Appendix i 



STATISTICAL METHODS 



In this, as in many other branches of biology, the phenomena are not sharp, 

 and conclusions must be examined statistically, if possible, before they can be 

 accepted. Throughout the book statistical tests have been mentioned, without 

 giving details, because it v^as thought that mathematical arguments are too 

 obtrusive when inserted in a text intended to be read through as a continuous 

 story. Chapter lo and tliis appendix contain the missing details. It has been 

 assumed that the reader is familiar with the common statistical tests, and the 

 main emphasis is on the particular way in wliich the tests have been apphed to 

 the data. The section dealing with the correlation analysis of the spawTi dates 

 has, however, been made rather more full, because the methods used do not 

 seem to be famihar in this field. 



{a) The Signihcance of the Weight Variations in the Colonies of 

 Tadpoles 



The occurrence of large weight differences was so common in the field that 

 no doubt was felt about the significance, but wliile the work was in progress 

 some calculations of t were made, and significant values were often found. 

 When many collections are examined in this way, however, this test is, as is 

 well knov^oi, not very satisfactory, because in a uniform population one in 

 twenty collections vdll turn out significant merely by chance, if t is taken 

 at the 0-05 level. In fact, far more than one in twenty were significant, but 

 this hardly makes the test a good one. The numbers of tadpoles in the col- 

 lections were not always the same, and the habits of the tadpoles and the 

 vagaries of weather often prevented the symmetrical design so desirable for 

 an analysis of variance, but this analysis was not impossible, and was apphed to 

 the results for Dagger Lane, 1947. 



It seems obvious that it is the relative weights, expressed as a proportion, 

 which is important. For example, a colony of tadpoles with an average weight 

 of 800 mg differs from one of 600 mg by a similar difference to that found 

 between colonies with weights of 60 and 80 mg, and not by one ten times as 

 great. A transformation of all the weights to logarithms was therefore made, 

 and had at the same time the desirable result of stabiHzing the variances in the 

 colonies, which were getting heavier as the season advanced. 



There were two criteria of classification : sites, and dates when the various 

 collections were made. The date classes were sub-classifications of the site 

 classes, and the variances due to date, so far as it was not already eliminated by 



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