208 ECOLOGY AND LIFE HISTORY OF THE COMMON FROG 



I tadpole in 200 survived. At Cat Hill, the number was about i in 50. My 

 estimate by eye of i in 100 was perhaps not far out. 



(Jt) Statistical Significance and Importance 



The methods of computing correlation coefficients require no comment but 

 the distinction between the statistical significance and the importance is some- 

 times overlooked. Many natural phenomena are very weakly correlated, but, 

 because there is so much data available, there is no doubt about the significance. 

 For example, everyone knows that in the winter there is a tendency for warm 

 and wet weather to occur together, but in fact the correlation is weak. There 

 comes a point when in such a case the relation, although it is based on such 

 a large sample that it is certainly significant, is so loose that it really does not 

 matter much, for it accounts for too small a proportion of the total variance. 

 Increasing the quantity of data of the same kind may sometimes move a cor- 

 relation from insignificance to significance, but unless the new data also raise 

 the correlation, which in general is unlikely, the factor will remain unimportant, 

 however certain its existence may be. 



(/) Migration Relation with Wind 



The test of significance follows standard methods. After calculating the 

 expected numbers, so that the total is divided in the proportion that the winds 

 occurred, and combining the neighbouring values so that no group was less 

 than five, the differences of the observed and the expected values was taken 

 and squared. Each of these numbers was divided by the number expected, and 

 the sum is ;^^. In this case it was 97*6, and, for seven degrees of freedom, this is 

 far more than is necessary for significance. There is no reasonable possibihty 

 that the observed connexion is due to chance. 



Curvilinear Correlations 



The method used here can be found in Ezekiel (1930), Chapter 16. Briefly. 

 It consists of plotting one variable, such as temperature, against migration and 

 drawing a rough curve by eye to correspond to the points. The departures of 

 every point from this curve are then plotted on another graph, with the next 

 variable as one axis. Another curve is drawn. The process is continued until 

 all variables have been plotted. The departures of the points from the last 

 curve are then plotted on a fresh graph which has the first curve drawn upon 

 it, as departures from this line, and correct the shape of this curve. The process 

 goes on and may be repeated a third time or even more. The final result is 

 that each curve is shown as if all the other factors were constant. The process 

 can deal vnth curves of any shape with equal ease, it is simple to carry out, 

 makes no mathematical assumptions as to the functions and in such a case as 

 this takes only a few hours to do. 



