SIGNIFICANT ACCURACY IN RECORDING GENETIC DATA 221 
than is necessary when an analysis of the hybrid progeny of it and 
N. alata grandiflora is contemplated? Biometrical methods are 
much too imperfect to demand more. There is no intention to dis- 
cuss here the reasons why the biometrical methods in general use in 
genetics are imperfect. But it must be emphasized that they are 
merely used in default of better, since many of them cannot be de- 
fended either mathematically or biologically. For example, common 
sense tells us that equal-sized classes should not be used for the two 
very different species shown in Table III, where the corolla of one is 
three times that of the other, yet no satisfactory method has been 
proposed which does away with the difficulties involved. Since it is 
necessary to use such poor methods in calculating our end results in 
genetic studies of size, however, one should remember that labor to 
record data far more precisely than these methods require is labor 
wasted. 
At the same time, though one may believe that biometrical methods 
are imperfect for certain purposes, they are founded on the theory of 
probability and when used should be used with this in mind. Having 
recorded his data with the precision desired, one should not try to 
analyze them until he has collected a sufficient number of observations 
to make calculations of residual errors have meaning. Just what the 
minimum number should be varies with the problem and cannot be 
discussed in this paper. There are several textbooks on the Theory 
of Measurements in which the matter is treated in detail. All I wish 
to point out here is that in every problem capable of biometrical 
analysis there is such a minimum, and if the data to be analyzed are 
far under this required minimum, no over precision (in cases where 
this is possible) in making the records will give them value. 
An excellent illustration of this is found in Goodspeed's third 
article on Quantitative Studies of Inheritance in Nicotiana Hybrids.^ 
The author used his method of recording measurements of flowers 
through a considerable portion of the flowering season in order to 
determine the phenotypes to which the plants belong, and yet has 
made analyses of frequency distributions having such a small number 
of entries that they possess no meaning whatever. Among 44 fre- 
quency distributions, 29 have less than 12 plants recorded. He 
recognizes the fact that the number of plants involved is too small, 
but feels that this deficiency is balanced by the accuracy of his records. 
^ Univ. Cal. Pub. Bot. 5: 223-231. 1915. 
