "Student," 3 who has previously contributed 

 to the pages of Bi<nn< I rika under the same nom <h plume. In 

 passing it may be remarked that the propriety of publishing 

 serious contributions to science under an assumed name seems 

 questionable; one had supposed that those conditions no longer 

 existed which in earlier times made such a course not merely de- 

 sirable, but often indeed necessary if the same individual were to 

 continue to contribute to science. To return to the point. In 

 all kinds of experimental science the following type of problem 

 very frequently arises; a series of say 10 or fewer experiments 



denoted by the letters a, b, c, d, . . . n. A second series of equal 

 extent is then tried with, say, one experimental condition changed 

 so that the conditions are now q, b, c, d, . . . n. With what 

 degree of probability may it be asserted that an observed differ- 



