38 



BULLETIN 1339, U. S. DEPARTMENT OF AGRICULTURE 



For the fall period the coefficients of correlation for both solar radi- 

 ation and hours of sunshine with changes of colony weight are prac- 

 tically zero, while negative correlations, having large probable errors, 

 exist between these variables and morning loss. 



THE EFFECT OF UNKNOWN FACTORS ON CHANGES IN COLONY 



WEIGHT 



In this investigation, correlations have been made between changes 

 in colony weight and 10 different factors in the accompanying weather 

 conditions, some of these also being used in correlations with the con- 

 ditions for the day or night previous to the change in weight. There 

 are so many external and internal factors which may influence the 

 physiological processes of nectar-secreting plants and the behavior of 

 bees in gathering and ripening nectar that it is not probable that the 

 factors for which data were obtained are the only ones which may in- 

 fluence the changes in 

 colony weight. For the 

 purpose of ascertaining 

 to what degree the influ- 

 ences have been deter- 

 mined and to what 

 degree unknown factors 

 are involved, an attempt 

 has been made mathe- 

 matically to find the val- 

 ues of all unknown fac- 

 tors. Such a determi- 

 nation throws no light 

 on the actual character 

 of these unknown fac- 

 tors, on the degree of 

 their influence individu- 

 ally, or whether some 

 are positive and some 

 negative, but merely 

 gives the mass value of 

 all factors so far unde- 

 termined. 



The method used in this work is based on Pearson's theory of mul- 

 tiple correlation. The square of the coefficient of multiple correla- 

 tion between one variable and a number of others measures the extent 

 to which the given variable is determined by the others, while 1 

 minus this square measures the degree of determination by independ- 

 ent residual factors. In a system of variables X, A, B and 0, in 

 which nothing is assumed of the causal relationships between them, 

 X, which in this case is change in colony weight, is determined by 

 the variables A, B, and C (weather factors) and by all other residual 

 actors. This method has been described in detail by Wright {35). 



In Figure 11, taken from Wright, the small letters represent the 

 path coefficients, and the capital letters the variables, used in deter- 

 mining the coefficients of correlation. The path coefficients are not 

 equal in value to the coefficients of correlation determined by direct 

 correlation methods, but may be defined as the ratio of the standard 



Fig. ill — Graphical representation of quantities and their relations 

 involved in the determination of coefficients of correlation 



