Haggerty : 



Study ix Arithmetic 



483 



to begin school work in arithmetic in the second year. In every 

 case the second-year beginners rank first for the total for each 

 grade and for the total for all grades. This holds both in medians 

 and in variabilities. The second best are the first-year beginners, 

 and the third-year beginners are the poorest of all. But one excep- 

 tion offers to this generalization, namely, in seventh grade medians 

 where the third-year beginners outrank the first-year beginners. 



If one goes back to the rankings in the several points the supe- 

 riority of the second-year beginners is not so clearcut. In thirteen 

 of the thirty-two median rankings the second-year beginners are 

 equalled or outranked by one of the other groups. Their supe- 

 riority is most distinct in seventh grade and least so in the eighth. 

 In the latter they are first but three of the eight times. Even 

 less distinction attaches to the first rank if one goes farther back, 

 to the difference in the medians which gives the rank. A difference 

 of .1 will give superiority in rank but it is highly questionable 

 whether a difference of .1 is a significant difference. As a matter 

 of fact second-year beginners get their first rank in sixteen cases 

 out of nineteen by a superiority over the next highest group of not 

 to exceed .5. Thus while the second-year beginners have a clear 

 right to first place, the margin of this excellence is so slight that 

 one may reasonably question whether or not it is not due to other 

 causes than the time of beginning. It would not be at all sur- 

 prising if another ten thousand children should show a superiority 

 for first-grade or even third-grade beginners. 



Similarly the variabilities of the three groups are somewhat 

 equivocal as to meaning. Here again, when one considers the 

 total, second-year beginners rank first : first -year, second : and third- 

 year, third. But going back to the rankings in individual points 

 one finds second-year beginners first in but fifty per cent of the 

 cases. Third-year beginners are first twice, first year beginners 

 twelve times, and first and second tie twice. Going back to the 

 variabilities themselves one sees again how slight a margin avails 

 to give superior rank. Seventeen times in ninety-six it is two per 

 cent or less. It is quite possible that a much larger number of 

 children would show a different order for the three periods of 

 beginning. 



The tables of dependabilities (XLIII and XLIY i do not indi- 

 cate different conclusions. Second-year beginners rank first in 

 the greatest number of tests and also in the composite ranking. 

 The margin of excellence is slight, however, in many cases. In 



