METHODS 193 



such comparisons. What we want to know is the nature o(^ the 

 function that really does describe the events, and we do not niind if it 

 looks Hke a corkscrew when it is plotted. Our graphs are therefore 

 free from any subjective bias at tliis point — we draw what the data tell 

 us to draw. There is, however, some judgment involved in drawing 

 curves free-hand, but far less than is usually realized. This is especially 

 true of these representations of surfaces, the joint functional diagrams, 

 for it is very difficult to draw a family of lines through a succession of 

 independent points in more than one way by following Ezekiel's 

 methods. Ezekiel suggests that the choice between a grapliical or a 

 mathematical method should depend on whether there is a logical 

 basis for expecting a mathematical function to fit, as there often is in 

 simple physics. If there is no such basis he thinks that graphical methods 

 should be used. It is surely very rare in ecology that we can expect 

 that any simple mathematical function could represent the immense 

 complexity of nature, and with Andrcwartha and Birch, I doubt the 

 value of attempts to use deductive mathematics as models for natural 

 events. Statistics is quite another thing : it is a tool for investigating 

 what really does happen. 



It is sometimes thought that in an investigation of this kind, in which 

 the weather records come from stations perhaps thirty miles or more 

 from the place where spawning took place, and therefore cannot be 

 quite right, the conclusions may be falsified and give rise to correlations 

 that are inaccurate. The true position is that random errors in the 

 independent variables lower the correlation below that which would 

 exist if the right values had been used, but leave the regression unaltered. 

 The danger that exists is thus not that the correlation will be falsely 

 high, but the reverse. Correlations already much higher than the level 

 of significance will be still significant but very low correlations may 

 shp down into the non-significant group, and escape notice. These 

 low correlations are ignored here anyway, so that there is nothing to 

 fear. Random errors in the dependent variable may lower the regres- 

 sion seriously, but the danger here is similar: regressions that really 

 exist but are small may be missed, but false ones are most unlikely to 

 be created. The position may be more complicated than this summary, 

 and Ezekiel should be consulted. 



A similar mistake is made when it is supposed that the use of approxi- 

 mations such as air temperatures instead of water temperatures, which 

 are almost certainly the true factors, could produce false results. Mean 

 13— {T.914) 



