192 ECOLOGY AND LIFE HISTORY OF THE COMMON FROG 



These processes may sound difficult, but this is not so. They are 

 intricate. One advantage, as pointed out by Ezekiel, is that the 

 investigator is forced into contact with his data. If research workers 

 pass on their data to others to compute, it is quite likely that the com- 

 putor will miss seeing something that the research worker would have 

 noticed if he had actually handled the data over and over again, 

 because, of course, statisticians cannot also be experts in every science. 

 When they write books 'Tor research workers" that is just what they 

 mean, and they should be taken at their word. 



I have not followed Ezekiel exactly, for, when the variables are as 

 closely spaced as mine, for example at intervals of single degrees, it is 

 not necessary to strike numerical averages as he does. The whole 

 process can be graphical. 



It is sometimes thought that mathematical equations are more 

 objective than graphs drawn free-hand. This is not always so, 

 particularly when the data refer to some complicated system. The 

 error Ues in a failure to reaUze that the subjective element enters into the 

 two methods at different stages. The first act in running a mathe- 

 matical correlation analysis is to decide on a simple function that fits 

 reasonably well. It is very difficult to deal with comphcated functions, 

 and, in fact, the investigator usually tries his utmost to find a function 

 that converts the curves on his first chart into straight lines. For 

 example, in the biological assays of drugs, statisticians have provided 

 highly objective tests for assays on which human hfe often depends, 

 but the processes by which these assays have been made to conform 

 to the essential requirement of linearity might very well shock those 

 who beheve that a mathematical equation somehow expresses natural 

 facts with an almost supernatural exactness. What actually happens 

 is that the biochemist explores conditions in the laboratory and on his 

 desk until he finds a limited range of concentrations and other variables 

 within which the relation between concentration and effect can be 

 expressed well enough by a straight line when the variables have been 

 converted into logarithms or reciprocals or some other functions. He 

 never expects that the line will be straight at all concentrations, and 

 does not beheve that it expresses anything fundamental. It is a working 

 device of great practical value in comparing Preparation A with 

 Preparation B. Once he has found out how "to straighten the line" 

 the mathematical processes are completely objective. 



On the other hand, in ecology we are usually not concerned with 



