ON MENTAL AND PHYSICAL FACTORS INVOLVED IN EDUCATION. 313 



of deviation around that average, is thus of little value. In conse- 

 quence, however, of the incomplete, though high, correlation betv^^een 

 performances in the several tests (Table VII.) and the high correlation 

 with age, the overlap in the totals for the tests is smaller than the 

 overlap in each test taken singly. 



Sex and Social Status. (Table V.) 



The children in the ' Good ' school gain about 50 per cent, more 

 marks than the children in the ' Poor ' school, despite the fact that 

 especial care 'is taken with the teaching of mechanical arithmetic in the 

 latter. In the ' Moderate ' school the average marks as a rule fall 

 between those gained at the ' Good ' and ' Poor ' schools respectively. 

 Except at 12, the averages of the boys in the mixed school surpass those 

 of the girls in every age. 



Defectives. 



Even in the highest and largest age-group (age 12), the averages 

 for the defectives are less than half those for the normal children of 

 the age of 8. Eoughly, they appear to be backward by nearly half their 

 age ; and deviate below the average for their age by nearly three times 

 the standard deviation. 



There is often, however, an appreciable overlap (Figure 1). In 

 nearly every ordinary school tested there are performances which are 

 worse than the best found among defectives of the same age. 



Correlations between the Several Tests. (Table VII.) 



Within each class the correlations between the several tests are 

 moderately high. "Within each age-group they would, of course, be 

 enormously higher. No decided hierarchy appears in the averages. 

 There is doubtless a common general factor. But this cannot be mere 

 general ability, since in general ability each class should be nearly homo- 

 geneous ; and, overlying the general factor, there seem also to be specific 

 factors in cychc overlap, — multiplication is most closely corre- 

 lated with division ; division nearly as closely with subtraction ; sub- 

 traction somewhat less closely with addition ; addition less closely still 

 with multiplication, and least of all with division. 



Sheffield Schools. (Tables VIII. and IX.) 



Four Sheffield schools have worked tests which were built up on 

 the same lines as those used in London, though the actual examples 

 used were different. The four schools included one large mixed school 

 in a neighbourhood rather above the average, a boys' school in an 

 average artisan district, a girls' school in a poor district, and a mixed 

 junior school in a district similar to the first school. There is, however, 

 some difficulty in using these necessarily inexact descriptive terms of 



