66 PSYCHE [June 
matical law of distribution. To find more bands on one sort of a twig than on another 
does not necessarily show that there has been any selection of twigs; it may indicate 
merely that there were more of that particular class of twigs available. ‘To deter- 
mine whether there has been any selection of twigs we must, in short, have measure- 
ments of series of twigs upon which the insects do not form bags as well as those 
upon which they do. The question which Dr. von Schrenk raises is one of very 
considerable biological interest, but for a trustworthy answer we should compare the 
means and variabilities of twigs bearing the bags with the same constants of those 
which do not. Naturally enough it would be necessary to confine attention to the 
one-year-old twigs in making the comparison. Perhaps the lengths of the twigs 
should be taken into consideration also, for other things being equal a larva would be 
more likely to form a bag upon a long twig than upon a short one. Actual data 
suitable to decide this interesting question should be collected by some one. 
The second question seems to me to be of considerable interest as well. If the 
larvae refuse to form bands around large twigs, it seems quite natural to ask whether 
they modify the size of the bands according to the size of the twig to which they are 
attached. Even if the insect does not ‘‘purposely” make any modification in the 
size of the band, is it possible that the amount of material available has any 
influence upon the width of the bands formed upon relatively large or small twigs ? 
This question can be answered preliminarily by a proper statistical analysis of 
the data in the table given. The relationship between the size of the twigs and the 
width of the bands is satisfactorily shown by the coefficient of correlation.’ ‘This 
constant may range from 0 to plus or minus 1. A coefficient of 1 denotes perfect 
relationship while a coefficient of 0 shows that there is no relationship between the 
magnitudes of two characters under consideration. Every statistical constant has a 
probable error which gives some indication of the significance which is to be attached 
to it. ‘Yo be considered significant the coefficient of correlation should be at least 
two and one half times its probable error. 
Calculating the correlation from the table given,? and using Sheppard’s correc- 
tions for the second moment in calculating the standard deviations, I find that the 
interdependence of band width and twig diameter is represented by 0.016 with a 
1For a discussion of the method of calculating the coefficient of correlation, see any of the text 
books on biometric methods, as Davenport’s Statistical Methods, Elderton’s Frequency Curves and 
Correlation, or Thorndyke’s Introduction to the Theory of Mental and Social Measurements. 
2The fewness of the bands recorded as 2.5 mm. in width as compared with those 2 and 3 mm, in 
width at once arouses the statistician’s suspicions that the result is not a biological condition but a 
result of the tendency of observers to read to whole numbers instead of fractions. In future work 
this point should be carefully watched. 
