METHODS 195 



It can be seen that the original simple coefficient, Tjo, is corrected by 

 subtracting the product of two small numbers, r^g and r23, wliich must 

 be very small, and then dividing by a number that cannot be far from 

 unity. It is therefore not much altered by the operation, and in fict 

 the important coefficients in the spawn investigation showed them- 

 selves to be so right from the beginning. The reservations about 

 multiple correlation have much less force in tliis field than when some 

 of the simple coefficients are large. 



The logical points are also important. A research worker ought not 

 to expect that any single factor should appear very important, and 

 must not be upset by criticism that since the correlation he has found is 

 low, he has not succeeded in finding what he was looking for. Of 

 course he has not — there is no large key, but only a number of small 

 ones, one of which he has found. It is also a fallacy to suppose that it 

 is a failure not to identify exactly the operating cause of an observed 

 correlation. If two variates can be shown to be correlated, it does not 

 at all follow that one is acting directly on the other, so that it can be 

 called a cause. It may merely be highly correlated with another factor 

 that is so acting. But the discovery is a great scientific advance, for we 

 have limited the field of search to a defined area. We must look for 

 factors correlated with those indicated by the mathematics — notliing 

 else is likely to be useful. 



In certain critical parts of the joint functional diagrams, such as the 

 region of the minimum at o°C, there were not very many records, so 

 that tests of significance were apphed. This was simply done by taking 

 the results contributing to the minimum point and testing by the 

 computation of t whether this mean differed from that of the two 

 peaks on each side. In this case there was no doubt about the 

 significance. 



In the 1935 paper, I pointed out that observers might very well be 

 late, but were unlikely to be early, so that a biased error was to be 

 expected. Williams (195 1) came to a similar conclusion, but drew 

 the further inference that the distribution of phenological dates could 

 not be normal, and should have the attention of research statisticians. 

 The distribution of these dates is not normal when tested by the 

 computation of the third and fourth moments (Fisher, 1932) but is 

 negatively skewed and sharply peaked, both conclusions being statisti- 

 cally significant. The negative skewness is contrary to the expectation 

 of Williams and myself It cannot surely be that observers never make 



