VARIATION IN BEES. /I 



I will now take up the more definite criticisms of Mr. Lutz. 

 In our paper we gave reasons which to us seemed good why we 

 did not employ the standard deviation method in our work, stat- 

 ing distinctly that " that would be undesirable except with far 

 more measurements " ; this could be interpreted only as a desire 

 on our part to avoid a high probable error and no one need 

 " wonder greatly " why we did not employ this simple test since 

 we distinctly stated that we did not think it desirable, giving full 

 reasons for such a decision. It was not our intention to take 

 exception to the methods of the workers in variation for I believe 

 that the results of variation work should be stated in mathemati- 

 cal formulae where such a thing is possible without too great a 

 " probable error." If our critic is trying to defend such methods 

 under the impression that we combat them, he is laboring under 

 a misapprehension. However Mr. Lutz has seen fit to figure out 

 the standard deviation and probable error for two of our tables 

 and concludes " that the differences between the two sexes, as 

 shown by these data are of no significance." I am still of the 

 opinion that it is unwise to use these methods for so few indi- 

 viduals on account of the large probable error but since this is 

 the way in which our results are questioned let us examine the 

 figures and see if there is not " great danger that, having collected 

 a set of measurements" our critic makes "a show of accuracy 

 that will lead " him " and others astray by reason of careless and 

 insufficient analysis." For ease of reference I give the results of 

 Mr. Lutz. 



The argument of Mr. Lutz is that since there is as much dif- 

 ference in standard deviation between various lots of drones as 

 there is between the averages of the standard deviations of drones 

 and workers, our conclusion that drones vary the more is false. 

 But is it not evident that in every case of the drones (except lot 

 II.) the standard deviation or index of variability is greater than 

 that of the workers ? I cannot see what bearing the differences 

 in the standard deviation of the various lots of drones has on the 

 question since in every case except one, the drones do vary more 

 than the workers ; and this it was that we attempted to prove. 

 In regard to this lot II. we said : " The drones in lot II. were 

 taken from a hive in which there were no drone cells except 



