Sept. 18, 1916 



Dwarf Eggs 



ion 



This distribution is shown graphically in figure 3. It does not show 

 a tendency of a dwarf egg to be produced at any particular position in 

 the litter — that is, the variation in the class frequencies are irregular. 

 The dash line in the figure represents the mean class frequency; in other 

 words, it represents graphically the frequency distribution for 183 

 observations evenly distributed among 10 classes. It is the ideal dis- 

 tribution of things equally likely to fall into any one of the 10 classes. 1 

 The question which concerns us is whether or not the actual distribution 

 differs from this ideal distribution by an amount greater than we would 

 expect if the differences are due entirely to errors in sampling. 



GO 



/O 





OS ./& 



.85 .95 



.25 .35 .45 .55 .65 7Z5 

 POS/T/OA/ /A/ L/TT5& 



Fig. 3. — Diagram showing the number of dwarf eggs which occurred in each tenth of a litter. Path line— 



the mean frequency. 



A frequency curve of a given area is defined by its mean and the 

 moments about this mean. The first four moments or the three con- 

 stants, standard deviation, /3 X and j3 2 , derived from these moments define 

 a curve sufficiently for practical purposes. Two frequency curves of 

 equal area which differ significantly from each other will show a signifi- 

 cant difference between one or more of the similar constants. These 

 constants and also the mean, which gives the location of the curve in 

 space, were computed for both the actual and the ideal distribution. 

 These constants, with their probable errors, and the difference between 

 the similar constants for the two curves, with the probable error of 

 difference, are given in Table XXV. 



1 A general treatment of this " horizontal line " frequency curve, which is a special case of Pearson's 

 Type II, will shortly be published elsewhere. 



