20 MAINE AGRICULTURAL* EXPERIMENT STATION. I9I5- 



STATISTICAL SIGNIFICANCE OE DEVIATIONS. 



The question next arises — are any of these deviations in the 

 direction of the selection greater than might be expected in 

 random samples drawn from a similar population? In other 

 words, are these deviations statistically significant ? 



In the first place it is clear that unless there is some influence 

 of the selection the number of rows showing plus and minus 

 deviations should be the same. This should be true not only of 

 all the rows grown in any one year, but also of the rows from 

 the plus selections and from the minus selections taken separ- 

 ately. From tables 3 to 5 it is seen that in many cases the 

 observed number of rows is not far from the expected. Thus 

 in table 3 for the rows grown in 19 12 there are in all ']'j rows 

 showing plus deviations and 79 rows showing minus deviations. 

 It can also be shown that in the plus selections or in the minus 

 selections the number of rows does not deviate sensibly from the 

 number expected if there was no influence of the selection. 



The same conclusion can be drawn from inspection of the 

 number of rows in each year, except those for 1913 (Tables 

 3 and 4). In this year there is obviously an excess of rows 

 showing minus deviations. In 1913 there were 11 1.5 rows show- 

 ing plus deviations and 146.5 rows showing minus deviations. 

 The expected number is 129 rows in each case. The deviation 

 from the expected is 17.5 rows. The question as to whether 

 such a deviation could arise in random sampling may be deter- 

 mined by comparing the deviation with the standard deviation 

 of simple sampling. The standard deviation of simple sampling 

 is given by 



^■°-= J/TTi 



In this case n =^ 258, p =: q ^ ^ and 



S. D. =^8.03 

 The actual deviation is just a little over two times the stand- 

 ard deviation and could arise from random sampling. But 

 from tables of the probability integral it is found that in ran- 

 dom sampling a deviation as .great or greater could be expected 

 only about 2 times in 100 trials. The odds against the occur- 

 rence of a deviation as great or greater than this one are about 

 49 to I. Thus it is extremely unlikely that the distribution of 

 rows showing plus and minus deviations in 1913 was due to 

 chance alone. 



