8 BULLETIN 1339, U. S. DEPARTMENT OF AGRICULTURE 



142 to 1. Until a deviation exceeds, then, 4 times the probable error, we cannot 

 feol any great confidence that it is likely to be " significant." 



To reduce the labor of calculating these data, in many cases the 

 original data were coded so that all might be included in 10 classes; 

 this was done so that the calculations could be made on sorting and 

 tabulating machines. Because of this grouping many of the coeffi- 

 cients of correlation are smaller than they would have been had the 

 original grouping been retained. In several cases calculations were 

 made by both methods ; the difference in results was in some cases 

 as much as 5 per cent. In no case is this difference sufficient to 

 invalidate the results, and, in fact, the results obtained from coding 

 into 10 groups are somewhat safer, since they tend to give a smaller 

 correlation. 



Many of the coefficients of correlation shown in Tables 2 and 5 

 have no direct bearing upon the problem, and therefore are not dis- 

 cussed in this bulletin. They are given, however, to the end that 

 partial correlations between any combination of factors may be cal- 

 culated. It will be seen that high correlations may exists between 

 variables having no direct relationship. In Table 2, for example, 

 there is a coefficient of correlation of .5510 between the net gain and 

 the average temperature of the nignt following. Obviously the tem- 

 perature of the night can not affect the preceding day's gain; the 

 correlation exists, nevertheless, owing to the combination of influences 

 of the causative factors upon both the net gain and the temperature 

 on the following night. 



METHOD OF PRESENTING DATA 



The graph in Figure 2 represents the manner in which the changes 

 in colony weight during the 24 hours are classified to secure tangible 

 and significant figures as a basis for all calculations. A is a fixed 

 point which, on the vertical scale, represents the weight of the colony 

 at 5 a. m. each day in th> month of May. Loss of weight caused by 

 departure of bees for the field begins at about this hour, sometimes 

 earlier and sometimes later, but a weight taken at 5 o'clock constitutes 

 a suitable average, since 4 o'clock is too early and 6 o'clock is too 

 late for such a start. For the fall honey flow the whole graph is shifted 

 one hour later, to adapt it to the shorter days, placing A at 6 o'clock. 

 B is at the point denoting the lowest weight reached during the 

 day and the hour at which this occurs. Although it may occur 

 either in the morning or in the afternoon, the diminution in weight 

 from A to B is called the morning loss, because this loss always pre- 

 cedes the day's gain in weight. This morning loss is due to the bees 

 leaving the hive in flight. Morning loss may be graphically repre- 

 sented by a vertical line equal on the scale chosen to the diminution 

 in weight, and will throughout this bulletin be designated by this name. 

 C represents in b ith weight and time the point at which the colony 

 regains its original morning weight. D represents in weight and time 

 the turning point at which the colony has ceased to gain and begins 

 to lose weight. The net gain for f he day is therefore represented by 

 a vertical line equal according to the scale to the difference in weight 

 between the early morning reading (at A) and the weight reading at D. 

 The latter poii.it has not necessarily a fixed hour. The vertical 

 distance between tti3 weight coordinates of D and of E represents the 



