ON BIOLOGICAL MEASUREMENTS. 287 



The chief fields in which statistical data, properly taken and analysed, can be of 

 great service are perhaps the following : — 



(a) Genetics. — Obviously, here all conclusions based upon ratios are valid only in 

 so far as statistically significant. In the early days of Mendelism much confusion 

 was brought about through lack of proper statistical treatment. It has, however, 

 recently become increasingly realised that a combination of Mendehan and statistical 

 (biometric) methods is in many cases necessary for full analysis. In human genetics 

 the statistical method is the main available weapon. 



(b) Variation. — Here the achievements of biometrics are too well known to need 

 statement or comment. It should be pointed out, . however, that in many cases a 

 technically perfect biometric analysis may tell us less than it ought owing to in- 

 adequate selection of material. E.g. without experiment, biometric methods cannot 

 tell us how much of a given variation range is genotypic, how much phenotypic. 

 Only properly directed work on variation can give us much needed information as 

 to the differences between different species as regards variability, the reasons for the 

 differences, and the bearing of the facts upon evolutionary theory. 



(c) Systematics. — With increased delicacy of systematic determination, measure- 

 ments are becoming more and more important as a criterion of the distinctness of 

 closely related species, sub-species or races. 



(d) Development. — Only by taking large numbers of measurements will it be 

 possible to discover the laws of relative growth of parts. 



(e) Evolution. — As more perfect palaeoirtological series are obtained, accurate 

 measurements of absolute and relative sizes of parts may enable us to establish simple 

 laws of evolutionary growth and development comparable to those which are being 

 obtained by similar methods in ontogeny. 



Naturally the taking of quantitative data constitutes the essence of much of 

 physiology ; but we have here been concerned mainly with data which may be called 

 statistical. 



It may be as well to begin by enumerating a few of the cases in which neglect of 

 simple precautions has made laboriously taken measurements of much less value 

 than they might otherwise have been ; for such examples will serve better than 

 anything else to convince the working zoologist of the need for improvement. The 

 defect may have lain in the failure to take the most suitable measurements, to record 

 them adequately when taken, or to analyse them in the most desirable way. 



A. Neglect of Biometric Analysis. (See also No. 2.) 



1. In the preparation of Witherby's 'Handbook of British Birds' (London, 1922) 

 considerable numbers of accurate measurements were made both upon the skins 

 (usually twelve specimens) and eggs (usually 100 specimens) of a large number of species 

 of birds. However, in recording these valuable data only the mean and high and low 

 extreme variants were set down (in the case of skins, the mean was omitted). Pre- 

 sumably the main purpose of such measurements is to give the systematist help in 

 distinguishing between closely related forms (sub-species, races, &c). Even for this 

 purpose, however, and especially when the ranges of two forms overlap, this method 

 of record is markedly inferior to one giving mean and standard deviation. In 

 addition, the recording of standard deviation would have enabled a wholly different 

 and very interesting problem to be attacked, namely, the suggestion originally made 

 by Darwin ('Origin of Species,' chapter ii) that wide ranging and abundant species 

 and genera are more variable than scarce and local ones. 



B. Numbers Inadequate for the Statistical Conclusions Drawn. 



2. Examples of the failure to realise the statistical invalidity of small numbers are 

 frequent. jB.gr. Kriiger (1920 and 1924, Zool. Jahrb. (Syst.), 42, 289, and 48, 1) dis- 

 tinguishes closely related ' species ' of Humble-bees by means of certain relative 

 proportions of parts. Considering, however, that the maximum number of any one 

 species measured is 25, and is often below 10, that the ranges frequently overlap, and 

 that only mean, maximum and minimum are recorded, it may be doubted whether 

 these quantitative results are at all significant. 



3. If data are properly taken and recorded, failure to use suitable analyses can be 

 remedied by subsequent workers. Nevertheless, conclusions based on unsatisfactory 

 analysis often, as a matter of fact, become generally accepted, and it is then difficult 

 to correct the error. The most frequent source of error is failure to discount chance 



