l88 ECOLOGY AND LIFE HISTORY OF THE COMMON FROG 



work is properly planned. Each table therefore needs only one sorting, 

 except when the combinations have been exhausted, and a new 

 variable is required. For example, if all the temperature combinations 

 have been found, and the last one has rainfall as the second variable, 

 the cards have only to be bundled according to rainfall for the process 

 to start again for all the rainfall combinations, without the need to sort 

 specially for rainfall. The sorting usually took about three hours. In 

 order to avoid the monotony of too much unreheved sorting or of 

 computation, I always computed the tables as they were completed. 

 Computation usually took about the same time. 



If one is doing a short computation needing a few hours, it is 

 reasonable to require a check of the exact number of the cards by a 

 re-count, and to require check sums and products to agree exactly. 

 On this scale, however, weeks or perhaps months of extra work would 

 have been needed to do this. I therefore tested by experiment to see 

 what effects small errors would have, and concluded that the larger 

 bundles of cards need not be counted twice, for any likely error could 

 not affect the final result. The smaller bundles were checked, but of 

 course this did not take long. A serious error would show, and was 

 followed up. In a similar way, although the check sums and products 

 often agreed exactly, and I never omitted the precaution of computing 

 them, I did not re-compute for errors in the units or tens columns, for 

 these did not affect correlation coefficients computed to two decimal 

 places. Care is needed in planning on these and similar points, for it 

 would be easy to spend weeks in wearily re-computing statistics 

 already quite accurate enough. 



It is quite interesting to watch these tables growing under one's 

 pencil. Before the actual computation has even begun, it is often 

 possible to get a fair idea of the size of the correlation coefficient that 

 will emerge some hours later, merely by looking at the way the 

 figures lie on the paper, and there is some satisfaction in finding at the 

 end that a guessed "0-4" turns out to be "0-36." 



In the end, all the possible combinations have been tabled and 

 computed, and all that is now needed is to put the variances and 

 covariances into a series of simultaneous equations and solve. This 

 can be done by eliminating one variable at a time, as taught in schools, 

 but on this scale it is better to use the Doolittle method. This is 

 described in detail in Ezekiel and also in Brownlee (1949). It is too 

 long and intricate to describe here. It requires rigid attention at first, 



