28 



Indiana University Studies 



sibility of error in estimating the achievements in arithmetic 

 for a state as a whole on a basis of the returns from a com- 

 paratively few cities that furnish the tests upon request. It 

 is not at all clear that the Iowa and Kansas Standards are 

 truly representative of the achievements in those states or 

 that the Indiana returns for either of the three years are rep- 

 resentative of Indiana. 



The Indiana Scores for 1917 Compared with the Courtis 

 Standard and with the Scores for Iowa (1916) and Kansas 

 (1915). In addition the Indiana achievement, as far as num- 

 ber of examples attempted is concerned, is distinctly lower 

 than the Courtis standard in all grades and noticeably lower 

 than the Iowa and Kansas standards in all grades. As far 

 as the number of examples worked correctly is concerned, 

 the Indiana 1917 achievements are lower than the Courtis 

 standards or other state standards. 



In subtraction the Indiana 1917 achievement is distinctly 

 lower than the Courtis or other standards in all grades in 

 number of examples attempted, and in number of examples 

 correctly solved. 



In multiplication the Indiana 1917 achievement in number 

 of examples attempted is lower in all grades than the Courtis 

 standard and other state standards, and in number of exam- 

 ples correctly solved the same thing is true. 



In division the Indiana 1917 achievement in number of 

 examples attempted is lower in all the grades. In examples 

 correctly solved it is lower in all grades. 



It may be argued that the data obtained are not represen- 

 tative of the state, because only 27 cities are included in the 

 study. Consider the scores for 1914 and 1915. Only one of 

 the 20 cities in 1914 gave the tests in 1917, and whereas 80 

 per cent of the cities and towns reporting in 1917 were under 

 3,000 in population, all but one of the 20 reporting in 

 1914 were over 3,000. Despite the fact that there was a dis- 

 tinctly different type of school represented in 1914, the 1914 

 medians fall far below those of Iowa and Kansas. By actual 

 count from Tables II to VI, where all the medians are collected, 

 it is found that out of twenty-two chances in attempts and 

 rights together, one Indiana 1914 median exceeds a Kansas 

 median by .1 and another just equals an Iowa median. In 



