200 



SCIENCE 



[N. S. Vol. LIV. No. 1392 



Kassowitz is obliged to admit, however, that 

 " in warm-blooded animals which are in a po- 

 sition to maintain their own body tempera- 

 ture under the most diverse conditions, one can 

 claim the appearance of some justification that 

 their living parts produce heat in order to pro- 

 tect the body against loss by radiation, etc." ^ 



"Whether this is a real justification or only 

 the appearance of one will not trouble the prac- 

 tical physiologist so long as the generalization 

 that human beings of different size produce 

 heat in proportion to surface rather than 

 weight, and therefore, require food energy in 

 this proportion, helps him to understand his 

 feeding problems; and there is no doubt that 

 the law of surface area has been immensely 

 useful in this connection. It explains the 

 much higher basal metabolism per unit of 

 weight of the small individual in comparison 

 with the large better than the so-called causal 

 explanation cited by Kassowitz. It explains 

 also much better the need for conservation of 

 heat in the infant, and the role which sub- 

 cutaneous fat plays in this connection. 



John E. Murlin 



University op Rochester 



on the significnace of an experimental 



difference, with a probability 



table for large deviations 



The results of experiments from which 

 scientific conclusions are drawn always con- 

 Btitute a sample, limited in number, of a 

 potentially unlimited universe. The argu- 

 ment is always from the limited number to 

 the infinite number, and assumes that the 

 sample is representative of the universe. This 

 is a priori not necessarily true, which is 

 proven in the fact that two sets of measure- 

 ments of supposedly the same quantity never 

 agree in any absolute sense, that they may 

 disagree widely, and that they therefore have 

 to be qualified by a measure of their precision, 

 which is derived from tlie magnitude of the 

 mutual disagreement of the individual meas- 

 urements of the same set. 



9 Kassowitz, M., ihid., p. 240. 



This fact becomes of trying significance in 

 many biological measurements. We may 

 make two sets of measurements, A and B, 

 under conditions alike except for one experi- 

 mentally varied factor, and find that al- 

 though their means show an apparently 

 definite diilerence, many of the measurements 

 A lie beyond the mean of B, and vice versa. 

 It may be that a plot of the aggregate of the 

 two distributions shows little or no bimodality 

 corresponding to the difference in the respec- 

 tive conditions of A and B. 



The usual mode of procedure in such a case 

 is, first, to compute the measure of precision 

 of the difference of the two means, accord- 

 ing to the formula: 



where A is the difference between the arith- 

 metic means (.M^ — M^), cr^ its standard devia- 

 tion, c^ and "„ are the standard deviations^ of 

 the two distributions A and B, respectively, 

 and Nj^ and N^ are the respective numbers of 

 measurements. 



Then the probability, P, of a deviation ly- 

 ing within the limits =t A, in a normal dis- 

 tribution of standard deviation a-^, is found 

 from the table.^ The complement of this, 

 1 — P, is the probability of such a deviation 

 lying outside the limits ± A. 



The accompanying probability table was 

 computed by the writer for deviations higher 

 than those included within the range of most 

 such tables extant, with a view to giving 

 values of P much nearer to unity than usual. 

 An approximate method of computation was 

 used. While the computation of values of 



s: 



dx 



1 This assumes that 



"' = VnT^ ■ 



Where N-^ is large the error due to the use of Ni 

 instead of {N^- — 1) tends to become negligible. 



2 Sueh as Table IV., pp. 119-125, Davenport, 

 "Statistical Methods," third edition, New York; 

 or Table 24 or Table 25, Smithsonian Physical 

 Tables, Seventh Edition, Washington, 1920. 



