STUDIES ON OAT BREEDING. 23 



From this figure it is seen : — 



1. That in every case the plus selections have shown a larger 

 average deviation in the plus direction. 



2. The minus selections on the other hand do not show such 

 a regularity. In only two out of the siix cases is there a larger 

 average deviation in the direction of the selection. 



3. It is of interest to note that the average deviation per 

 plant row is much smaller in 19 13 than in the other two years. 

 It has been pointed out in a previous paragraph that the 19 13 

 yields were much lower than in the other years. It has also 

 been noted that there is an excess of rows showing minus devia- 

 tions in this year. This latter fact is evidently associated with 

 the fact that in this year the minus selections show a very much 

 larger average deviation in the direction opposite to the selection. 



In the 191 1 selection and 1912 rows and the 1913 selection 

 and 1914 rows the average deviation in both the plus and minus 

 selections is in the direction of the selection. It will be further 

 noted that these are rows grown the next year after the selec- 

 tion. The question arises as to whether in these years the 

 deviations are greater than might be expected in random sam- 

 pling. This question can perhaps be tested easiest by determin- 

 ing the goodness of fit of the expected and observed average 

 deviations. 



Slutsky"' has recently extended Pearson's tests for the good- 

 ness of fit to include other types of curves than frequency distri- 

 butions. It isi possible to apply this method to the present data 

 and determine from Elderton's tables the probability that our 

 observed deviations could have arisen fro.m random sampling. 

 The. data for the 191 1 selection and 1912 rows have been chosen 

 for this purpose since these rows show the most consistent devia- 

 tions in the direction of the selection. The theoretical points are 

 determined by considering that if there were no effect of selec- 

 tion the average deviation of the rows from plus selections 

 would be equal in the plus and the minus directions. Tlie same 

 would be true of the minus selections. The test is then made to 



"Slutsky, E. On the Criterion of Goodness of Fit of the Regression 



lines and on the Best Method of Fatting Them to the Data. Jour. Roy. 



Stat. Soc, Vol. 'LXXVII, Pt. i, pp. 78-84. See also, Pearl, R. Amer. 

 Nat. Vol. 48, pp. 505-507, Augiist, 1914. 



