October 18, 1912] 



SCIENCE 



519 



produced 166,562 tons of alkali, less than -was 

 imported, -while in 1900 the production was 

 539,541 tons and in 1905, 734,209 tons. In 

 the last two periods the importation of 

 hleaching-powder into the United States had 

 decreased from 136,403 tons to 96,110 tons. 

 Unfortunately this statistical portion is the 

 only part of the book not brought well down 

 to date. 



J. L. H. 



The Elements of Statistical Method. By 

 WiLLFORD I. King, M.A. New York, The 

 Macmillan Company. 1912. Pp. xvi + 250. 

 It is " the purpose of this book to furnish 

 a simple text in statistical method for the 

 benefit of those students, economists, adminis- 

 trative officials, writers, or other members of 

 the educated public who desire a general 

 knowledge of the more elementary processes 

 involved in the scientific study, analysis and 

 use of large masses of numerical data." 



With this purpose in mind, the author pre- 

 sents only the most simple of the mathe- 

 matical theorems on which the statistical 

 method is based. The book is arranged so as 

 to treat the subject in four main parts: (1) 

 The historical development and general char- 

 acteristics of statistics; (2) the gathering of 

 material; (3) analysis of material collected; 

 (4) comparison of variables. The great va- 

 riety of topics dealt with under these general 

 headings indicates the breadth of view desir- 

 able for an adequate treatment of statistical 

 problems, and suggests the many pitfalls that 

 endanger the certainty of conclusions drawn 

 from some kinds of statistical data. The 

 book is to be commended for the clearness 

 with which it brings a large number of topics 

 concerning statistics to the attention of the 

 educated public. This is surely a matter of 

 the highest importance. 



It seems desirable to criticize the treatment 

 of the notion of " the probable error." On p. 

 78, we find the following statement : "li JE :^ 

 the possible error of the arithmetical average, 

 the probable error of the same is approximately 

 E/\/n." Torf proof, we are referred to Bow- 



ley, " Elements of Statistics," pp. 303-315. I 

 fail to find that Bowley attempts to obtain a 

 relation between probable and possible errors. 

 He does show, within the limits of this refer- 

 ence, that the probable error of the arithmetic 

 mean of n variates is E/\/n, where E is the 

 probable error of a single variate. It seems to 

 the reviewer that the book is not clear on the 

 notion of a probable error, and even presents 

 an incorrect conception of this subject. On 

 pp. 213-214, the statement is made that the 

 probable error of a coefficient of correlation 

 varies inversely both with the number of 

 pairs of items and with the size of the coeffi- 

 cient. Then the well known formula 

 0.67(1 — r") 

 Vu 

 is given for this probable error. It is therefore 

 obvious that the author does not use the ex- 

 pression " varies inversely " in its usual mean- 

 ing in mathematical sciences. Later, on p. 

 214, is the statement that the probable error 

 indicates that the chances are that r actually 

 lies between 



, 0.67(1 — r^) ^ , 0.67(1 — )-') 



)■ H -= and r H — 



l/n i/n 



This statement is obvious but useless when 

 taken in one sense. It tends to give an incor- 

 rect conception of the meaning of a probable 

 error, when taken in another and important 

 sense. 



To summarize, it seems to the reviewer that 

 the strength and usefulness of the book lies 

 in its popular presentation of some of the 

 leading ideas of the best statistical method of 

 the present day. The weakness of the book 

 lies in its presentation of a vague and even 

 incorrect conception of the meaning of the 

 probable error of a statistical result. 



H. L. EiETZ 



University op Illinois 



popular and technical books on heredity 



Einjuhrung in die Vererbungswissenschafi. 



By EiCHARD GoLDSCHMiDT. Leipzig, Wil- 



helm Engelmann. 1911. Pp. x + 502. 



Price, 12.25 M., paper, 11 M. 



